#C A collection of some spaceships of speeds c/3, c/4, and c/5.
#C Paul Tooke, July 2000
;ru N2ac01i,2ad01i,2ae01i,2af01i,2ag01i
;ru NA2be01i,2bf01i,2bg01i
;ru NA2ce01i,2cf01i,2cg01i,2ch01i
;ru NA2dg01i,2dh01i
;ru NA2eg01i,2eh01i
;ru NA2bd01i,2bh01i
;ru NA2df01i
;ru NA2fh01i
;ru NA12abcdefgh1i
;read -inline
x = 200, y = 140
6bo14bo$4b3o12b3o$bboo3bo9boo3bo$5b3o12b3o$bbo4bo7bo6bo$7bo13bo$4bobbo
7boobobbo$boo3boo12boo78boo8b4o18boo$4b3o11b3o79bo12boo17bo$bo15bo13b
oo3bo67bo7bo6bo$31bo4bo64boo5boboboo3bobo13boobo$3bo11bobboo11boo71boo
3boo6boobo$bbo13boo17bo3bo73b3oboo12boobo$bboo14bobo14bobo65boo6boo4bo
13bobbo$5b3o10bo3bo10boo71bo3bobbo18b3o$oo4boo24bobboo24bo45b3o4bo18bo
$o15bobboo19bo18bobo44bo3bobbo16boobo$oo3bo11boo11bobb4o18boo3bo42boo
6boo4bo12bo$4bobo12bo11boo3boo17bo57b3oboo13bo$6bo14bo11b4obbo15boo4bo
42boo3boo6boobo12bo$60boo39boo5boboboo3bobo11boo$57boo45bo7bo6bo13bo$
57bobbo39bo12boo19bo$57boo41boo8b4o20bobo$60boo$31boo3bo18boo4bo$33bo
bbo18bo78bobo$31boobboo18boo3bo73bo$14bo20bo23bobo71bo$3boo7bobo18b3o
25bo69boo$oo6boo3bo18bobbo97bo$obbobbo28bobbo93bo$oo4boboo4boo14bobb3o
bbo61boo8b5o3bo11bo$3b3o7b3o15boo4bo62bo12boboobo11boobo$6b6o21b4o67bo
7bo4b3o13bo$101boo5boboboo6bo11b3o$104boo3boo8boo10bobbo$113b3o4bo10b
oobo$103boo6boo4bobbo$106bo3bobbo19boobo$107b3o4bo$40bo65bo3bobbo18bo$
8bo7bobbo12boo5boo62boo6boo4bobbo11boo$5boo7bo4bo14boboo75b3o4bo$5bobb
5o5bo13boobbobboo20bo42boo3boo8boo$3b4o5boo18bobooboobbo17bo41boo5bobo
boo6bo$oo5bobobbo5bo16bobobbo16boo45bo7bo4b3o$obbo6bobbooboo12bobb3obo
bbo15bobboo39bo12boboobo$oo4boboo5bo15boo6bo60boo8b5o3bo$3b5o25b6o19bo
3bo$58bobo72b3o$56boo74bobboo$55bobboo73bobbo$133boobo$57bo42boo8b4o$
58boo40bo12boo16boobo$59bo44bo7bo18bobbo$12boo18boo5bo19bo41boo5bobob
oo3bo14b3o$7bo6bo19boboo20boo44boo3boo6bo15bo$5boo5bo3bo15boobbobb3o
15bo55b3oboo11boobo$4bobb5obboo16bobooboo64boo6boo4bo12bo$oo8b3o22bobo
bbobo12bobboo46bo3bobbo18bo$o4bo3bobobboo14bobb3obobbo3bo11boo49b3o4bo
18bo$oo3bo3bo5bo15boo6bo18bobo45bo3bobbo17boo$9boo22b6o19bo3bo40boo6b
oo4bo15bo$113b3oboo15bo$56bobboo43boo3boo6bo16bobo$57boo42boo5boboboo
3bo$59bo44bo7bo$61bo38bo12boo19bobo$100boo8b4o20bo$133bo50bo8b3o$10bo
120boo55boobbo$8bobo30bo3bo87bo49bobo4bob3o$4boo3bo18b4o7bobobo88bo48b
oobboo5bobbo$4bo22bobbob5obb3o88bo53bo12bobo$5bo4bo3bo22bobb3o87boobo
48b3o10boo$oo7boobo12bobboobb3o6bo91bo47bobbo8boobbo$o4b3o18boo5bo4boo
4bo73bo13b3o48bo4bo$oo6b4o16bo6bo5bo65boo3bobb4obo10bobbo45bo3bobbobo$
109bo11bobo7boobo48bo$101boo4bobbobobboo4bo58bo3bobbobo$101bo5boobo22b
oobo46bo4bo$118bo14bobbo44bobbo8boobbo$56boo44boobob9o16bobboo45b3o10b
oo$59bo73b3o48bo12bobo$56bo3boo39boobob9o66boobboo5bobbo$7b6o48bo55bo
65bobo4bob3o$4boo31boo16boo4boo37bo5boobo78boobbo$4bobbobb4obo12b4o23b
o5bo38boo4bobbobobboo4bo63bo8b3o$5b5o3boobo10bobboboo4boobo13bob3obo
46bo11bobo$oo7bobobo23boboobo13bo49boo3bobb4obo$o4b3o5bobbo8bobboobboo
bbo3bobbo12boobo57bo$oo7boo4boo9boo5boo5bobbo15bo$11b5o12bo7bo21b3o$
59bo$56boobo$56bo$55bob3obo45boo3bobboo3bo5bo$55bo5bo47bo10boobboo$55b
oo4boo38boo4bobbobobb3o3b3o6bo$61bo39bo5boobo5bobobo6bo$10bo45bo3boo
58boboo5bo$8bobo17b4o3b4o20bo42boobob13o$4boo3bo17bobbob3obboboo15boo$
4bo36bo59boobob13o$5bo4boo13bobboobb3o7bo76boboo5bo$oo7b3o14boo5bo5bo
bbo57bo5boobo5bobobo6bo$o4b3o20bo8bo62boo4bobbobobb3o3b3o6bo$oo33boo
71bo10boobboo$106boo3bobboo3bo5bo6$5b3o$bboo51boo3bo41b3o4b3o$bbobbobo
bbo17b4o3b4o16bo4bo40bobboobbo3bo$3boo5boo15bobboboo5bo15boo45bobboboo
4bo$4bo5bo24bobobbo18bo42boobobob3obo$5bo3boo14bobboobb4obobbo16boo48b
o$oo6bo17boo5bob3o63boobobobbobo$o4boo21bo7bo18bo3bo46boobobobo$oo34bo
21boo40bo9bo$55boo43boo$57b3obo$61bo$60b3o$61bo$57b3obo$5b4o46boo45boo
10boo$bboo4boo48boo42bo11bo$bbobboobbobo27bo15bo3bo54bobbo$3boo23b4o5b
obo63boobo8b3o$4bobbo19bobbob3o3bo18boo$5b3o3bo47bo41boobo8boobo$oo7bo
15bobboobb3o4boo14boo$o4b4o17boo5bo4b3o14bo4bo39bo11bo$oo26bo6boo18boo
3bo39boo10boo!

--
Paul Tooke
paultooke@hotmail.com


From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Wed, 5 Jul 2000 17:01:58 -0700
Subject: [LifeCA] Just friends: big glider eater and c/4 wickstretcher

Here's an eater for the big glider:

x = 5, y = 13
2bo$3o$4bo$2b2o6$5o2$bo$bo!

I found it by firing a stream of big gliders at some junk until the
eater formed spontaneously.

One of Paul Tooke's c/4 spaceships can be turned into a wickstretcher:

x = 18, y = 13
6b2o3bo3b3o$6bo5b2o$b2o12b2o$3bo3b2obo$bo2bo$b2obob12o2$2obob12o$o2bo$
2bo3b2obo$2o12b4o$5bo5b2o$5b2o3bo3b3o!

Dean Hickerson
dean@math.ucdavis.edu


From: David Bell <dbell@pcug.org.au>
Date: Thu, 6 Jul 2000 17:33:15 +1000 (EST)
Subject: [LifeCA] Re: Just friends: big glider eater and c/4 wickstretcher

That c/4 wickstretcher can be shrunk to just one pair of lines:

x = 13, y = 9
bb3o5boo$bobboob3o$bbobbo4b3o$bboobo$$oobo$obbo$bbo$oo!


The wick can burn with at least three modes, all of which move faster
than c/4.  At least one of the burning modes can be stopped before it
destroys the engine.  The following shows a glider which ignites the
wick, demonstrating the burning mode.  A backward c/3 wickstretcher is
also produced, and a little bit of transient junk.  Otherwise the
wickstretcher begins growing again just as it started:

x = 53, y = 18
50bo$51boo8$bboo3bo3b30o$bbo5boo$11b29o$3boobo$12boobo$boobo$bobbo6bo$
obboo6boo$b3o!


Maybe a perturbation or something can turn the transient junk into a
new glider so that two of these can support each other to form a
non-growing puffer.  Or maybe the c/3 wickstretcher can be turned
into a glider by a perturbation.

The burning reaction reaches out a ways too as it burns.  Maybe it can
be perturbed as it passes by too.

BCNU,
-dbell-


From: David Bell <dbell@pcug.org.au>
Date: Thu, 6 Jul 2000 22:33:44 +1000 (EST)
Subject: [LifeCA] Just Friends: Another c/4 wickstretcher and long c/4 spaceship

Here is another c/4 wickstretcher created from a perturbation of another
of Paul Tooke's ships:

x = 13, y = 9
boo5boo$bo$$bboobo3b4o$7bo$b3o5bobo$obbobboobobo$o7b5o$oo!


Here is a termination for this wick to create an arbitrarily long c/4 ship:

x = 53, y = 9
bb3o4b42o$bobboobbo$bbobboboo43bo$bboobobob44o$7bo$boobobobbobo36boobo
$6boobobobo$o9bo36bo$oo45boo!


On a different topic, the small c/4 ship can turn one glider into two
gliders (plus two dominos):

x = 8, y = 14
5bo$5b3o4$bboo$4bo$bbobbo$bboobo$$b3o$obbo$o$oo!


BCNU,
-dbell-


Date: Fri, 7 Jul 2000 14:41:40 -0700
From: Dean Hickerson <dean@math.ucdavis.edu>
Subject: Re: Your perturbation program and Just Friends

> That perturbation program of yours that finds those ripples through
> still lifes might produce good results for Just Friends.

That occurred to me too, but I haven't had time to work on it.  I don't
remember enough details about how the program works to decide if this
will be a simple modification or a major rewrite.

One of these days I'll find time to take a look at it.

Dean Hickerson
dean@math.ucdavis.edu

From: David Bell <dbell@pcug.org.au>
Date: Sun, 9 Jul 2000 10:42:13 +1000 (EST)
Subject: [LifeCA] Just Friends: Glider turning and duplicating, one-row wickstretcher

There are some easy glider turning reactions using the small c/4 ship.


Here is a frontward glider converted into a backward glider:

x = 6, y = 15
3bo$4boo5$bboo$bbo$bbobbo$3b3o$$boobo$$o$oo!


Here is a backward glider converted into a frontward glider:

x = 7, y = 14
4bo$bb3o4$bboo$bbo$$3boobo$$boobo$bobbo$obboo$b3o!


By combining these reactions, you can produce other results.
Here is a frontward glider converted into another frontward glider:

x = 14, y = 18
4bo$4b3o4$bboo$bbo$$3boobo$10boo$boobo7bo$bobbo5bobbo$obboo5boobo$b3o$
9b3o$8bobbo$8bo$8boo!


Here is a backward glider converted into another backward glider:

x = 15, y = 24
9boo$9bo$9bobbo$10b3o$$11boobo$11bobbo$13bo$bbo8boo$3o6$5boo$5bo$$6boo
bo$$4boobo$4bobbo$3bobboo$4b3o!


The almost-clean glider duplicator reaction I showed earlier can be
turned into a totally clean glider duplicator using these reactions:

x = 48, y = 33
5bo$5b3o4$bboo$4bo$bbobbo$bboobo36b3o$41bobboo$b3o38bobbo$obbo38boobo$
o$oo42boobo$$43bo$43boo4$30boo$32bo$30bobbo$30boobo$37boo$29b3o5bo$28b
obbo$28bo9boobo$28boo$36boobo$36bobbo$35bobboo$36b3o!


So now when a c/4 dirty rake is found (which I am close to having),
these reactions could be used to turn it into a totally clean rake by
bombarding the debris with enough duplicated gliders.


In other stuff, I found a single-row wickstretcher:

x = 11, y = 11
6b3o$5bobboo$oo4bobbo$o5boobo$obbo$b3ob6o$$bb3o$bobbo$bo$boo!


The engine in this can be used to "paste" a single row onto existing
rows.  Here is how it can be used to build a huge (useless) crystal:

x = 59, y = 19
54boo$56bo$42boo4boo4bobbo$44bo3bo5boobo$30boo4boo4bobbo$32bo3bo5boobo
3boobob5o$18boo4boo4bobbo$20bo3bo5boobo3boobob16o$6boo4boo4bobbo$8bo3b
o5boobo3boobob27o$oo4bobbo$o5boobo3boobob38o$$boobob49o$$bboobo$$bo$b
oo!


BCNU,
-dbell-


From: David Bell <dbell@pcug.org.au>
Date: Sun, 9 Jul 2000 19:55:12 +1000 (EST)
Subject: [LifeCA] Just Friends: Period 8256 forward rake

Here is a slightly dirty period 8256 forward rake:

x = 899, y = 209
12b3o$11bobboo$12bobbo23bo$12boobo23bo$32bo$bb3o5b21obo$bobboob3o22bo
5bo$bbobbo4b20obo6bo$bboobo25bo5bo$11boobo$oobo7bobbo$obbo9bo$bbo8boo$
oo5$459boo$459bo$459bobbo$460b3o$$461boobo$461bobbo$463bo$461boo36$
647boo$647bo$647bobbo$333b3o312b3o$332bobboo$333bobbo312boobo$333boobo
312bobbo$325boo324bo$325bo9boobo310boo$325bobbo$326b3o5bo$334boo$327b
oobo$327bobbo$329bo$327boo325boo204boo$654bo205bo$860bobbo$655boobo
202b3o$340boo$340bo312boobo205boobo$653bobbo205bobbo$297boo42boobo307b
obboo207bo$297bo213b3o139b3o206boo$297bobbo38boobo167bobboo$298b3o38bo
bbo168bobbo162boo$338bobboo168boobo70b3o91bo$299boobo36b3o161boo79bobb
oo88bobbo$299bobbo200bo9boobo68bobbo88boobo$301bo201bobbo78boobo$299b
oo203b3o5bo163b3o$512boo73boobo84bobbo$505boobo166bo$505bobbo77bo88boo
$507bo78boo$505boo4$518boo$518bo$$475boo42boobo$475bo$475bobbo38boobo$
476b3o38bobbo$516bobboo$477boobo36b3o$477bobbo$479bo$288boo187boo$288b
o$$289boobo$$287boobo$287bobbo$286bobboo$287b3o$$882boo$561boo319bo$
561bo$393boo488boobo$395bo166boobo$393bobbo172boo310boobo$393boobo36b
3o124boobo7bo309bobbo10boo$432bobboo123bobbo5bobbo307bobboo12bo$392b3o
38bobbo122bobboo5boobo308b3o11bobbo$391bobbo38boobo123b3o332boobo$391b
o176b3o$391boo42boobo128bobbo323b3o$567bo325bobbo$434bo132boo324bo$
434boo457boo4$421boo$423bo$421bobbo$421boobo$428boo$420b3o5bo$419bobbo
$419bo9boobo$419boo$427boobo$427bobbo$426bobboo$427b3o22$526boo$526bo
$$527boobo$$525boobo$525bobbo$524bobboo$525b3o3$593b3o$592bobboo$593bo
bbo$593boobo$$595boobo$$594bo$594boo7$589boo$591bo$589bobbo$589boobo$$
588b3o$587bobbo$587bo$587boo!


I have made no attempt to minimize the number of components or to pack
them closer together.  (Just getting it to work was hard enough.)
An arbitrarily large period rake can be build using the same mechanism.

This can be turned into a totally clean rake by running duplicated gliders
into the object at the back to delete it, but I saw no point in doing that
right now.  Interestingly, one of the first impacts to start with in
deleting the object creates a period 236 oscillator.

BCNU,
-dbell-


From: "Paul Tooke" <paultooke@hotmail.com>
Date: Tue, 11 Jul 2000 08:58:50 -0000
Subject: [LifeCA] Just Friends: Orthogonal c/8 wickstretcher

x = 11, y = 28
5bo$4bobo$bbo5bo3$bbo5bo$bbobobobo$bbobbobbo$3bobobo$4bobo3$5bo$$3bo3b
o$3bo3bo$$3bobobo$obo5bobo$ob3ob3obo$obobbobbobo$obobbobbobo$obobbobbo
bo$obob3obobo$obo5bobo$oboo3boobo$o9bo$o9bo!

--
Paul Tooke
paultooke@hotmail.com


From: Kellie Michele Evans <kellie.m.evans@csun.edu>
Date: Sat, 15 Jul 2000 15:32:55 -0700
Subject: Re: [LifeCA] Nonstandard rule: Glider duplicating reactions

David Bell said:

> I have been trying to find reactions which allow a glider gun to be
> built.  I have found some interesting things, which may be sufficient.
> But they haven't been combined in the right way yet.

Below is a p4484 gun for the c/6 glider that uses the following of David's
reactions:

> Unfortunately, the pairs of gliders are on close paths so that I cannot
> use the p26 turning reaction to separate them and loop them back.  If they
> could be turned, then a glider gun could probably be built.  They can be
> separated along their paths, but that doesn't seem to help turn them:
> 
> x = 49, y = 65
> 42b7o$$45bo$45bo$44bobo$$44bobo4$32bo$32b3o$32bo4$44bobo$$44bobo$45bo$
> 45bo$$42b7o15$25bobbo$28bo$23bobbobo$28bo$25bobbo16$3bo4bo$3bo4bo$boob
> 4oboo$b3o4b3o$bo8bo$b10o$$12o!

The previous reaction is used twice (once to separate a pair of gliders and
once to reflect a solo glider).
 
> The p236 cyclic oscillator can turn one glider into two gliders reflected
> back along the same path:
> 
> x = 47, y = 47
> bo$$oo39$44bo$43bobo$38boo$42bo3bo$$44bo!

> A p236 oscillator can turn a glider into a bent triomino which stays
> around.  A second p236 oscillator can turn the triomino back into
> another glider.  The path of the glider is shifted by one cell.
> Furthermore, the phase of the output glider can easily be adjusted.
> So this reaction might be used to separate those close packed gliders,
> and be used to make the phase of glider reactions correct.  Perhaps
> this will allow guns to be built.  I haven't examined this possibility.
> 
> x = 32, y = 31
> bbo27bo$3o27bo5$28boobo$27bo3bo$27bo16$9bo$9bo$3boobbobbo3$10bo$10bo!

This reaction is used three times - once on the way up the glider's path and
twice on the way back.

The gun is in the form of an MCell file (see Jason Summers' message from June
22 for more about this). 

#MCell 3.00
#GAME Weighted Life
#RULE NW1,NN2,NE4,WW128,ME256,EE8,SW64,SS32,SE16,HI0,RS257,RS258,RS259
#RULE ,RS260,RS261,RS262,RS264,RS265,RS266,RS268,RS272,RS273,RS274,RS2
#RULE 76,RS280,RS288,RS289,RS290,RS292,RS296,RS304,RS320,RS321,RS322,R
#RULE S324,RS328,RS336,RS352,RS384,RS385,RS386,RS388,RS392,RS400,RS416
#RULE ,RS448,RB5,RB9,RB10,RB17,RB18,RB20,RB33,RB34,RB36,RB40,RB65,RB66
#RULE ,RB68,RB72,RB80,RB130,RB132,RB136,RB144,RB160
#BOARD 500x500
#WRAP 0
#L 29$35.A$35.A$35.A.A.A$35.A$35.A.A.A.A$35.A.A$35.A.A$35.A.A.A.A$35.A$
#L 35.A.A.A$35.A$35.A13$80.A3.AA$80.A..A$83.A$83.A$83.AA$83.AA$80.3A$82.A
#L 11$70.3A$72.A$72.A$73.A3.AA$71.AA35$153.A$153.A$151.AA$147.3A..A$152.A
#L $154.A$152.A.A13$133.A$134.A$127.AA..AA.A$129.A..A$132.A3$130.A$130.A
#L 56$232.A$233.A$226.AA..AA.A$228.A..A$231.A3$229.A$229.A13$222.A$222.A$
#L 220.AA$216.3A..A$221.A$223.A$221.A.A122$369.12A$$371.8A$$372.A4.A$371.
#L A..AA..A$372.A4.A11$374.A$372.AA$376.A.AA$379.A$375.A..AA$376.A.AA$
#L 376.A..A$379.A$374.AA3.A

-- Kellie

From: Jason Summers <jason@med-web.com>
Date: Sun, 16 Jul 2000 15:21:48 -0500
Subject: [LifeCA] MCell format

The MCell file format is essentially just a variant of RLE with support for
multiple states. Here's a 1-line Perl script that will convert most MCell
files to RLE. It doesn't add the "x = ... y = ..." line, though.

while(<>) { if(s/^#L //) { tr/\.A-X/bo/; print; } } print "!\n";


The MCell rule definition for Just Friends I posted was a little crude, thanks
to me getting confused by some apparently unnecessary redundancy in MCell's
definition feature. Here's an improvement, though it's still just brute force:

#MCell 3.00
#GAME Weighted Life
#RULE NW1,NN2,NE4,WW128,ME0,EE8,SW64,SS32,SE16,HI0,RS1,RS2,RS3,RS4,RS5
#RULE ,RS6,RS8,RS9,RS10,RS12,RS16,RS17,RS18,RS20,RS24,RS32,RS33,RS34,R
#RULE S36,RS40,RS48,RS64,RS65,RS66,RS68,RS72,RS80,RS96,RS128,RS129,RS1
#RULE 30,RS132,RS136,RS144,RS160,RS192,RB5,RB9,RB10,RB17,RB18,RB20,RB3
#RULE 3,RB34,RB36,RB40,RB65,RB66,RB68,RB72,RB80,RB130,RB132,RB136,RB14
#RULE 4,RB160
#BOARD 400x400
#WRAP 1
#L 7.AA$6.A$6.A$AA$6.AA

From: David Bell <dbell@pcug.org.au>
Date: Mon, 17 Jul 2000 08:10:16 +1000 (EST)
Subject: [LifeCA] Re: MCell format

My Life program has a more human understandable definition of Just Friends
and similar rules.  (But then MCell is more versatile.)  In my program,
the commands for setting up Just Friends are:

;ru N2ac01i,2ad01i,2ae01i,2af01i,2ag01i
;ru NA2be01i,2bf01i,2bg01i
;ru NA2ce01i,2cf01i,2cg01i,2ch01i
;ru NA2dg01i,2dh01i
;ru NA2eg01i,2eh01i
;ru NA2bd01i,2bh01i
;ru NA2df01i
;ru NA2fh01i
;ru NA12abcdefgh1i

Here 'N' means this is a "new-style" rule definition instead of the old
Bnn/Snn format, 'A' means add the following conditions to the existing
rule instead of replacing it, 'S' means subtract the following conditions
to the existing rule instead of replacing it (unused in this example).
The cells for a neighborhood are defined by the letters a-i by the array:
  abc
  hid
  gfe
with 'i' being the middle cell to be changed.  A piece of a rule specifies
a set of total cell counts and a set of cells having those counts, with
unnamed cells having a count of 0.  So for example, the last rule 
'NA12abcdefgh1i' means add the condition that there must be 1 or 2 live
cells ON around the central cell which must be ON.  The rule 'NA2fh01i'
means that both f and h must be ON, all of abcdeg must be OFF, and i can
be ON or OFF.  Commas simply specify a number of pieces having the same
add or subtract behavior as the previous piece.

I mention this because if someday the RLE format is extended to allow
for such rules, maybe a readable format such as this could be used.
My format currently isn't part of RLE format, it uses my own Life
program's command line syntax (the ';ru' to mean set a rule).  But an
appropriate keyword could be used in RLE to introduce such rules.

BCNU,
-dbell-


From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Mon, 17 Jul 2000 14:51:27 -0700
Subject: [LifeCA] Re: MCell format

Jason Summers said:

> The MCell rule definition for Just Friends I posted was a little crude,
> thanks to me getting confused by some apparently unnecessary redundancy
> in MCell's definition feature. Here's an improvement, though it's still
> just brute force:

Yeah, it's odd that MCell requires a weight for the central cell but then
lists the birth and survival rules separately.

Here's another improvement, which uses 38 birth and survival conditions
instead of 56.  (This is a p34 billiard table.)

#MCell 3.00
#GAME Weighted Life
#RULE NW1,NN33,NE37,WW17,ME0,EE29,SW9,SS13,SE45,HI0,RS1,RS9,RS10,RS13,
#RULE RS14,RS17,RS18,RS22,RS26,RS29,RS30,RS33,RS34,RS37,RS38,RS42,RS45
#RULE ,RS46,RS50,RS54,RS58,RS62,RS66,RS70,RS74,RS78,RS82,RB10,RB14,RB3
#RULE 0,RB38,RB42,RB46,RB50,RB54,RB62,RB78,RB82
#BOARD 400x400
#WRAP 1
#L .A13.A$AA.11A.AA$$.A..A..A7.A$.A..A.AA4.AA.A$.A13.A$.A10.A..A$.A10.AA.
#L A$.A13.A$.A.AA10.A$.A..A10.A$.A13.A$.A.AA4.AA.A..A$.A7.A..A..A$$AA.11A
#L .AA$.A13.A

Dean Hickerson
dean@math.ucdavis.edu

From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Mon, 17 Jul 2000 16:33:08 -0700
Subject: [LifeCA] Re: Nonstandard rule: Glider duplicating reactions

Kellie Evans wrote:

> Below is a p4484 gun for the c/6 glider that uses the following of David's
> reactions:

Kellie's gun uses p19 oscillators to reflect gliders, in addition to the
p236 oscillators to duplicate and delay them.  So the period of the gun
must be divisible by  lcm(19,236) = 4484.  But p236 oscillators can
also reflect gliders, so we can eliminate the p19s and obtain smaller
periods.  Here's a p944 gun:

x = 92, y = 98
15bo$15bo2$2o$14bo2$11bobo4bo2$11b2o7$38bo$38bo2$32b2o2bo3bo2$37bobo2$
16b3o$18bo3b2o$17bo2$15bobo14$28bo$28bo3$28b3o3b2o$29bo$29bo5$73bo$73b
o$67b2o3b3o3$74bo$74bo14$85bobo2$85bo$79b2o3bo$84b3o2$63bobo2$62bo3bo
2b2o2$64bo$64bo20bo$85bo$84bo5$90b2o2$84bo4bobo2$88bo3$87bo$87bo!

This gun uses the glider duplication at both ends, and can be made
double-barrelled by deleting the domino at the northwest end.  It
might be possible to get a smaller period by using a reflector instead
of a duplicator at one end, as in Kellie's gun; I haven't tried that
yet.

By moving the southeast half 118n units southeast, we can increase the
period by 1416n.  Here's the p2360 version:

x = 210, y = 216
15bo$15bo2$2o$14bo2$11bobo4bo2$11b2o7$38bo$38bo2$32b2o2bo3bo2$37bobo2$
16b3o$18bo3b2o$17bo2$15bobo14$28bo$28bo3$28b3o3b2o$29bo$29bo123$191bo$
191bo$185b2o3b3o3$192bo$192bo14$203bobo2$203bo$197b2o3bo$202b3o2$181bo
bo2$180bo3bo2b2o2$182bo$182bo20bo$203bo$202bo5$208b2o2$202bo4bobo2$
206bo3$205bo$205bo!

By changing the phases of the glider delay reactions, it should be
possible to get other multiples of 236.

Dean Hickerson
dean@math.ucdavis.edu

From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Tue, 18 Jul 2000 17:50:25 -0700
Subject: [LifeCA] Just friends: p472 glider gun

I said:

> This gun uses the glider duplication at both ends, and can be made
> double-barrelled by deleting the domino at the northwest end.  It
> might be possible to get a smaller period by using a reflector instead
> of a duplicator at one end, as in Kellie's gun; I haven't tried that
> yet.

It works, yielding period 472:

x = 43, y = 59
11bo$11bo3$11bo$9bo$8bo4b2o$9bo$11bo8$26bo$26bo3$25bo2bo$28bo$23b2o5bo
$28bobo3$36bo3$41b2o$38bo$36bo$34bo$5bobo26bobo2$2o2bo3bo2$6bo$6bo$34b
o$32b2o13$39bobo$34b2o4bo$40bo2$41bo$41bo!

Dean Hickerson
dean@math.ucdavis.edu

From: "Paul Tooke" <paultooke@hotmail.com>
Date: Wed, 19 Jul 2000 11:24:00 -0000
Subject: [LifeCA] Just friends: c/5 & c/5 wickstretchers

Three related c/5 wickstretchers with some c/5 reactions that reduce 
wick size.

x = 110, y = 30
18bo41bo34bo$12b4obbobb4o29b4obbobb4o22b4obbobb4o$12bobobbobobbobo29bo
bobbobobbobo22bobobbobobbobo$14bo7bo33bo7bo26bo7bo$10bo4bo5bo4bo25bo4b
o5bo4bo18bo4bo5bo4bo$14b3o3b3o33b3o3b3o26b3o3b3o$9bobbobobo3bobobobbo
23bobbobobo3bobobobbo16bobbobobo3bobobobbo$8bo5booboboboo5bo21bo5boobo
boboo5bo14bo5booboboboo5bo$9boboboboo3boobobobo23boboboboo3boobobobo
16boboboboo3boobobobo$9bobobob3ob3obobobo23bobobob3ob3obobobo16bobobo
3bobo3bobobo$9bobobo9bobobo23bobobo9bobobo16bobo13bobo$9bobobo9bobobo
23bobobo9bobobo16boboboo7boobobo$9bobobo8bobbobbo22bobobo8bobbobbo15bo
bo3bobobobo3bobo$8bobbobbo6bo7bo19b3obobo7bo7bo14bobobobo5bobobobo$7bo
7bo3bobo7bobo17bo5bo5bobo7bobo12bobobobobobobobobobo$5bobo7bobobobbo5b
obbo15bobo5bo5bobbo5bobbo12boboboboboboboboboboo$5bobbo5bobbobobo7bobo
15bobboo3bo5bobo7bobo12bobobobobobobobobo5bo$5bobo7bobobobobo3bobobo
17bobboobo5bobobo3bobobo12bobobobobobobobobobo3bo$5bobobo3bobobobobobo
3bobobo17bobobobo5bobobo3bobobo12bobobobobobobobobobbobbo$5bobobo3bobo
bobobobo3bobobo16boobobo9bobooboobo14bobobobobobobobobobbo$4boobobo3bo
bobobobobo3bobobo19bo12bo5bo15bobobobobobobobo7boo$bo5bobo3bobobobobob
o3bobobo17boboboo11bobo17boboboboboboboboboo$bo3bobobo3bobobobobobo5bo
18bobbobbo7bo9bo13bobobobobobobobo$bobbobbobo3bobobobobobo24bobbobbo7b
o9bo13bobobobobobobobo$4bobbobo3bobobobobobo27bo10bo9bo13bobobobobobob
obo$oo7bo3bobobobobobo23bo3bo9boo9boo12bobobobobobobobo$6boobo3bo3bo3b
o43bobobo16bobobobobobobobo$9bo42bo12b5o16bobobobobobobobo$67bo18bobob
obobobobobo$88bo3bo3bo3bo!

Two copies of a 'wallwalking' wickstretcher supported by a c/7 ship. 
The wicks are reduced by two different c/7 reactions.

x = 32, y = 42
15bobo$$15b3o$5b3o7b3o7b3o$5bobo7b3o7bobo$6bo8bobo8bo$13bobobobo$3bobb
obbo3bobbobbo3bobbobbo$3bobobobobbo7bobbobobobo$3bobobobobbo7bobbobobo
bo$3bob3obobbo3bo3bobbob3obo$3bo8bo3bo3bo8bo$3bo8bo3bo3bo8bo$3bobobbo
bbo3bobo3bobbobbobo$3bobobbobboboo3boobobbobbobo$5bobobobo9bobobobobo$
boobbobobobobbobobobbobobobobo$o6bobo5bobo5bobobobo$o3bobbobo3booboboo
3bobobobo$oobbobbobo5bobo5bobobo$b3o3bobo13bo4bo$bo7bo6bo6bobobo$9bo6b
o6bo6bo$9bo4bo3bo4bob3obbo$9bobb4ob4obbo6bo$9bobobobobobobobo3bobbo$9b
o13bo3bobbo$9bo3bo5bo3bo6bo$9bo4bo3bo4bobboobboo$9bob4o3b4obo$9bo4bo3b
o4bo$9bo3bobobobo3bo$9bo3bob3obo3bo$9bo3bo5bo3bo$9bo3bo5bo3bo$9bo3bo5b
o3bo$9bobbo7bobbo$9bobbobooboobobbo$9bobbo3bo3bobbo$9boboo7boobo$9bo
13bo$9bo13bo!

--
Paul Tooke
paultooke@hotmail.com



From: KiwiCado23@aol.com
Date: Thu, 20 Jul 2000 17:28:09 EDT
Subject: [LifeCA] Re: Just Friends Arbitrarily wide c/4 ships

The previously shown c/4 wickstretcher component can be combined to make 
arbitrarily wide ships(sorry, this is in the MCell format):

#MCell 3.00
#GAME Weighted Life
#RULE NW1,NN2,NE4,WW128,ME256,EE8,SW64,SS32,SE16,HI0,RS257,RS258,RS259
#RULE ,RS260,RS261,RS262,RS264,RS265,RS266,RS268,RS272,RS273,RS274,RS2
#RULE 76,RS280,RS288,RS289,RS290,RS292,RS296,RS304,RS320,RS321,RS322,R
#RULE S324,RS328,RS336,RS352,RS384,RS385,RS386,RS388,RS392,RS400,RS416
#RULE ,RS448,RB5,RB9,RB10,RB17,RB18,RB20,RB33,RB34,RB36,RB40,RB65,RB66
#RULE ,RB68,RB72,RB80,RB130,RB132,RB136,RB144,RB160
#BOARD 600x660
#WRAP 0
#L 35.3A$34.A..A$29.A.AA.A$29.A..A.AA$30.A$31.AA$$29.A.A3$29.A.A$29.A.A$
#L 29.A.A$29.A.A$18.AA9.A.A9.AA$18.A..A3.A3.A.A3.A3.A..A$21.A.AA.A..A.A..
#L A.AA.A$23.A..A..A.A..A..A$21.A3.AA..A.A..AA3.A$23.3A3.A.A3.3A$20.AA7.A
#L .A7.AA$20.A.3A4.A.A4.3A.A$24.AA3.A.A3.AA$20.AA.A..A..A.A..A..A.AA$19.A
#L 3.A..A..A.A..A..A3.A$20.AA.A..A..A.A..A..A.AA$23.A..A..A.A..A..A$20.A
#L ..A..A..A.A..A..A..A$23.A..A..A.A..A..A$23.A..A..A.A5.A$23.A..A..A.AA
#L 4.A$12.AA9.A..A..A7.A9.AA$12.A..A3.A3.A..A..A7.A3.A3.A..A$15.A.AA.A..A
#L ..A..A7.A..A.AA.A$17.A..A..A..A..A7.A..A..A$15.A3.AA..A..A..A7.A..AA3.
#L A$17.3A3.A..A..A3.AA..A3.3A$14.AA7.A..A..A.A..A..A7.AA$14.A.3A4.A..A..
#L A.A5.A4.3A.A$18.AA3.A..A..A7.A3.AA$14.AA.A..A..A5.A.A5.A..A..A.AA$13.A
#L 3.A..A..A4.AA7.A..A..A3.A$14.AA.A..A..A13.A..A..A.AA$17.A..A..A13.A..A
#L ..A$14.A..A..A..A13.A..A..A..A$17.A..A..A13.A..A..A$17.A..A..A3.AA3.AA
#L 3.A..A..A$17.A..A..A.A..A3.A..A.A..A..A$6.AA9.A..A..A.A9.A.A..A..A9.AA
#L $6.A..A3.A3.A..A..A13.A..A..A3.A3.A..A$9.A.AA.A..A5.A.A9.A.A5.A..A.AA.
#L A$11.A..A..A4.AA13.AA4.A..A..A$9.A3.AA..A25.A..AA3.A$11.3A3.A25.A3.3A$
#L 8.AA7.A25.A7.AA$8.A.3A4.A25.A4.3A.A$12.AA3.A25.A3.AA$8.AA.A..A..A25.A
#L ..A..A.AA$7.A3.A..A..A25.A..A..A3.A$8.AA.A..A..A25.A..A..A.AA$11.A..A
#L ..A25.A..A..A$8.A..A..A..A25.A..A..A..A$11.A..A..A25.A..A..A$11.A..A..
#L A3.AA15.AA3.A..A..A$11.A..A..A.A..A15.A..A.A..A..A$AA9.A..A..A.A21.A.A
#L ..A..A9.AA$A..A3.A3.A..A..A25.A..A..A3.A3.A..A$3.A.AA.A..A5.A.A21.A.A
#L 5.A..A.AA.A$5.A..A..A4.AA25.AA4.A..A..A$3.A3.AA..A37.A..AA3.A$5.3A3.A
#L 37.A3.3A$..AA7.A37.A7.AA$..A.3A4.A37.A4.3A.A$6.AA3.A37.A3.AA$..AA.A..A
#L ..A37.A..A..A.AA$.A3.A..A..A37.A..A..A3.A$..AA.A..A..A37.A..A..A.AA$5.
#L A..A..A37.A..A..A$..A..A..A..A37.A..A..A..A$5.A..A..A37.A..A..A$5.A..A
#L ..A3.AA27.AA3.A..A..A$5.A..A..A.A..A27.A..A.A..A..A$5.A..A..A.A33.A.A
#L ..A..A$5.A..A..A37.A..A..A$5.A5.A.A33.A.A5.A$5.A4.AA37.AA4.A$5.A49.A$
#L 5.A49.A$5.A49.A$5.A49.A$5.A49.A$5.A49.A$5.A49.A$5.A49.A$5.A49.A$5.A49.
#L A$5.A49.A$5.A49.A$5.A49.A$5.A49.A$5.A49.A$5.A49.A$5.A49.A$5.A49.A$5.A
#L 49.A$5.A49.A$5.A49.A$5.A9.AA27.AA9.A$5.A3.A3.A..A27.A..A3.A3.A$5.A..A.
#L AA.A33.A.AA.A..A$5.A..A..A37.A..A..A$5.A..AA3.A33.A3.AA..A$5.A3.3A37.
#L 3A3.A$5.A7.AA31.AA7.A$5.A4.3A.A31.A.3A4.A$5.A3.AA39.AA3.A$5.A..A..A.AA
#L 31.AA.A..A..A$5.A..A..A3.A29.A3.A..A..A$5.A..A..A.AA31.AA.A..A..A$5.A
#L ..A..A37.A..A..A$5.A..A..A..A31.A..A..A..A$5.A..A..A37.A..A..A$AA3.A..
#L A..A37.A..A..A3.AA$A..A.A..A..A37.A..A..A.A..A$3.A.A..A..A9.AA15.AA9.A
#L ..A..A.A$5.A..A..A3.A3.A..A15.A..A3.A3.A..A..A$3.A.A5.A..A.AA.A21.A.AA
#L .A..A5.A.A$5.AA4.A..A..A25.A..A..A4.AA$11.A..AA3.A21.A3.AA..A$11.A3.3A
#L 25.3A3.A$11.A7.AA19.AA7.A$11.A4.3A.A19.A.3A4.A$11.A3.AA27.AA3.A$11.A..
#L A..A.AA19.AA.A..A..A$11.A..A..A3.A17.A3.A..A..A$11.A..A..A.AA19.AA.A..
#L A..A$11.A..A..A25.A..A..A$11.A..A..A..A19.A..A..A..A$11.A..A..A25.A..A
#L ..A$6.AA3.A..A..A25.A..A..A3.AA$6.A..A.A..A..A25.A..A..A.A..A$9.A.A..A
#L ..A9.AA3.AA9.A..A..A.A$11.A..A..A3.A3.A..A3.A..A3.A3.A..A..A$9.A.A5.A
#L ..A.AA.A9.A.AA.A..A5.A.A$11.AA4.A..A..A13.A..A..A4.AA$17.A..AA3.A9.A3.
#L AA..A$17.A3.3A13.3A3.A$17.A7.AA7.AA7.A$17.A4.3A.A7.A.3A4.A$17.A3.AA15.
#L AA3.A$17.A..A..A.AA7.AA.A..A..A$17.A..A..A3.A5.A3.A..A..A$17.A..A..A.
#L AA7.AA.A..A..A$17.A..A..A13.A..A..A$17.A..A..A..A7.A..A..A..A$17.A..A
#L ..A13.A..A..A$12.AA3.A..A..A13.A..A..A3.AA$12.A..A.A..A..A13.A..A..A.A
#L ..A$15.A.A..A..A13.A..A..A.A$17.A..A..A13.A..A..A$15.A.A5.A9.AA..A5.A.
#L A$17.AA4.A3.A3.A..A..A4.AA$23.A..A.AA.A5.A$23.A..A..A7.A$23.A..AA3.A5.
#L A$23.A3.3A7.A$23.A7.AA4.A$23.A4.3A.A4.A$23.A3.AA8.A$23.A..A..A.AA4.A$
#L 23.A..A..A3.A3.A$23.A..A..A.AA4.A$23.A..A..A7.A$23.A..A..A..A4.A$23.A
#L ..A..A7.A$23.A..A..A7.A$23.A..A..A7.A$23.A..A..A7.A$23.A..A..A7.A$23.A
#L ..A..A7.A$23.A..A..A..A.AA.A$23.A..A..A..A..A.A$23.A..A..A3.A3.A$23.A
#L ..A..A4.AA.A$23.A..A..A7.A$23.A..A..A..A.A..A$23.A..A..A7.A$23.A..A..A
#L 7.A$23.A..A..A..A.A..A$23.A..A..A..A.A..A$23.A..A..A..A.A..A$23.A..A..
#L A..A.A..A$23.A..A..A..A.A..A$23.A..A..A..A.A..A$23.A..A..A..A.A..A$23.
#L A..A..A..A.A..A$23.A..A..A..A.A..A$23.A..A..A..A.A..A$23.A..A..A..A.A$
#L 23.A..A..A..A.AA$23.A..A..A..A$23.A..A..A..A$23.A..A..A..A$23.A..A..A
#L ..A$23.A..A..A..A$23.A..A..A..A$23.A..A..A..A$23.A..A..A..A$18.AA3.A..
#L A..A..A3.AA$18.A..A.A..A..A..A.A..A$21.A.A..A..A..A.A$23.A..A..A..A$
#L 21.A.A8.A.A$23.AA6.AA

   Keith Amling

From: Kellie Michele Evans <kellie.m.evans@csun.edu>
Date: Thu, 20 Jul 2000 15:08:51 -0700
Subject: [LifeCA] Just friends: p236 glider gun

Here is a p236 glider gun:

#MCell 3.00
#GAME Weighted Life
#RULE NW1,NN2,NE4,WW128,ME256,EE8,SW64,SS32,SE16,HI0,RS257,RS258,RS259
#RULE ,RS260,RS261,RS262,RS264,RS265,RS266,RS268,RS272,RS273,RS274,RS2
#RULE 76,RS280,RS288,RS289,RS290,RS292,RS296,RS304,RS320,RS321,RS322,R
#RULE S324,RS328,RS336,RS352,RS384,RS385,RS386,RS388,RS392,RS400,RS416
#RULE ,RS448,RB5,RB9,RB10,RB17,RB18,RB20,RB33,RB34,RB36,RB40,RB65,RB66
#RULE ,RB68,RB72,RB80,RB130,RB132,RB136,RB144,RB160
#BOARD 500x500
#WRAP 1
#L 17$21.A$21.A3$19.A.A$19.A.A.A$17.3A.AA$19.A.A.A$19.A.A3$35.A$35.A$33.
#L AA.AA$29.AA3.A.A$34.A.A9$49.A$49.A$49.AA$49.AA3.AA$49.A$49.A.A$47.A$
#L 47.3A5$25.A$25.A$25.3A14.A$32.A7.AA$44.A.AA$25.AA4.A15.A$43.A..AA$44.A
#L .AA$44.A..A$47.A$42.AA3.A

Dean wrote: 

> By changing the phases of the glider delay reactions, it should be
> possible to get other multiples of 236.

There are actually examples for all multiples of 236, in some cases at least
two varieties. I'll say more about this in another message.

-- Kellie



From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Thu, 20 Jul 2000 19:16:23 -0700
Subject: [LifeCA] Re: Just friends: p236 glider gun

Kellie Evans said:

> Here is a p236 glider gun:

Nice work!  (I had incorrectly concluded that this couldn't be done
with these reactions.)

Putting 2 of these guns together gives a p236 gun for the big glider:

x = 92, y = 64
58bo2$58bobo27bo$87bobo$64b2o19bo$58b2o24bo6bo$85bo$87bobo$64bo23bo2$
64b2o7bo13bo$87bo$47bo23bo3bo$47b3o17b2o$45b2o25bobo$45b2o26bo$46bo$
46bo$46bo2bo$44b2o3bo10$28b2o$24bo$21b2o45bobo$21bo2bo45bo$21bo46bo$
21b2o43bo$62b2o3$68bo7$42bo2bobo$42bo$45bo2$17bobo2$16bo3bo2b2o18bo$
43bo$4bo13bo$18bo7b3o$28bo3$bobo3bo$2obo28b2o$bobo3bo18b2o3bo$32bo$2bo
29bo$32b3o!

Putting 3 guns together gives a pseudo-p118 glider gun:

x = 96, y = 94
7bobo2$7bobo3b2o$7b3o11$19bo$15bo3bo$15bob2o3$38bo2$16bo19bo3bo$16bo
18bo5bo$12bo23bo3bo2b2o$11b2o$7bo29bobo$6bobo29bo$8bo$2o4bo$6bo$3bob2o
55bobo$4bo$64bo28bobo$bo63bo3b2o22bobo$bo61b3o22b3o2bo$93bobo$94bo2$
68bo$68bobo7bo$17b2o59bo$17bo35bo23bobo$17bob2o32bo18b2o$17bo58b5o$18b
obo57bo$78bo$17bo3bo$24b2o25b2obo$19bo30bo3bo$50bo$43bo$41b2o7$33b2o$
28bo45b2o$26bo3bo42bo$73bo$28bo42b2ob2o$26b3o44bo$67b2o5$62bo$62bo$61b
2o2$51bo$47bo3bo$47bob3o$48bo$23bo2$21bo3bo$28b2o18bo$22bobo23bo$32bo$
23bo9bo$33bo2$6b3o$6bobo$5b2obo2b3o22bobo$6bobo22b2o$6bobo27b2o$7bo28b
2o$38bo$38bo!

With 7 we get a pseudo-p59 glider gun:

x = 156, y = 169
bo$bo4$2o$obobo$o$4bo4$12bo$11b4o$9b2o4bo$11bobobo$12bo3bo$12bobobo$
16bo$14b2o$14b2o$31bo$31bo3$31bo$33bo$28b2o$33bo$31bo$90bobo$91bo$89b
5o2b2o2$2b2o14bo71bobo$8bo$6bo3bo6b2o40b3o$56bobo$8bo47bo2bo$8b3o46bob
o$57b2o24bo$22b4o33bo23bo$22bo2bo31b2o2$21bobo$84bo$82b2o$79b2o3bo$20b
o$20bo$59bo$52b2o45bo$52b2o5b2o38bo$51bo$51bobobo$51bo3bo42bo$52bobobo
41bobo$52bo4b2o37b3o2b2o$53b4o41bobo$55bo11b2o29bo$66bo5b2o47bo$68b2o
51bo$50bo17bo2bo$50bo19b2o37bo$29bo19bo20bo38b3o11bo$29bo40bo$70bo51bo
2b2o$126bo$28bo2bo91bo2bo$28b4o$26b2o5bo$31b3o$46b2o$41bo5bo$43bobobo$
48bo32bobo26bobo$44bo3bo61bo$48bo27b2o2b5o27bo$39b2o40bobo28bo2b3o$41b
o39b3o28b2o$111bo$111bo$70bo$15bo2b3o47b3o$14bo2b2o104bo$15bo$121bo3bo
$117b2o$40b3o79bobo29b2o$16bo23bo2bo79bo26bo$16bo22bo2bo57bo47bobo$40b
o106bob2o$40bo2bo14bo24bo63bo$41bobo16b3o20bobo17b2o43bo$38b5o15b2o41b
o$8bo51b3o37bo2bobobo$8bo94bo3bo$103b2o$2b2o2bo3bo66bo30bo25b2o$63bo
14bo27bo$7bobo53bo14bo27bo28bo$8bo80bo2$88b2o$149bo$149bo$50bo98bo$50b
o2$147b4o$50bo28bobo69bo$48bobobo94b2obo$50b2o29bo28bob2o9bo$48bobobo
29bo3b2o25bo10b2o$50bo29b3o27bob2o3$128bo$112bo15bo4b2o$112bo16bo$130b
2o$109bo19bobo$109bo17bo$39b2o3bo63bo16b4obo$39bo85bo$39b4obo80b3o2$
96b2o$42bo7bobo44bo$42bo9bo41bo2bo$42bo53b2o$94bo16bo7bo$64bo2b2o20b2o
20bo5bobo$62b2o2$64bo$109bo$112bo$64bo42bobo2bo$64bo9bo21b3o$74bo23bo
2$68b2o2bo3bo2$73bobo5$89bo$90b2o9$74bo$98b3o$69bo3bobo24bo$73bob2o23b
o$69bo3bobo25bo3b2o$99b2o4$72bo!

Pseudo-p118 and pseudo-p59 guns could be built for the big glider too.

Each of the p236 guns can produce a crystal growing upstream in at least
two ways.  Here are two for the small glider gun:

x = 309, y = 139
15bo163bo2$10bo3bobo157bo3bobo$14bob2o160bob2o$10bo3bobo157bo3bobo5$
26bobo161bobo2$11bo13bo3bo2b2o141bo13bo3bo2b2o$9bobo161bobo$27bo163bo$
27bo163bo5$46b2o162b2o$47bo163bo$44bo2bo160bo2bo$46b2o162b2o$44bo163bo
$6b2o31b2o129b2o31b2o$2o3bo158b2o3bo$6bo163bo$6bo163bo$6b3o161b3o9$40b
o163bo$40bo163bo$39bo163bo2$25bo2bobo158bo2bobo$25bo163bo$28bo163bo4$
26bo163bo$26bo163bo28$79bo163bo2$78b2o162b2o30$273b2o$115bo$115bo161b
3o2$110b8o$283b2o$116bo3bo$116bo3bo$113b2obo$116bob5o$116bo168b3o$121b
o3bo$121bo3bo$118b2obo169b2o$121bob5o$121bo$126bo3bo$126bo3bo$123b2obo
166b3o$126bob5o$126bo$131bo3bo163b2o$131bo3bo$128b2obo$131bob5o$131bo$
136bo3bo160b3o$136bo3bo$133b2obo$136bob5o164b2o$136bo!

And here are two for the big glider:

x = 488, y = 262
58bo199bo2$58bobo27bo169bobo27bo$87bobo197bobo$64b2o19bo178b2o19bo$58b
2o24bo6bo166b2o24bo6bo$85bo199bo$87bobo197bobo$64bo23bo175bo23bo2$64b
2o7bo13bo176b2o7bo13bo$87bo199bo$47bo23bo3bo171bo23bo3bo$47b3o17b2o
178b3o17b2o$45b2o25bobo170b2o25bobo$45b2o26bo171b2o26bo$46bo199bo$46bo
199bo$46bo2bo196bo2bo$44b2o3bo194b2o3bo10$28b2o198b2o$24bo199bo$21b2o
45bobo150b2o45bobo$21bo2bo45bo150bo2bo45bo$21bo46bo152bo46bo$21b2o43bo
154b2o43bo$62b2o198b2o3$56bo11bo187bo11bo$56bo199bo$55b2obo196b2obo$
58bo199bo$57bo199bo3$42bo2bobo194bo2bobo$42bo199bo$45bo199bo2$17bobo
197bobo2$16bo3bo2b2o18bo172bo3bo2b2o18bo$43bo199bo$4bo13bo185bo13bo$
18bo7b3o189bo7b3o$28bo199bo3$bobo3bo193bobo3bo$2obo28b2o166b2obo28b2o$
bobo3bo18b2o3bo169bobo3bo18b2o3bo253bobo$32bo199bo254bo$2bo29bo169bo
29bo$32b3o197b3o16$94b2obo196b2obo2$96b2o198b2o36$135bo199bo$133bobo
197bobo$137bo199bo$135b3o197b3o4$139b3o2$145bo$145bobo$147bo$147bo3$
151bo203bo3bo$151bobo201bo3bo$153bo$153bo$367bobo$369bo$157bo$157bobo$
159bo$159bo188bo$348bo$349bo$163bo$163bobo194b3o$165bo$165bo19$381b3o
21$402b3o21$423b3o21$444b3o21$465b3o9$272bo$272bo$273bo!

Of these four, only the last one depends on the fact that the stream's
period is 236.

Dean Hickerson
dean@math.ucdavis.edu

From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Fri, 21 Jul 2000 17:20:26 -0700
Subject: [LifeCA] Just friends:  More wickstretcher reactions

Here are some more reactions involving lines produced by wickstretchers.

First, a pair of lines produced by the small c/3 wickstretcher is converted,
at c/3, to a closer pair of lines:

x = 30, y = 7
16bo$18b9o$b11o4bo10b2o$13bob3o8bo2bo$12o4bo10b2o$18b9o$16bo!

Here the pair of lines produced above decays at 4c/14, producing a
slowly lengthening spaceship:

x = 18, y = 7
10bo$bo10b3o$3b3o4bo4b2o$o6bob3o2bo2bo$4b2o4bo4b2o$2bo9b3o$10bo!

4 lines decay at c/8:

x = 10, y = 15
6b2o$8b2o2$o7b2o$ob6o2$b5o$bo4bo$b6o2$ob6o$o7b2o2$8b2o$6b2o!

1 line decays at c/20:

x = 20, y = 11
11b3o$10b2o2bo$10bo2bo4b2o$2bo7bob2o5bo$2o14bo2bo$2bo5b7ob3o2$15b3o$
15bo2bo$18bo$17b2o!

Here 3 lines, produced by one of Jason Summers's c/5 wickstretchers,
decay at 8c/44, giving another slowly lengthening spaceship:

x = 25, y = 24
2bo3bo3b2o$2bo2bobobo$5bobo2bobo$11bobo$ob8ob6o$o9b3o$5bo2bo3b6obobo$
5bobo10b2o2b2o$4bo3b9o3bo$20b3o$20bo2bo$16bo4bo$15bobo2bo3bo$21bo$15bo
bo2bo3bo$16bo4bo$20bo2bo$9bo10b3o$7b2ob7o3bo$9bo8b2o2b2o$12b6obobo$11b
o$11bob4o$11bo!

Dean Hickerson
dean@math.ucdavis.edu

From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Fri, 21 Jul 2000 17:21:44 -0700
Subject: [LifeCA] Just friends:  More oscillators

Here's an updated oscillator collection.  It includes oscillators of
several new periods (15, 27, 28, 34, 37) and new oscillators of several
old periods.  I also threw in the only p2 that I know of; has anyone
seen any others?

x = 559, y = 269
6o2bo301b6o21b2o108bo95bo13bo$8bo323bo112bobobo92b2ob11ob2o$8bo300b2ob
obo17bob3o15b5o25b6o2bo6bo2b3o2bo18bo20bobobo$8bo303bobo14bo2bo5bo11b
2o38bo6bo7bo18bo19bo5bo56b4o2bo6bo7bo14bo7bo2bo2bo$8bo11b2o2b2o177bo6b
o2b3o2bo110bo4b2o17bobo34bo6bo7bo20b2o18bob3o62bo6bo7bo14bob3o3bo2bo2b
o$o2b3o2bo13b2o179bo6bo7bo34b4o5b4o37bo25bob2o16b3o38bo6bo7bo17b2o5b2o
14bo66bo6bo7bo14bo3bo5b2o2bo$o18b3o2b3o176bo6bo7bo56bo27bob2o11bo8bob
2o59bo6bo7bo20bo3bob5o76bo6bo7bo14bo13bo$o202bo6bo7bo13b2o5b2o11b4o7b
4o8bo18bo8bo8bo5bobo6bo3bo4bo45bo2b3o2bo6bo7bo14b5obo3bo20bo61bo6bo7bo
14bob2o10bo$o202bo6bo7bo13bo7bo14bo7bo23bo3bo2bo8bob2o3b3o7bo10bo4bo3b
o41bo14bo7bo19b2o5b2o13b3obo55b4o2bo6bo2b3o2bo14bo13bo$o202bo6bo7bo10b
2obobo3bobob2o9bob3o3b3obo21bobobo2bo8bo7b3o3b2obo16b2obo41bo14bo7bo
23b2o16bo5bo59bo14bo14bo10b2obo$o2b6o194bo6bo7bo13bobo3bobo12bo11bo10b
obo13b3obo6bobo5bo8bo14b2obo13b3o27bo14bo7bo26bo15bobobo60bo14bo14bo
13bo$203bo6bo7bo13bobo3bobo12bob3o3b3obo7b3obo11bo6bo8bo11b2obo11b2o4b
o9bobo31bo14bo7bo26bo15bobobo60bo14bo14bo2b2o5bo3bo$203bo6bo7bo13bo7bo
14bo7bo14bo10bo30bo8bo5bo2bo13b2o28bo2b6o6bo2b3o2bo44bo62bo14bo14bo2bo
2bo3b3obo$203bo6bo7bo33b4o7b4o7b2o55b3obo11b5o155b4o2bo14bo14bo2bo2bo
7bo$203bo6bo2b3o2bo57b5o28bobo23bo$253b4o5b4o43bobob2o14b2o211b2ob11ob
2o$543bo13bo$308b6o4$2b4o2bo$8bo$8bo11bo33bobo38bo15bo6bo5bo$8bo11bo
12bo48b4o7bobob2o12bo6bob3obo8bo12bo14b3o108bo275b7o$8bo22bobo20bobo8b
obo9bo15bo24bo5bo5b2obo9b2obo125bo$2b4o2bo10bob2o8bobo9bobo31bob4obo
13b2o8bob3o5bobobobo25bo7b3obo133bo136bo75b4o2bo6b4o2bo16bo4bobo$8bo
21bo3bo30bobobo7bo4bobo7b2o24bo5bo7bobo11bobobo118b5o22bo31bo4b4o4bo
91bo81bo12bo16bo4bobo$8bo12bo8b5o8bobo31bob4obo13bo9bo9bobobobo25bo8b
2o3bo103b2o23b2obo14b3o4bo9bob3o4b3obo48b6o2bo6bo25bo2bobo13b5o60bo12b
o16bo$8bo12bo32bobo10bobo7bo15b2obobo6b2obo9bo5bo8bob2o8b2obobo117bo2b
o24bobo17bobobo7bo5b2o5bo6b10o40bo6bo26bo3bo78bo12bo$8bo20b7o46b4o10bo
11bo9bob3obo8bo24b3obo49bo5bo12bo13bo22b2obo19b6obo11b3o5bobo7bob3o4b
3obo56bo6bo15bo10bo82bo12bo$2b4o2bo45bobo61bo5bo23b4o60bo5bo12bobo11bo
bo21b3o5bo17b2obobo12b3obo2bo7bo12bo7bob2o3bo41bo6bo15bo87b4o2bo12bo$
161b3o48bo5bo12bobo11bobo16b3o10bob2o7b7obobobo10bo5bo10bob4o2b4obo7bo
bob2obo41bo6bo45b3o61bo12bo$212bo5bo13bo13bo16b2ob2o5b3obo14b2o3b2o14b
o3bo10bo4b4o4bo7bobo4bo33bo2b3o2bo6bo45bobo61bo12bo23bo$212bo5bo44bo3b
o5bo3bo12bobobob7o10bo5bo8bob4o2b4obo7bobo4bo33bo14bo17bo15bo75bo12bo
16bobo4bo$212bo5bo44bob3o5b2ob2o12bobob2o14bo2bob3o10bo12bo7bob4obo33b
o14bo13bo3bo11bo3bo9b2obob2o59bo12bo16bobo4bo$212bo5bo24b3o2b2o10b2obo
10b3o15bob6o10bobo5b3o7bob3o4b3obo7bo6bo33bo14bo13bobo2bo10bobo2bo11bo
56b4o2bo12bo$212bo5bo14bo29bo5b3o20bobo15bobobo13bo5b2o5bo48bo14bo16bo
15bo104b7o$212bo5bo13bobo7b9o18bob2o21bob2o14bo4b3o8bob3o4b3obo48bo2b
6o6bo16bo15bo$212bo5bo13bobo34bo2bo21bo33bo4b4o4bo$112bo99bo5bo15bo36b
2o21bo$100bo8b2obob2o151b5o$81bo18bo11bo13bo$o7bo58bo13bobobo25bobo10b
obo10b2o129bo$o7bo23b4o13bo17b2o12bo17b3o22bobo20bo3bo2bo113bo$o7bo37b
7o10b3o15bobobo11b2o11b5o9bo13bob2o5bob3o2bo$o7bo11bo13b4o11bo12b2o2bo
14bo16bo13bo10b3o12bo8bobo2bobo$o7bo11b3o9bo12b3o3b3o8bobobo13b7o8b2ob
o13bo11bo13b2o7bob3o2bo$o2b3o2bo10b3o13bo26bo2b2o8b7o30bo11bobo8b3o9bo
6bo$8bo12bo8b2obobo12b3o12b3o14bo16bob2o11bo11bobo20bob4obo130b5o214bo
7bo6bo2b3o2bo$8bo24bobo24b2o14bobobo16bo12b5o9bo13b2o7bo6bo349bo7bo6bo
7bo14b10o$8bo24bo27bo18bo16b2o187bobo215bo7bo6bo7bo$8bo67bobobo13b3o
14bobo172bobo215bo7bo6bo7bo17b3o$8bo71bo31bo142bo14b2o14bo14b5o133bo
11bo52bo7bo6bo7bo15bo4bo$95bo13b2obob2o136bo2bobo27b2o33bo118bobo9bobo
50bo2b3o2bo6bo7bo16b4ob3o$95bo16bo124bo14bo2bobo13bob4o9bo16b5o10bobo
116bobobobo5bobobobo56bo6bo7bo15bo4bo$233bo3bobo9b2o3bo32bo11b5o14bobo
62b6o2bo6b6o2bo30bo3bobo5bo3bobo56bo6bo7bo17b3o$233bo3bobo12b3obob2o
12bo3b3o24bob2o11bobo70bo14bo13b9o8bo5bo5bo5bo56bo6bo7bo$236b2o10b3o5b
o13b5o28b2o17bo68bo14bo30bo5bo5bo5bo56bo6bo7bo14b10o$231b3o3b5o9b2o3b
2o13b5o26b2o13b2obobo68bo14bo15bobo12bo2bo2bo5bo2bo2bo56bo6bo2b3o2bo$
252bo5b3o6b3o3bo14bo11b2obo18bo68bo14bo16bob3o9bobobobo5bobobobo$234b
5o10b2obob3o32bo13b5o6b3o66bo2b3o2bo6bo2b3o2bo15bobo2bo9bobobobo5bobob
obo$254bo3b2o9b4obo14b2o8b5o79bo14bo28bo9bobobobo5bobobobo$251bobo2bo
32bo27b2o64bo14bo38bo2bo2bo5bo2bo2bo$251bobo2bo17b2o11bobo11b5o77bo14b
o22b9o7bo5bo5bo5bo$38bo214bo33bobo93bo14bo38bo5bo5bo5bo$o2b6o29bobo2bo
87bo251bo2b6o6bo2b6o30bobo3bo5bo3bobo$o37bobo2b3o71bo2bo10bo18b2o2b2o
130b5o146bobobobo5bobobobo90bo$o39bobob2o9b8o35b5o14bo2bo10bo3b7o10b2o
30b2o253bobobo5bobobo92bo$o18bo2bo17bobo2b2o37bo32bo3b2o8b3o4bo10b3o2b
3o13bo270bo9bo61bo7bo6bo13b3obo$o18bo2b3o18b2o12b5o7b2o3b2o8bobo12bobo
15bobo11bobob4o9bo8bo6bo5bo10b3o329bo7bo6bo16b2obo$o2b3o2bo10bobob2o7b
3o20b2o4bo10bo11bobo12bobo29bobo15bobo2bobo7bobo3bo14bo327bo7bo6bo19bo
$8bo10bobo2b2o13bo3b4o8b3ob3o6b9o6bo3bo10bo3bo9b4o3b4o8bobo3bobo373bo
7bo6bo$8bo13b2o9b4o3bo14bo4b2o10bo10b5o10b5o34bobo7bo10bo7bobo9bo2bobo
79b6o8b9o8b9o210bo7bo6bo$8bo36b3o7b5o9b2o3b2o39bobo14b4obobo26bobobo7b
o334bo2b3o2bo6bo15bo$8bo13b4o9b2o45bob3obo9b5o9b2o3bo14bo4b3o9bobo2bob
o11bobo7bo2bo80b2obobo10bo3bobo10bo3bobo219bo6bo15bo$6o2bo24b2o2bobo
14b8o20bo5bo25bo2bo11b7o3bo8bo8bo12bo5bo26bo6b6o2bo29bo16bobo10bobobob
o10bobobobo219bo6bo13b2ob2o$34b2obobo56b3o3b3o9bo2bo21bo9b3o2b3o19bo2b
o23bo14bo29bo14bo16bo16bo144b3o76bo6bo15bo$34b3o2bobo97bo12b2o49bo14bo
13bo10bo4bo4bo9bo16bo16bo223bo6bo$36bo2bobo108b2o2b2o47bo14bo13bo10bob
2o3b2obo9bo6bo9bo6bo9bo6bo140b3o73bo6bo12b7o$41bo161bo14bo13bo10bo9bo
10bo3bobo10bo3bobo10bo3bobo$203bo6bo2b3o2bo13b3o8bobo5bobo7bobo3bo10bo
bo3bo10bobo3bo83b6o2bo6b4o2bo16bo3bo18b3o$203bo6bo23bo8bo9bo7bo6bo9bo
6bo9bo6bo90bo12bo13b2obo3bob2o$203bo6bo23bo8bob2o3b2obo14bo16bo16bo90b
o12bo16bo3bo15bob3o$203bo6bo23bo8bo4bo4bo14bo16bo16bo90bo12bo16bo3bo
10b2o$203bo6bo37bo15bobo14bobo14bobobobo88bo12bo16bo3bo17b4o$203bo6bo
2b6o29bo15bobob2o11bobob2o11bobo3bo80bo2b3o2bo6b4o2bo13b2o7b2o6b4o$
385bo20bo16bo3bo18b2o$263b6o11b6o11b9o79bo20bo16bo3bo10b3obo$385bo20bo
16bo3bo$385bo20bo13b2obo3bob2o6b3o$o2b6o376bo2b6o6b4o2bo16bo3bo$o437b
3o$o65bo10bo5bo407b6o2bo6b4o2bo6bo2b6o$o33bo31bob2o4b2obo5bob2o354b3o
55bo12bo6bo$o46bobo12bobo14bobo417bo12bo6bo$o2b3o2bo13bobo7bobo9b4ob4o
6b4ob3o10b3ob3o415bo12bo6bo$o7bo490bo12bo6bo$o7bo13bo9bo14b3o12b6o8b9o
406bo2b3o2bo6b4o2bo6bo2b3o2bo$o7bo482bo20bo6bo7bo26bobo$o7bo269bo34b9o
34bo134bo20bo6bo7bo28bo$o2b3o2bo228bo3bo34bobo18bo39b3o13b2obo134bo20b
o6bo7bo26bo$205bo6b4o2bo18b5o34bobo18bobo16bo3bo35bo134bo20bo6bo7bo21b
3o2bo$205bo12bo18bo3bo34bobo18bobo13b2obobobo12b3obo12b2obo2bo134bo2b
6o6b4o2bo6bo2b3o2bo25b2o$205bo12bo18b5o32bo5bo12bo5bobo16bobo10b2o23bo
198bo$205bo12bo20bo57bobo14bo3bobo14b3o14bobobo198bo$205bo12bo13b4o7b
4o10bo7bo8bo5bo10b5o3bo18bobo9b6o2bo17bo$205bo6b4o2bo14bobo7bobo11bo7b
o45bo7bo2bo12bo2bo8bo5bo2bo63bo13bo8b6o$205bo12bo14bob2o5b2obo44b3obo
5bob3o6bo10bo8bo6bo8bo2bo5bo63bo13bo$205bo12bo14bobo7bobo65bo2bo7bo8bo
2bo12bo35b6o2bo6bo7bo13bo13bo7b5o$205bo12bo13b4o7b4o11bo5bo9bo5bo14bo
3b5o9bobo15bo2b6o7bobobo39bo6bo7bo13bo13bo11b3o$205bo12bo20bo55bobo15b
obo3bo12b3o12bo43bo6bo7bo13bob3o5b3obo8b2o3bo$205bo6b4o2bo18b5o16bo5bo
9bo5bo12bobo5bo11bobo21b2o8bo2bob2o37bo6bo7bo13bobo9bobo$237bo3bo18bob
o13bobo16bobo15bobobob2o11bob3o10bo43bo6bo7bo13bob3o5b3obo9bobo$237b5o
18bobo13bobo16bobo15bo3bo29bob2o32bo2b3o2bo6bo2b3o2bo13bo13bo9bobobob
3o$103bo15bo8bo108bo3bo18bobo13bobo18bo32b3o14bo35bo22bo13bo13bo$101bo
bo15bo8bo131bo15bo35b9o26bo35bo22bo13bo13bo8b7o$58b7o18bo17bo6bo274bo
22bo13bo13bo$81bobobo11b3obobob2obo274bo22bo$25bo16bo3bo12bo3bo17bobob
o22bo11bobo2bobo255bo2b6o14bo$2b4o2bo16bo16bo3bo12bo3bo17bobo2bo11bob
2o4bo13bobo2bobo$8bo16bo16b2ob2o12b2ob2o18bobobo11bo7bob3o8b2o6b2o$8bo
30b3o5b3o6b3o5b3o17bo36b2o2b2o$8bo12b3o3b3o46b3o16b2obo9bob2o9bo4bo$8b
o31bo7bo8bo7bo13bo41bo4bo$8bo16bo14bo7bo8bo7bo9b4o17b3obo7bo12b2o2b2o$
8bo16bo53b2o19bo4b2obo10b2o6b2o$8bo16bo50b2o20bo21bobo2bobo$8bo69b2o
18bob2obobob3o10bobo2bobo75bo6bo7bo$8bo89bo6bo97bo6bo7bo53b9o12b4o$8bo
94bobo97bo6bo7bo47bo$103bo15bo8bo74bo6bo7bo31bo15bob4o7bo14bobob2o$
119bo8bo74bo6bo7bo31bo15bo5b2o2b2obo14bobo$203bo6bo2b3o2bo30bo6b2o8bo
2b3o7bo14bo$203bo14bo30b4o13bo8b3obo$203bo14bo12bobo32bob3o8bo10bo144b
4o9b9o9b3o$203bo14bo30b4o13bo7b3o2bo10bo2b4o$203bo14bo14bo10b2o6bo13bo
b2o2b2o5bo10bo93b6o2bo6bo2b6o28bobob2o7bobo3bo8b2obo$203bo14bo14bo17bo
14bo7b4obo10bo2b5o94bo6bo36bobo10bobobobo11bo$251bo27bo112bo6bo36bo12b
o3bobo6b3o$265b9o15b5o98bo6bo53bobo$392bo6bo53bo$384bo2b3o2bo6bo2b3o2b
o14bo13bo12bo3bo11bo$384bo14bo7bo14bo13bo12bo3bo11bo$384bo14bo7bo12b2o
b2o9b2ob2o8b2ob2obo9b2ob2o$384bo14bo7bo13bobo11bobo10bobo2bo10bobo$42b
2o340bo14bo7bo13bobo11bobo10bobo2bo10bobo$o2b3o2bo52bo12bo10bo205b5o
88bo2b6o6bo2b3o2bo$o7bo31bob3o16bobo10bobo8bobo332b5o9b5o8b8o8b5o$o7bo
10bo20bo4b2o12bobobobo8bobo8bobo148b7o13b7o25b3o2bo$o7bo10bob4o6bo10b
5o12bobo3bo8bo9bo2bo116bo6bo2b6o71bobo$o7bo10bo4b6obo7b2o5b3o10bob2o2b
o8b2o8bo3bo115bo6bo28bo19bo13bo14bobo$o2b3o2bo10bob6o4bo10bo4b2o10bob
3obo8b3o7bob3o115bo6bo25b2obo11bo4b2obo11bobo14bo3b2o$o7bo10bo6b4obo9b
o5bobo9bobobobo8bobo7bo3bo115bo6bo27b2o11bo6b2o11bobo4bo9bo$o7bo22bo
11bo3bobobo7bobobobo8bobo8bobo116bo6bo19bo42b2o3bo$o7bo36bobobobo7bobo
bobo8bobo8bobo116bo6bo2b3o2bo11bo2bo35b4o3bobo$o7bo35bo16bobo21bo118bo
14bo11bo2bo4b4o10b2o6bo15bo14bo$o2b3o2bo37bob2o11bo11b5o126bo14bo11bo
3bo2b2o13bob2o4bo11b3obo9b2o3bo$46bo157bo14bo11bob3o2bo14bo23bo12bobo
142bo$204bo14bo11bo6bo49bobo95b6o2bo6b4o2bo17b3o5bobo$204bo6b6o2bo11bo
6bo12b7o30bo2b3o100bo12bo25bobo$394bo12bo12b5o7bo$287b4o103bo12bo17b2o
6bo$394bo12bo13b3o7b2o$386bo2b3o2bo12bo16b2o7b3o$386bo20bo15bo6b2o$
386bo20bo16bo7b5o$386bo20bo13bobo$386bo20bo13bobo5b3o$386bo2b6o12bo13b
o3$63b9o23bo161b9o$48b5o40bobo16bo$32bo31b7o11bo10bobo16bo41b6o98bobob
obo$o2b3o2bo10b5o5b2obob2o13bobo12bo5bo9bobo10bobo30b4o10b4o114bo5bo$o
7bo23bo16bobo12bobobobo9bobo8bobobobo9bo2bob2o39b4obo99bobobobo$o7bo
11bobo9bo9bo6bobo14bobo9bobobobo6bo5bo6b2obo15b4obo8b4obo13bobo44bo6bo
2b6o41bobo$o7bo11bobo8bobo8bob3o19bobo9bobobobo6bo5bo11bobo14bobo11bob
o7b4o4bo44bo6bo49bobo20bo33bo$o7bo11bobo8bobo8bo13bo21bo5bo7bo3bo10bo
5bo14bo13bo10bo3bo45bo6bo39bo10bo10bo10bo31bobo103bo11bo$o2b3o2bo33bob
3o5b3obo21bo5bo7bo3bo12bobo15bo13bo11bo3bo45bo6bo20bo7bo10bob3o13b3obo
27bo12bobobo102b2ob9ob2o$8bo33bo13bo21bo5bo6bo5bo15bob2o10bo13bo10bo4b
4o42bo6bo20bo2bo4bo10bo21bo8b7o12bo12bobobo67b6o2bo6bo2b3o2bo$8bo43b3o
bo9bobo9bobobobo6bo5bo9b2obo2bo10b4o11b3o10bobo48bo6bo2b3o2bo12bo7bo
10bobob3o9b3obobo15bo9b4obo13bob2o72bo6bo7bo12bo3b3o5bo9b12o$8bo11bobo
8bobo13bobo6bo9bobo9bobobobo6bobobobo54bob4o45bo6bo7bo12bo4b2obo10bo6b
o7bo6bo7b5o3bob2o6bob4o7b2obo3bo74bo6bo7bo12bo11bo$8bo11bobo8bobo13bob
o14bobobobo9bobo10bobo12bo18b2o7b3o64bo6bo7bo12bo7bo10bobob3o9b3obobo
28bo91bo6bo7bo12bo5bo3bobo7b4o3b2o3b3o$6o2bo11bobo9bo14bobo14bo5bo9bob
o10bobo12bo42b6o46bo6bo7bo12bo2bo4bo10bo21bo11b5o12bo12b7o72bo6bo7bo
12bo9bobo13bo$32bo31b7o9bo12bobo43b2o62bo6bo7bo12bo7bo10bob3o13b3obo
112bo2b3o2bo6bo2b3o2bo12bobobo3bobobo8b2o4b2o4b3o$19b5o5b2obob2o10b5o
44bo107bo6bo2b3o2bo31bo10bo10bo112bo14bo7bo12bobo9bo$32bo30b9o188bobo
122bo14bo7bo12bobo3bo5bo9b13o$260bobo122bo14bo7bo12bo11bo$258bobobobo
120bo14bo7bo12bo5b3o3bo$258bo5bo120bo2b6o6bo2b3o2bo$258bobobobo155b2ob
9ob2o$421bo11bo$257b9o8$256b2o2$233bo10bo13b3o13b3o$205bo6b4o2bo14bobo
6bobo$205bo12bo12bo5bo2bo5bo22bo3b3o$205bo12bo13bob2o6b2obo12bo10bo$
205bo12bo13bo12bo14bo8bo5b3o$205bo12bo39bo10bo$205bo12bo56b4o$205bo12b
o48b4o$205bo12bo13bo12bo9bo20bo$205bo12bo13bob2o6b2obo7bo14b3o5bo$205b
o12bo12bo5bo2bo5bo8bo20bo$205bo12bo14bobo6bobo25b3o3bo$233bo10bo$253b
3o13b3o2$256b2o5$249bo15bo$248b2ob13ob2o2$249bo2bo3bobo6bo10b11o$203bo
6bo2b3o2bo30bo2bo3bobo3b2obo$203bo6bo7bo12b9o9bo3bo2bobo2bo3bo11bo5bob
o$203bo6bo7bo30bo5bobo7bo11bo7bo$203bo6bo7bo13b6o11bo10bo4bo11bobo3bo$
203bo6bo7bo13bo4bo11bob3o7b3obo11bo5bo$203bo6bo2b3o2bo17b3o10bo4bo5bo
4bo11bo2bo2bo$203bo6bo7bo18bobo9bob3o7b3obo11bo2bo2bo$203bo6bo7bo16b2o
2bo9bo4bo10bo11bo5bo$203bo6bo7bo30bo7bobo5bo11bo3bobo$203bo6bo7bo13b9o
8bo3bo2bobo2bo3bo9bo7bo$203bo6bo2b3o2bo30bob2o3bobo3bo2bo9bobo5bo$249b
o6bobo3bo2bo$274b11o$248b2ob13ob2o$249bo15bo7$330bo$310b4o16bo$325b3o$
295bo13b2obo$269bo16b8obo27b5o$203bo6bo2b3o2bo47b3o2bo5bo17bobo10b3o2b
o$203bo6bo7bo19b3o34bobo6b6o5bobo27bobo$203bo6bo7bo48b5o3bobo15bobobo
8b3obo$203bo6bo7bo17b4o10b3o2b3o17bo2bo6bo2bo6bobo$203bo6bo7bo21b2o8bo
2b2o2bo17bo9bo4bobo4bo9b2o$203bo6bo2b3o2bo19bo11b3o2b3o17bobo7bo11bo
15b2o$203bo14bo14bo5bo26bobo16bo4bobo4bo$203bo14bo14bo3bo12b8o10bo16bo
bo6bo2bo13bob3o$203bo14bo12bobobo29bo2bo16bobobo38bobo$203bo14bo12bobo
2bo11b12o6bobo3b5o8bobo5b6o9bo2b3o$203bo6b6o2bo12bo2bo31bobo16bobo40b
5o$234bo31bo5bo2b3o9bob8o12bob2o$274bo12bo40b3o$307b4o14bo$325bo!

Dean Hickerson
dean@math.ucdavis.edu

From: David Bell <dbell@pcug.org.au>
Date: Sun, 23 Jul 2000 19:20:44 +1000 (EST)
Subject: [LifeCA] Just Friends: Some spaceship and wickstretcher reactions

Here is a c/4 convoy which converts a forward glider into a
forward big glider.  (This is probably more complicated than it
needs to be):

x = 282, y = 114
40b3o$39bobboo$40bobbo$40boobo$32boo$32bo9boobo$32bobbo$33b3o5bo$41boo
$34boobo192boo$34bobbo194bo$36bo193bobbo$34boo194boobo$$232boobo$232bo
bbo$231bobboo$232b3o3$205boo$207bo$205bobbo$205boobo$51boo184boo$51bo
155boobo26bo$207bobbo26bobbo$52boobo150bobboo27b3o$207b3o$50boobo182b
oobo$50bobbo$49bobboo181bo$50b3o182boo$$5bo$5b3o4$bboo$4bo$bbobbo$bboo
bo271boo$277bo$b3o$obbo274boobo$o18boo$oo17bo256boobo$19bobbo253bobbo$
20b3o252bobboo$276b3o$18boobo$$17bo$17boo51$166boo$166bo$166bobbo$167b
3o$$165boobo$$164bo$164boo!


Here is a c/4 convoy which converts a forward glider into a
backward big glider:

x = 51, y = 62
39boo$39bo$39bobbo$40b3o$$29boo10boobo$29bo11bobbo$29bobbo10bo$30b3o8b
oo$$31boobo$31bobbo$33bo$31boo$$46boo$46bo$$47boobo$$45boobo$45bobbo$
44bobboo$45b3o6$5bo$5b3o4$bboo$4bo$bbobbo$bboobo36b3o$41bobboo$b3o38bo
bbo$obbo38boobo$o$oo42boobo$$43bo$43boo4$30boo$32bo$30bobbo$30boobo$
37boo$29b3o5bo$28bobbo$28bo9boobo$28boo$36boobo$36bobbo$35bobboo$36b3o
!


Paul's c/7 ships can indeed be turned into wickstretchers.
Here are the ones which I found.  The last one is interesting in that
the wick is an optional addition to the ship, and can be turned "on"
and "off" by glider impacts at the connection point.  That is, a
glider can start the construction of a new wick from the bare ship,
and another glider can disconnect the wick from the ship.

x = 53, y = 88
28bo$13b4o6bo5b5o$21bobob3o6boo$12b4o4bobo5bo$15bo8b3o9b5o$11b3obbobo
3bo3b3o6bobbo$15bo8b3o9b5o$12b4o4bobo5bo$21bobob3o6boo$13b4o6bo5b5o$
28bo8$5boo$18bo3bo8b4o$6bob4o6bo4bo11b5o$12b5oboboboo5bo3bo6boo$10bo6b
3o3boo4bobobo$10bo4boo5boo4bobo3bo6b5obo$9bo5bo9boobbobo3b3obbobb3o$
10bo4boo5boo4bobo3bo6b5obo$10bo6b3o3boo4bobobo$12b5oboboboo5bo3bo6boo$
8b4o6bo4bo11b5o$8bo9bo3bo8b4o9$4bo$5boo16bo14bo$bboo3b7o7bobob3o6bo4b
5o$4bobo8boo17b5o5boo$4boo4boboo6bo3boo17bobbo$3boo5bo4boo13bobobboo3b
o3boo4bo$3bobobb3obbo4bob5obo14bo4bo4boo$3boo5bo4boo13bobobboo3bo3boo
4bo$4boo4boboo6bo3boo17bobbo$oo4bo8boo17b5o5boo$7b7o7bobob3o6bo4b5o$4b
3o16bo14bo8$3boo$5boo16bo14bo$bboo3b7o7boboboo6bo5b5o$5bo8boo5bobo4boo
5b3o6boo$11bobo3b4ob3oboboo20bo$4bo4bo5boobo13bo3b5o3boo$3bo9boo5b4obo
bo3boobo3bo5bo6boo$4bo4bo5boobo13bo3b5o3boo$11bobo3b4ob3oboboo20bo$oo
3bo8boo5bobo4boo5b3o6boo$7b7o7boboboo6bo5b5o$4b3o16bo14bo9$3boobbo11bo
3boo7b4o$7bob4o6bo11bo4b5o$13b5o3boo7bo3bo6boo$11bo9bo10bobo12bo$5bo5b
o4bo6bo4boo4boo5boo$5bo4bobo5bo3bo3boo4bobobboobbo6boo$5bo5bo4bo6bo4b
oo4boo5boo$11bo9bo10bobo12bo$13b5o3boo7bo3bo6boo$7bob4o6bo11bo4b5o$7bo
11bo3boo7b4o!


Since c/7 ships travel slower than the c/6 gliders, it should be
possible to create rakes from them by impacting forward gliders into
them to create mew forward gliders.  Unfortunately, I haven't found
such a straightforward reaction.  But I have found some reactions
which might be of use in a more complicated manner.


Here is a forward glider being converted into a backward glider and a
domino by a c/7 ship:

x = 48, y = 17
bbo$oo5$6bo12b4o8b4o$7b5o6bobo14b5o$12b5obob3o6bobobo6boo$8bobo6bo5bo
5bo3bo$10bob3o10bo4bo10boo3boo$3bobo5b3obo7bo5bo5b3o5bobobo$10bob3o10b
o4bo10boo3boo$8bobo6bo5bo5bo3bo$12b5obob3o6bobobo6boo$7b5o6bobo14b5o$
6bo12b4o8b4o!


Here is a forward glider being converted into a domino by a c/7 ship:

x = 45, y = 17
25bo$23boo5$3bo12b4o8b4o$4b5o6bobo14b5o$9b5obob3o6bobobo6boo$5bobo6bo
5bo5bo3bo$7bob3o10bo4bo10boo3boo$obo5b3obo7bo5bo5b3o5bobobo$7bob3o10bo
4bo10boo3boo$5bobo6bo5bo5bo3bo$9b5obob3o6bobobo6boo$4b5o6bobo14b5o$3bo
12b4o8b4o!


Big gliders can perform more impressive reactions using the c/7 ships.
Here are three ways that a big glider can be converted into two forward
gliders and two dominos:

x = 46, y = 100
4bo$bbobo$6bo$4b3o4$17bo$7bo5bo4b5o$5boobo4b5o5boo$8bo13bobbo$9bobobb
oo3bo3boo4bo$20bo4bo4boo$9bobobboo3bo3boo4bo$8bo13bobbo$5boobo4b5o5boo
$7bo5bo4b5o$17bo22$3bo$bobo$5bo$3b3o4$17bo$6bo5bo5b5o$4bobobo3bob3o6b
oo$7bo9boo$11bo4bobo5boo3boo$10booboobbobo6bobobo$11bo4bobo5boo3boo$7b
o9boo$4bobobo3bob3o6boo$6bo5bo5b5o$17bo22$bbo$obo$4bo$bb3o8$5bo9bo3boo
8b3o$5boboo6bo16b5o$9b7obobo8boobo6boo$8bo10bo11bo4bobbo$6bobo4bo3bo3b
oboo3bo3bobb3obbobbo$7bo3bobbobo3boo7bobobbobobbobbobbo$6bobo4bo3bo3bo
boo3bo3bobb3obbobbo$8bo10bo11bo4bobbo$9b7obobo8boobo6boo$5boboo6bo16b
5o$5bo9bo3boo8b3o!


Here are three ways that a big glider can be converted into a forward
and backward glider (and two dominos):

x = 51, y = 80
bbo$obo$4bo$bb3o6$7bo11b4o8b4o$9b3o6bobo14b5o$12b5obob3o6bobobo6boo$
10bo6bo5bo5bo3bo$10bob3o10bo4bo10boo3boo$11b3obo7bo5bo5b3o5bobobo$10bo
b3o10bo4bo10boo3boo$10bo6bo5bo5bo3bo$12b5obob3o6bobobo6boo$9b3o6bobo
14b5o$7bo11b4o8b4o11$bbo$obo$4bo$bb3o6$8bo9bo3boo8b3o$8boboo6bo16b5o$
12b7obobo8boobo6boo$11bo10bo11bo4bobbo$9bobo4bo3bo3boboo3bo3bobb3obbo
bbo$10bo3bobbobo3boo7bobobbobobbobbobbo$9bobo4bo3bo3boboo3bo3bobb3obbo
bbo$11bo10bo11bo4bobbo$12b7obobo8boobo6boo$8boboo6bo16b5o$8bo9bo3boo8b
3o11$5bo$3bobo$7bo$5b3o6$11bo9bo3boo8b3o$11boboo24b5o$12bo3b4obo3bo8b
oobo6boo$14bo8bobobbo4bo3bo$12bobo3b8oboboo3boobb3o5b5o$11bo3bo4b3obo
6bobob3obbo4bobbo$12bobo3b8oboboo3boobb3o5b5o$14bo8bobobbo4bo3bo$12bo
3b4obo3bo8boobo6boo$11boboo24b5o$11bo9bo3boo8b3o!


A second c/7 spaceship can be used to slightly perturb these reactions.
Here is a forward big glider converted into a forward glider and two
straight triominos (which is useful because a triomino can convert a
glider into a big glider):

x = 65, y = 33
19bo$17bobo$21bo$19b3o6$25bo9bo3boo8b3o$25boboo24b5o$26bo3b4obo3bo8boo
bo6boo$28bo8bobobbo4bo3bo$26bobo3b8oboboo3boobb3o5b5o$25bo3bo4b3obo6bo
bob3obbo4bobbo$26bobo3b8oboboo3boobb3o5b5o$28bo8bobobbo4bo3bo$26bo3b4o
bo3bo8boobo6boo$25boboo24b5o$25bo9bo3boo8b3o3$13bo$bbo5bo5b5o$3ob3obob
3o6boo$5bobo5bo$7bobo4bo5boo3bo$13bo6bo5bo$7bobo4bo5boo3bo$5bobo5bo$3o
b3obob3o6boo$bbo5bo5b5o$13bo!


Here is a forward big glider converted into a forward glider, two
backward gliders, and two straight triominos:

x = 66, y = 31
20bo$18bobo$22bo$20b3o6$26bo9bo3boo8b3o$26boboo24b5o$27bo3b4obo3bo8boo
bo6boo$29bo8bobobbo4bo3bo$27bobo3b8oboboo3boobb3o5b5o$26bo3bo4b3obo6bo
bob3obbo4bobbo$27bobo3b8oboboo3boobb3o5b5o$29bo8bobobbo4bo3bo$27bo3b4o
bo3bo8boobo6boo$26boboo24b5o$26bo9bo3boo8b3o$12bo$bboo4bo5b4o$oobo4bob
3o6boo$3bobobo5bo3bobbo$3b3o3boo3b5obbobbo$3boob3obbobobobobbobbobbo$
3b3o3boo3b5obbobbo$3bobobo5bo3bobbo$oobo4bob3o6boo$bboo4bo5b4o$12bo!


The T-pentomino explosion created in the above reactions can be
perturbed by a domino to create big gliders and a little junk.
Here are three such reactions:

x = 9, y = 86
6bo$4bobo$6b3o$4bobo$6bo4$oo30$4bo$bbobo$4b3o$bbobo$4bo6$4boo26$4bo$bb
obo$4b3o$bbobo$4bo6$5bo$5bo!


Here are two reactions which convert a backward big glider into dominos:

x = 56, y = 71
22bo$22bobo$20bo$20b3o7$7b3o16bo14bo$11b7o8bob3o6bo5b4o$3boo4bo8boo3b
4o10bob3o6boo$5bo3bo3boboo3bo6boo5bobo5bo3bobbo$9bo8b3o8bo4bo3boo3b5o
bbobbo$8bobbo10b7o3boob3obbobobobobbobbobbo$9bo8b3o8bo4bo3boo3b5obbobb
o$5bo3bo3boboo3bo6boo5bobo5bo3bobbo$3boo4bo8boo3b4o10bob3o6boo$11b7o8b
ob3o6bo5b4o$7b3o16bo14bo30$18bo$18bobo$16bo$16b3o7$4b3o16bo14bo$8b7o8b
ob3o6bo5b4o$oo4bo8boo3b4o10bob3o6boo$bbo3bo3boboo3bo6boo5bobo5bo3bobbo
$6bo8b3o8bo4bo3boo3b5obbobbo$5bobbo10b7o3boob3obbobobobobbobbobbo$6bo
8b3o8bo4bo3boo3b5obbobbo$bbo3bo3boboo3bo6boo5bobo5bo3bobbo$oo4bo8boo3b
4o10bob3o6boo$8b7o8bob3o6bo5b4o$4b3o16bo14bo!


Here is a forward big glider being converted into a forward glider:

x = 45, y = 20
7bo$5bobo$9bo$7b3o6$bbo11bo3boo7b4o$bbob4o6bo11bo4b5o$8b5o3boo7bo3bo6b
oo$6bo9bo10bobo12bo$o5bo4bo6bo4boo4boo5boo$o4bobo5bo3bo3boo4bobobboobb
o6boo$o5bo4bo6bo4boo4boo5boo$6bo9bo10bobo12bo$8b5o3boo7bo3bo6boo$bbob
4o6bo11bo4b5o$bbo11bo3boo7b4o!


I have a feeling that these reactions are sufficient to create c/7
rakes,  but the complexity of the interactions eludes me.  The simple
methods I tried failed.  Maybe someone with more grasp of the
interactions could do better.

PS: Another c/7 ship with a new back end would be nice to find.
It might happen to make the construction of a rake very easy.

BCNU,
-dbell-


From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Wed, 26 Jul 2000 10:49:18 -0700
Subject: [LifeCA] Re: Just friends:  More wickstretcher reactions

I wrote:

> ... one of Jason Summers's c/5 wickstretchers

Jason replied:

> Paul Tooke's, not mine.

Oops, sorry about that.

Here are some more c/3 reactions.  First, I mentioned that a pair of lines
with distance 4 could be converted to a pair with distance 2.  The reverse
can also be done:

x = 45, y = 7
31bo$15o18b9o$15b12o4bo10b2o$28bob3o8bo2bo$15b12o4bo10b2o$15o18b9o$31b
o!

One of Paul's ships can be modified to convert 2 lines with distance 4
to 3 lines with distance 2:

x = 20, y = 6
8b9o$b7obo7b2o$16bo2bo$7obo8b2o$10b7o$b9o!

At 2c/6 we can add any even number of lines, 2 apart, between existing
lines:

x = 24, y = 23
16bo$18b3o$12o4bo4b2o$13bob3o2bo2bo$b11o4bo4b2o$18b3o$6o10bo$6bo$b6o2$
4o$4bo$b4o2$6o$6bo$b6o2$12o$12b2o$11bo2bo$12b2o$b11o!

We can modify that to leave out some of the lines:

x = 24, y = 23
16bo$18b3o$12o4bo4b2o$13bob3o2bo2bo$b11o4bo4b2o$18b3o$5bo10bo$6bo$b6o
2$3bo$4bo$b4o2$6o$6bo$4b3o2$12o$12b2o$11bo2bo$12b2o$b11o!

I haven't figured out exactly which combinations of lines can be produced
using these reactions.

Here are three c/5 reactions, which shift (by 3 or 4 units) or duplicate
lines:

x = 77, y = 35
8bo$10b67o3$9o9$76o2$7bobob66o4$9o9$77o2$b7o$8bo$8o3b65o2$b76o!

And three c/9 reactions, which delete 3, 4, or 5 lines:

x = 76, y = 43
76o2$7b68o$4b3o$4bo3b68o$4b3o$7b68o2$76o6$75o2$7b69o$4b3o$4bo3b67o$4b
3o$7b69o$2bo$2bob71o2$76o6$76o2$2bob71o$2bo$7b69o$4b3o$4bo3b67o$4b3o$
7b69o$2bo$2bob71o2$76o!

It would be nice to have c/3 versions of these.  Paul, could your version
of gfind look for such reactions?

Dean Hickerson
dean@math.ucdavis.edu


From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Wed, 26 Jul 2000 10:52:26 -0700
Subject: [LifeCA] Just friends: c/7

David Bell said:

> Paul's c/7 ships can indeed be turned into wickstretchers.
> Here are the ones which I found.

It's also possible to add 2 lines to 2 existing lines, at 3c/21:

x = 68, y = 12
21o$21b2o16bo14bo$b5o4bob8o3b7o7bobob2o6bo5b5o$6b2o2bo10bo8b2o3bobobo
5bo3bob3o6b2o$6o15bo5bo12bobobo3b3o4bo$20b3o2bob2o2b2obo6bobo4bo3b2o7b
5obo$b8o14b2o2bo4bo2b5obobo6b2o4bo3bo2b3o$20b3o2bob2o2b2obo6bobo4bo3b
2o7b5obo$17bo3bo5bo12bobobo3b3o4bo$21bo8b2o3bobobo5bo3bob3o6b2o$16bo6b
7o7bobob2o6bo5b5o$20b3o16bo14bo!

Dean Hickerson
dean@math.ucdavis.edu

From: "Paul Tooke" <paultooke@hotmail.com>
Date: Thu, 27 Jul 2000 09:22:13 -0000
Subject: [LifeCA] Re: Just friends:  More wickstretcher reactions

--- In LifeCA@egroups.com, Dean Hickerson <dean@m...> wrote:
> I wrote:
> 
> > ... one of Jason Summers's c/5 wickstretchers
> 
> Jason replied:
> 
> > Paul Tooke's, not mine.
> 
> Oops, sorry about that.

No problem.

[wick reactions...]
> 
> It would be nice to have c/3 versions of these.  Paul, could your 
version
> of gfind look for such reactions?
> 
Yes. Two simple modifications allow the wick pattern at the front and 
rear of the 'spaceship' to be individually specified.  A third 
enables the program to search for wickstretchers without specifying 
the wick pattern to be produced.  Combining these, the program can 
search for wickstretchers, wick modifying reactions (including those 
that burn the wick cleanly), and signals that travel along a wick.

At c/3, the program finds these so quickly that I stopped saving 
them.  It appears that just about every combination is possible. It's 
quicker to find a desired reaction by re-running the program with the 
appropriate parameters.

Here is a set of c/3 examples that combine wickstretchers, wick 
modifying reactions, clean burning reactions, and one signal. (This 
is a representative sample, my apologies if any of these have been 
posted to this group before).

x = 131, y = 70
120bo3bo3bo$105bo3bo3bo4bobobobobobobo$obo11bobo15bobo14bobo5bobo13bob
o11bobo13bobobobobobo4bobobobobobobo$obo11bobo15bobo14bobo5bobo13bobo
11bobo13bobobobobobo4bobobobobobobo$bo13bo15bo3bo14bo7bo15bo13bo14bobo
bobobobo4bobobobobobobo$31bo3bo18bo48bobobobobobo4bobobobobobobo$bb3o
11b3o12bo3bo15boo3boo14bobobo12boobo10bobobobobobo4bobobobobobobo$3obo
9b3obo13bo17bobooboobo29bobobo10bobobobobobo4bobobobobobobo$bbo13bo16b
oobo13bobo3bobo12bobobobo10bo4bo9bobobobobobo4bobobobobobobo$3bobo11bo
bo12bo3bo15b5o14bo5bo10bo4bo9bobobobobobo4bobobobobobobo$3bo13bobo12bo
bobo12bobo5bobo11b3ob3o9bo5bo9bobobobobobo4bobobobobobobo$3bo13bobo12b
obobo12bobo5bobo11bobbobbo9bobo3bo9bobobobobobo4bobobobobobobo$3bo13bo
bo12bobobo12bobo5bobo11booboboo9bobo3bo9bobobobobobo4bobobobobobobo$3b
o13bobo12bobobo12bobo5bobo10bo3bo3bo8bobo3bo9bobobobobobo4bobobobobobo
bo$3bo13bobo12bobobo12bobo5bobo10bobobobobo8bobo3bo9bobobobobobo4bobob
obobobobo$3bo13bobo12bobobo13bo7bo11bobobobobo8bobo3bo9bobobobobobo4bo
bobobobobobo$3bo13bobo12bobobo17bo15bobobobobo8bobo3bo9bobobobobobo4bo
bobobobobobo$3bo13bobo12bobobo14boo3boo12bobobobobo8bobo3bo9bobobobobo
bo4bobobobobobobo$3bo13bobo12bobobo13bobooboobo11bobobobobo8bobo3bo9bo
bobobobobo4bobobobobobobo$3bo13bobo12bobobo13bobo3bobo11bobobobobo8bob
o3bo9bobobobobobo4bobobobobobobo$3bo13bobo12bobobo15b5o13bobobobobo8bo
bo3bo9bobobobobobo4bobobobobobobo$3bobobo9bobo12bobobo12bobo5bobo9bobo
bbobbobo7bobob3o9bobobobobobo4bobobobobobobo$3bobobo10bo9bobobobobobob
o8bobo5bobo9bo9bo7bo5bo9bobobobobobo4bobobobobobobo$3bobbo21bo5bo5bo8b
obo5bobo9bobbooboobbo7bo5bo9bobobobobobo4bobobobobobobo$3bo15boobo11bo
14bobo5bobo9bobob3obobo13bo9bobobobobobo4bobobobobobobo$3boobboo9bobob
o6bo9bo9bobo5bobo9boboo3boobo9bo13bobobobobobo4bobobobobobobo$4boboo
10bo4bo6bobbobobbo10bobo5bobo9bo9bo10boo11bobobobobobo4bobobobobobobo$
7b3o8bo4bo6b9o10bobo5bobo10bo7bo9bo14bobobobobobo4bobobobobobobo$17bo
4boo25bobo5bobo11boo3boo10bobobo10bobobobobobo4bobobobobobobo$17bobobb
o26bobo5bobo27bobobbo10bobob3obobo4bobobobobobobo$17bo3bo27bobo5bobo
27bo4bo10bo3boo4bo4bobobobobobobo$17bobobo27bobo5bobo27bo3bobo9bob3o5b
o4bobobbobobbobo$17bobobo27bobo5bobo27bo3bobo9bo4bo4bo4bobo7bobo$17bob
3o28bo7bo28bo3bobo9bo3bo5bo4boboo5boobo$19boo33bo32bo3bobo9boboo6bo4bo
4b3o4bo$22bo28boo3boo29bo3bobo9bo9bo4bo11bo$18bo31bobooboobo28bo3bobo
9bo9bo4bo11bo$19bo3bo26bobo3bobo28bo3bobo$52b5o30bo3bobo$49bobo5bobo
27bo3bobo$51bobobobo29bo3bobo$51bobobobo29bo3bobo$51bobobobo29bo3bobo$
51bobobobo29bo3bobo$51bobobobo29bo3bobo$51bobobobo29bo3bobo$51bobobobo
29bo3bobo$51bobobobo29bo3bobo$51bobobobo29bo3bobo$51bobobobo33bobo$51b
obobobo31bobobo$51bobobobo32bobbo$51bobobobo30bo4bo$51bobob3o30bobb3o$
51b3obbobbo28bobobo$49bobbo3bobobo27boboo$48bobobo3bobobo29bo$48bobobo
3bobbobo25boboo$47bobobbo3bo30bo3bo$52bobbobo29bobobo$51bobobobbo28bob
obo$50bobbobobobo27bobbo$49bobobobobobo27bo$49bobobobo31boobboo$53bobo
32boboo$53bo6bo30b3o$48bo7bobbo$49bobbo3boobboo$47boobboo3boo$51boo!

--
Paul Tooke
paultooke@hotmail.com


From: "Paul Tooke" <paultooke@hotmail.com>
Date: Thu, 27 Jul 2000 09:52:24 -0000
Subject: [LifeCA] Re: Just Friends: Some spaceship and wickstretcher reactions

--- In LifeCA@egroups.com, David Bell <dbell@p...> wrote:

[...]

> PS: Another c/7 ship with a new back end would be nice to find.
> It might happen to make the construction of a rake very easy.
> 
Moving to a slightly faster machine, (all of my searches so far in 
this rule have been short runs on a Toshiba Libretto :) yields the 
following critter:

x = 13, y = 27
5bobo$$5b3o$5b3o$5b3o$5bobo$3bobobobo$3bobbobbo$bbo7bo$bbo7bo$bbo7bo$
bbo7bo$4bobobo$bobobobobobo$bo9bo$bo9bo$bobbo3bobbo$bo4bo4bo$bo3bobo3b
o$o4bobo4bo$o4b3o4bo$o11bo$3o7b3o$bobobbobbobo$5bobo$6bo$5bobo!

There may be more to follow, but the search is slowly getting bogged 
down so I don't expect anything Real Soon Now.

--
Paul Tooke
paultooke@hotmail.com



From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Thu, 27 Jul 2000 17:00:26 -0700
Subject: [LifeCA] Re: Just friends:  More wickstretcher reactions

Mostly to Paul Tooke

> Here is a set of c/3 examples that combine wickstretchers, wick 
> modifying reactions, clean burning reactions, and one signal.

Thanks.  Putting two of your reactions together allows us to add a
single line near an existing set of lines, even if the distance is
only 2:

x = 59, y = 13
5bo8b3o$7bo5b2o2b2o$9b4o$8b2o7b2o$5bo2b4obo4bo2b3o6b2o$6bo8b3o2bo3b3o
2bo$9b6o6b2o4bo2b2o$26b2o2$26b2o$b25o2$59o!

So we can build any pattern of lines (as long as no 2 are adjacent).
Can you find a simpler way to do this?

We can also use your reactions to remove the surrounding lines from the
6c/18 tromino puffer that David Bell found:

x = 37, y = 21
13bo$15bo$17b3o$16b2o2bo10bo3b2o$13bo2b4o11bo2bo$14bo15b3o2b2o$17b13o
2bo$31b2o$27b3o$21bo3bobo$3o3b3o3b3o6bob2o$21bo3bobo$27b3o$31b2o$17b
13o2bo$14bo15b3o2b2o$13bo2b4o11bo2bo$16b2o2bo10bo3b2o$17b3o$15bo$13bo!

It would be nice to see a wickstretcher that makes something other than
lines.  Maybe your program could find a 2c/6 wickstretcher that makes this:

    ooooooooooooo
    .............
    .o.o.o.o.o.o.
    .o.o.o.o.o.o.
    .............
    ooooooooooooo

Or the same with longer vertical pieces.

Dean Hickerson
dean@math.ucdavis.edu

From: "Paul Tooke" <paultooke@hotmail.com>
Date: Fri, 28 Jul 2000 09:59:48 -0000
Subject: [LifeCA] Re: Just Friends: Some spaceship and wickstretcher reactions

Another c/7 ship:

x = 16, y = 15
bbobo6bobo$$bb3o6b3o$bb3o6b3o$ob3obobbob3obo$obobobobbobobobo$o5bobbo
5bo$obobobobbobobobo$bo4bobbo4bo$6bobbo$bbo3bobbo3bo$5bo4bo$oo12boo$bo
12bo$bo12bo!

--
Paul Tooke
paultooke@hotmail.com


From: "Paul Tooke" <paultooke@hotmail.com>
Date: Fri, 28 Jul 2000 14:18:54 -0000
Subject: [LifeCA] Re: Just friends:  More wickstretcher reactions

Mostly to Dean Hickerson

[single line wickstretcher]

> So we can build any pattern of lines (as long as no 2 are adjacent).
> Can you find a simpler way to do this?
> 
A smaller example found by direct search:

x = 41, y = 9
16b3o$19b3o$15bo6boo$13bo5bo$22boo$19b3o$b18o$$41o!

[..]

> It would be nice to see a wickstretcher that makes something other 
than
> lines.  Maybe your program could find a 2c/6 wickstretcher that 
makes this:
> 
>     ooooooooooooo
>     .............
>     .o.o.o.o.o.o.
>     .o.o.o.o.o.o.
>     .............
>     ooooooooooooo
> 
Not at present, but it could be modified to look for such a thing. I 
will try it out over the weekend.

--
Paul Tooke
paultooke@hotmail.com


From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Sat, 29 Jul 2000 15:12:45 -0700
Subject: [LifeCA] Just friends: Pseudo puffers and new oscillators

Here are 4 pseudo-puffers; each produces a line and various dominoes
and trominoes.  Each starts with David Bell's 6c/18 tromino puffer.
Then a c/4 wickstretcher, based on one of Paul Tooke's spaceships, adds
2 lines.  Finally, a 12c/48 component, assisted in some cases by another
c/4 spaceship, changes that into other stuff.  I haven't found any
variants that release gliders.

x = 66, y = 130
36b2o$27bo9bo4bo$24bobobob2o12bo$26bobo2bobob2o9b3o$30bo14b2o2bo10bo3b
2o$3b26obobob2o6bo2b4o11bo2bo$29b2obo2bo7bo15b3o2b2o$24bo4bo2b2o2bo9b
13o2bo$22bo3b3o4b3o24b2o$6b2o10b2o4bo31b3o$49bo2b3obo$5b2o10b2o9b3o3b
3o3b3o6bobobo$49bo2b3obo$56b3o$60b2o$46b13o2bo$43bo15b3o2b2o$42bo2b4o
11bo2bo$45b2o2bo10bo3b2o$46b3o$44bo$42bo9$36b2o$27bo9bo4bo$24bobobob2o
12bo$26bobo2bobob2o9b3o$30bo14b2o2bo10bo3b2o$3b26obobob2o6bo2b4o11bo2b
o$29b2obo2bo7bo15b3o2b2o$4b2o10b2o6bo4bo2b2o2bo9b13o2bo$22bo3b3o4b3o
24b2o$6b2o10b2o4bo31b3o$49bo2b3obo$4b3o9b3o9b3o3b3o3b3o6bobobo$49bo2b
3obo$56b3o$60b2o$46b13o2bo$22b3o5b2o11bo15b3o2b2o$31bo10bo2b4o11bo2bo$
28bo2bo13b2o2bo10bo3b2o$19bob4obob3o15b3o$26bo17bo$21bobo5bob2o9bo$25b
2o2bo2bo$20bo9bo$31b2o14$36b2o$27bo9bo4bo$24bobobob2o12bo$26bobo2bobob
2o9b3o$30bo14b2o2bo10bo3b2o$29obobob2o6bo2b4o11bo2bo$29b2obo2bo7bo15b
3o2b2o$24bo4bo2b2o2bo9b13o2bo$22bo3b3o4b3o24b2o$6b2o10b2o4bo31b3o$2o
10b2o35bo2b3obo$bo3b2o6bo3b2o9b3o3b3o3b3o6bobobo$49bo2b3obo$56b3o$60b
2o$46b13o2bo$22b3o18bo15b3o2b2o$21b2o2bo16bo2b4o11bo2bo$21bo2bo20b2o2b
o10bo3b2o$21bob2o21b3o$44bo$23bob2o15bo$23bo2bo$24bo$25b2o13$36b2o$27b
o9bo4bo$24bobobob2o12bo$26bobo2bobob2o9b3o$30bo14b2o2bo10bo3b2o$29obob
ob2o6bo2b4o11bo2bo$29b2obo2bo7bo15b3o2b2o$24bo4bo2b2o2bo9b13o2bo$22bo
3b3o4b3o24b2o$6b2o10b2o4bo31b3o$2o10b2o35bo2b3obo$5b2o10b2o9b3o3b3o3b
3o6bobobo$49bo2b3obo$56b3o$60b2o$46b13o2bo$24b2o17bo15b3o2b2o$23bo18bo
2b4o11bo2bo$22bo2bo19b2o2bo10bo3b2o$22bob2o20b3o$44bo$24b3o15bo$24bo2b
o$27bo$26b2o!

Paul:  Can your program find a c/4 component to delete the remaining line?


Here are some new oscillators, with periods 35, 37, 43, 46, and 76.  (The
first p37 isn't new; it's included for comparison with the other two.)

x = 89, y = 111
b4o2bo6bo2b6o13b17o$7bo6bo$7bo6bo22bo6b3o2bobo$7bo6bo22bo11bobo$7bo6bo
22bobobo3bo3bobo$b4o2bo6bo2b3o2bo22bo$7bo14bo16bobo3bo3bobobo$7bo14bo
16bobo11bo$7bo14bo16bobo2b3o6bo$7bo14bo$b4o2bo6b6o2bo15b17o7$73bo$73bo
b12o$59b7o7bo$42b7o24bobob2o4bo$62bo10bobo5bo3bo$3b4o2bo6b4o2bo16bo5bo
10bo3bo3bo8bo3bo$9bo12bo16bo3bo3bo8bo16bo3bo5bo$9bo12bo16bo16bo5bo$9bo
12bo22bo42bo$9bo12bo65bo$3b4o2bo12bo55bo5bo3bo$9bo12bo17bo16bo5bo20bo
3bo$9bo12bo23bo16bo12bo3bo5bobo$9bo12bo15bo3bo3bo8bo3bo3bo14bo4b2obobo
$9bo12bo17bo5bo10bo30bo$3b4o2bo12bo52b12obo$37b7o10b7o27bo14$44bo$44bo
bo$44bobo$2bo7bo6b4o2bo14bo5bo3bo$2bo7bo12bo14bob2o6bo$2bo7bo12bo14bob
o7bo$2bo7bo12bo14bobo7bo$2bo7bo12bo14bobo7bo$2bo2b3o2bo6b4o2bo12bo2bo
5bo2bo$10bo12bo12bo7bobo$10bo12bo12bo7bobo$10bo12bo12bo7bobo$10bo12bo
12bo6b2obo$10bo6b4o2bo12bo3bo5bo$38bobo$38bobo$40bo8$44b5o$o7bo6bo2b6o
$o7bo6bo$o7bo6bo$o7bo6bo22bo$o7bo6bo22bobo3bobo$o2b3o2bo6bo2b3o2bo14bo
bo3bobo$8bo6bo7bo14bobo3bobo$8bo6bo7bo22bo$8bo6bo7bo$8bo6bo7bo$8bo6bo
2b3o2bo$36b5o13$37bo11bo$36b2ob9ob2o$2b4o2bo6bo2b6o$8bo6bo21bo11bo$8bo
6bo21bo4bobo4bo$8bo6bo21bo4bobo4bo$8bo6bo21bo11bo$8bo6bo2b3o2bo13bo2b
7o2bo$8bo6bo7bo13bo11bo$8bo6bo7bo13bo4bobo4bo$8bo6bo7bo13bo4bobo4bo$8b
o6bo7bo13bo11bo$8bo6bo2b3o2bo$36b2ob9ob2o$37bo11bo!

Dean Hickerson
dean@math.ucdavis.edu

From: David Bell <dbell@pcug.org.au>
Date: Sun, 30 Jul 2000 12:09:40 +1000 (EST)
Subject: [LifeCA] Just Friends: 5-speed growing spaceship

I don't know how to to terminate the line from Dean's new pseudo-puffers
at speed c/4, but a previous reaction can do it at c/5.  I also found
glider reactions for the domino-pair pseudo-puffer which consume the
dominos.  This shows both reactions in a 5-speed growing spaceship
(c/3, c/4, c/5, 6c/35, and 6c/47):

x = 92, y = 60
68bo$68bobo$69bo3boo$74bo10bobb3o$67boo4boo12boobbo$67b3o18b3o$71b13o$
85boo$81boboo$6bo46bobo18bobobbobo$6bo23boo10boo9bo5b3o3b3o6bobo4boo$
7b3o42bobbo18bobobbobo$7bo23boo10boo3bo4bo27boboo$bb3o9boo37boboo4b3o
21boo$48bobobbo3bobboobbo6b13o$35bo21boobobbo3b3o18b3o$35bob20oboboboo
3boo4boo12boobbo$35boo21bo15bo10bobb3o$35bo18bobobboboboo4bo3boo$36b7o
5boobboboboboo8bobo$35bo11bo7bo9bobbo$35boo6bobbobbo14boo$35bob6obobob
oo$32bobbo8bo$32bo7bobobboboboo$31boo5b3ob3obbobbo$47boobbo$48b3o$25bo
$26bo$26bo$$48b3o$47boobbo$38b3ob3obbobbo$20bo19bobobboboboo$18bobo14b
o8bo$35bob6oboboboo$35boo6bobbobbo14boo$12bo22bo11bo7bo9bobbo$12bo23b
7o5boobboboboboo8bobo$o10bo23bo18bobobboboboo4bo3boo$bo33boo21bo15bo
10bobb3o$bo33bob20oboboboo3boo4boo12boobbo$35bo21boobobbo3b3o18b3o$48b
obobbo3bobboobbo6b13o$53boboo4b3o21boo$19boo10boo10boo3bo4bo27boboo$
52bobbo18bobobbobo$18boo10boo10boo9bo5b3o3b3o6bobo4boo$53bobo18bobobbo
bo$81boboo$85boo$71b13o$67b3o18b3o$67boo4boo12boobbo$74bo10bobb3o$69bo
3boo$68bobo$68bo!

BCNU,
-dbell-



From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Sun, 30 Jul 2000 03:35:59 -0700
Subject: [LifeCA] Re: Just Friends: 5-speed growing spaceship

Very pretty, David!

Here's a 3-speed growing puffer that creates a glider and a domino
every 240 gens; the speeds are c/3, c/4, and 6c/120:

x = 54, y = 22
24b2o$15bo9bo4bo$12bobobob2o12bo$bo12bobo2bobob2o9b3o$4o14bo14b2o2bo
10bo3b2o$bo2bo3b9obobob2o6bo2b4o11bo2bo$4o13b2obo2bo7bo15b3o2b2o$bo10b
o4bo2b2o2bo9b13o2bo$10bo3b3o4b3o24b2o$12bo31b3o$37bo2b3obo$16b3o3b3o3b
3o6bobobo$37bo2b3obo$44b3o$48b2o$34b13o2bo$31bo15b3o2b2o$30bo2b4o11bo
2bo$33b2o2bo10bo3b2o$34b3o$32bo$30bo!

And a 2-speed growing wickstretcher, with speeds c/3 and 6c/32, making
2 lines and a row of straight tetrominoes:

x = 55, y = 18
49bo3b2o$49bo2bo$48b3o2b2o$13b35o2bo$49b2o$45b3o$b4o33bo2b3obo$7bob5o
3b3o3b3o3b3o6bobobo$6obo30bo2b3obo$45b3o$b22o26b2o$23b3o9b13o2bo$26b2o
4bo15b3o2b2o$17bo5bo7bo2b4o11bo2bo$19bo6b2o6b2o2bo10bo3b2o$23b3o9b3o$
20b3o10bo$31bo!

Dean Hickerson
dean@math.ucdavis.edu

From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Sun, 30 Jul 2000 03:53:07 -0700
Subject: [LifeCA] Re: Just Friends: 5-speed growing spaceship

I said:

> Here's a 3-speed growing puffer that creates a glider and a domino
> every 240 gens; the speeds are c/3, c/4, and 6c/120:

Make that 12c/240.                             ^^^^^^^

Also the c/4 is partly 12c/48.

Dean Hickerson
dean@math.ucdavis.edu

From: "Paul Tooke" <paultooke@hotmail.com>
Date: Mon, 31 Jul 2000 08:46:23 -0000
Subject: [LifeCA] Re: Just friends: Pseudo puffers and new oscillators

Dean Hickerson wrote:
> Here are 4 pseudo-puffers; each produces a line and various dominoes
> and trominoes

[...]

> Paul:  Can your program find a c/4 component to delete the 
remaining line?
> 

Either of these reactions will work for three of those puffers.  
Neither of them will do when there is an omino too close to the line 
being deleted.

x = 26, y = 16
4bobb7obbo3boo$3oboboo6b3o4bo$bobo5bo3bobbobobbo$bo9bo6b3o$5boboobo$5b
o3b15o$24boo$$24boo$8bo3b12o$8bo$7boo8boboo$10bobo4bobbo$7bo5b3oboobbo
$7b3obbo5b3o$7bo!

Other results in this rule:

Gfind can indeed be modified to find more interesting 
wickstretchers.  These produce period 3 oscillating wicks at c/3.

x = 51, y = 84
15b21o$13boo21boo$12bobb4obobobobobobob4obbo$20bobobobobobo$14bobbobb
ooboboboboobbobbo$15boob4obobobob4oboo$17bobbobobobobobobbo$20bobobobo
bobo$17bobbobobobobobobbo$15boob4obobobob4oboo$14bobbobbooboboboboobbo
bbo$20bobobobobobo$12bobb4obobobobobobob4obbo$13boo21boo$15b21o10$18b
15o$16boo15boo$15bobb3obobobobob3obbo$20bobobobobobo$17bobobobobobobob
obo$18b3obobobobob3o$13boo4bobobobobobobo4boo$13bo5bobobobobobobo5bo$
13boo4bobobobobobobo4boo$18b3obobobobob3o$17bobobobobobobobobo$20bobob
obobobo$15bobb3obobobobob3obbo$16boo15boo$18b15o9$18b15o$16boo15boo$
15bobbob11obobbo$11boo6bo11bo6boo$11bo4bo3booboboboboo3bo4bo$11boo3bo
4bobobobobo4bo3boo$22bobobobo$22bobobobo$11boo3bo4bobobobobo4bo3boo$
11bo4bo3booboboboboo3bo4bo$11boo6bo11bo6boo$15bobbob11obobbo$16boo15b
oo$18b15o8$7bo7boo17boo7bo$4boo7boo4bo11bo4boo7boo$4bobb5o4bo17bo4b5o
bbo$oobb3o6bo5b13o5bo6b3obboo$bbobbo5bo3boo17boo3bo5bobbo$oo3bo4bobboo
bb3obobobobobob3obboobbo4bo3boo$11b3o5bobobobobobobo5b3o$20bobobobobob
o$20bobobobobobo$11b3o5bobobobobobobo5b3o$oo3bo4bobboobb3obobobobobob
3obboobbo4bo3boo$bbobbo5bo3boo17boo3bo5bobbo$oobb3o6bo5b13o5bo6b3obboo
$4bobb5o4bo17bo4b5obbo$4boo7boo4bo11bo4boo7boo$7bo7boo17boo7bo!

Finally, another c/7 ship.

x = 13, y = 36
5bobo$$5b3o$5b3o$5b3o$5bobo$3bobobobo$3bobbobbo$bbo7bo$bbo7bo$bbo7bo$
bbo3bo3bo$bbobo3bobo$bo9bo$bobobobobobo$bobobobobobo$bobobbobbobo$bo4b
o4bo$obbooboboobbo$o4bobo4bo$o11bo$o11bo$oboo5boobo$obo7bobo$o11bo$o
11bo$obbo5bobbo$oboo5boobo$o11bo$oboo5boobo$o11bo$oboo5boobo$3bobobobo
$3bobbobbo$bbobbobobbo$oo4bo4boo!

--
Paul Tooke
paultooke@hotmail.com



From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Mon, 31 Jul 2000 12:25:34 -0700
Subject: [LifeCA] Just friends: Period 30, speed c/5 rake

I found a 6c/30 reaction that changes 2 lines into 1 line, and produces
a spark.  Using David Bell's method for deleting the remaining line, and
adding 4 copies of a c/5 1-line wickstretcher, we get a sparking 6c/30
spaceship.  Paul, can gfind simplify the front end of this?

x = 108, y = 37
2bo8b2o$4b2o2bo$6bob3ob3o$11bo2bo3bo10bo8b2o$2b8obo2b4obo11b2o2bo$o9bo
10bo11bob3ob3o$6bob3o3b4o20bo2bo3bo$4b3o12bo3b2o4b8obo2b4obo$9b9o6bo2b
o9bo10bo$18b3ob3o8bob3o3b4o12bo8b2o$16b3ob2o2bo6b3o12bo3b2o7b2o2bo$16b
2ob2o15b9o6bo9bob3ob3o$16bobo4bo21b3ob3o14bo2bo3bo10bo8b2o$7bo16b2o17b
3ob2o2bo5b8obo2b4obo11b2o2bo$9b3o4bobo4bo19b2ob2o7bo9bo10bo11bob3ob3o$
12bo3b2ob2o22bobo4bo10bob3o3b4o20bo2bo3bo$10b3o3b3ob2o2bo9bo16b2o6b3o
12bo3b2o4b8obo2b4obo$10bobo5b3ob3o11b3o4bobo4bo13b9o6bo2bo9bo10bo$10bo
bob4o6bo14bo3b2ob2o25b3ob3o8bob3o3b4o$19bo3b2o12b3o3b3ob2o2bo19b3ob2o
2bo6b3o12bo3b2o$6bob10o19bobo5b3ob3o19b2ob2o15b9o6bo$3bo17bo15bobob4o
6bo19bobo4bo21b3ob3o$3bob13obo26bo3b2o10bo16b2o17b3ob2o2bo$4bo13bo14bo
b10o19b3o4bobo4bo19b2ob2o$48bo18bo3b2ob2o22bobo4bo$4b41obo18b3o3b3ob2o
2bo9bo16b2o$45bo19bobo5b3ob3o11b3o4bobo4bo$4bo60bobob4o6bo14bo3b2ob2o$
3bob2o67bo3b2o12b3o3b3ob2o2bo$3bo57bob10o19bobo5b3ob3o$76bo15bobob4o6b
o$7bob64obo26bo3b2o$7bo65bo14bob10o$5bo97bo$o6b93obo$o4bo94bo$obo!

Two sparks can interact to form a glider, so we get a glider puffer:

x = 129, y = 79
23bo2b7o$23bo2bobobo2bo$26bobob2ob2o$22bo27bo2b7o$21bob8o5b2o12bo2bobo
bo2bo$21bo17bobo11bobob2ob2o$26bob3o4b4obobo6bo$26bobo14b2o3bob8o5b2o$
25b14o9bo17bobo$43b2o8bob3o4b4obobo8bo2b7o$44bo8bobo14b2o6bo2bobobo2bo
$36b3obob4o6b14o15bobob2ob2o$36bobo2bobo26b2o5bo27bo2b7o$28bo6b2ob3obo
b3o24bo4bob8o5b2o12bo2bobobo2bo$28bob3o3bobo2bobo19b3obob4o3bo17bobo
11bobob2ob2o$29bo6b3obob4o17bobo2bobo10bob3o4b4obobo6bo$44bo10bo6b2ob
3obob3o7bobo14b2o3bob8o5b2o$29b3obo9b2o10bob3o3bobo2bobo9b14o9bo17bobo
$28bo2bobob4o17bo6b3obob4o25b2o8bob3o4b4obobo$27bo15b2o26bo27bo8bobo
14b2o$27bob10obobo13b3obo9b2o19b3obob4o6b14o$24bo14bobo13bo2bobob4o25b
obo2bobo26b2o$24b14o16bo15b2o11bo6b2ob3obob3o24bo$54bob10obobo13bob3o
3bobo2bobo19b3obob4o$66bobo15bo6b3obob4o17bobo2bobo$25b40o34bo10bo6b2o
b3obob3o$84b3obo9b2o10bob3o3bobo2bobo$83bo2bobob4o17bo6b3obob4o$24b4o
54bo15b2o26bo$24bo57bob10obobo13b3obo9b2o$94bobo13bo2bobob4o$29b64o16b
o15b2o$27bo81bob10obobo$b2o21bo96bobo$o20b3o3b93o2$23bo$23bo$12b2o$11b
o3$20bobo$118bo$19b2obob94obo$21b3o97bo$25bo65bo14bob10o$25bob64obo26b
o3b2o$94bo15bobob4o6bo$21bo57bob10o19bobo5b3ob3o$21b4o67bo3b2o12b3o3b
3ob2o2bo$83bobob4o6bo14bo3b2ob2o$63bo19bobo5b3ob3o11b3o4bobo4bo$22b41o
bo18b3o3b3ob2o2bo9bo16b2o$66bo18bo3b2ob2o22bobo4bo$36bo14bob10o19b3o4b
obo4bo19b2ob2o$21b15obo26bo3b2o10bo16b2o17b3ob2o2bo$21bo17bo15bobob4o
6bo19bobo4bo21b3ob3o$24bob10o19bobo5b3ob3o19b2ob2o15b9o6bo$37bo3b2o12b
3o3b3ob2o2bo19b3ob2o2bo6b3o12bo3b2o$28bobob4o6bo14bo3b2ob2o25b3ob3o8bo
b3o3b4o$28bobo5b3ob3o11b3o4bobo4bo13b9o6bo2bo9bo10bo$28b3o3b3ob2o2bo9b
o16b2o6b3o12bo3b2o4b8obo2b4obo$30bo3b2ob2o22bobo4bo10bob3o3b4o20bo2bo
3bo$27b3o4bobo4bo19b2ob2o7bo9bo10bo11bob3ob3o$25bo16b2o17b3ob2o2bo5b8o
bo2b4obo11b2o2bo$34bobo4bo21b3ob3o14bo2bo3bo10bo8b2o$34b2ob2o15b9o6bo
9bob3ob3o$34b3ob2o2bo6b3o12bo3b2o7b2o2bo$36b3ob3o8bob3o3b4o12bo8b2o$
27b9o6bo2bo9bo10bo$22b3o12bo3b2o4b8obo2b4obo$24bob3o3b4o20bo2bo3bo$18b
o9bo10bo11bob3ob3o$20b8obo2b4obo11b2o2bo$29bo2bo3bo10bo8b2o$24bob3ob3o
$22b2o2bo$20bo8b2o!

Dean Hickerson
dean@math.ucdavis.edu

From: "Paul Tooke" <paultooke@hotmail.com>
Date: Tue, 01 Aug 2000 08:59:54 -0000
Subject: [LifeCA] Re: Just friends: Period 30, speed c/5 rake

Mostly to Dean Hickerson:

Nice rake, Dean.

Two copies of a wick modifying reaction convert the lines from a 
single wickstretcher into the required configuration for the back end 
reactions, producing a single engined sparker.  This reduces the size 
of the rake somewhat.

x = 49, y = 43
18bo$18b16obbo7bo$39boo3bo$11bo9b3obb4obob3o7bobo$11b8o6boo3bobbo3bo8b
oo$19bo3bo17bobbo$45bo$12b9obb10o14bo$45b3o$39bobo4bo$11b4o23booboobbo
bbo$11bo27bobo4bo$45b3o$16b5obb10o14bo$14bo30bo$10bo8bo3bo17bobbo$12b
7o6boo3bobbo3bo8boo$9bobbo8b3obb4obob3o7bobo$39boo3bo$11bo6b16obbo7bo$
18bo$3o$o14bo$15b16obbo7bo$8b3o25boo3bo$8bobo7b3obb4obob3o7bobo$8bobob
4o6boo3bobbo3bo8boo$8bo7bo3bo17bobbo$12bo29bo$12bob4obb10o14bo$42b3o$
8bo27bobo4bo$8b4o23booboobbobbo$36bobo4bo$42b3o$9b9obb10o14bo$42bo$16b
o3bo17bobbo$8b8o6boo3bobbo3bo8boo$8bo9b3obb4obob3o7bobo$36boo3bo$15b
16obbo7bo$15bo!

Overnight, the following wickstretcher dropped out of a 2c/6 search.  
The vertical bars are a trifle longer than originally specified, but 
this is the first wickstretcher I've found so far that produces a 
static wick that isn't just a bunch of parallel lines.

x = 27, y = 13
bb3o5b4obb11o$oo3bob3o3boo$6bo4bobbobobbobobobo$oo5bo6bo4bobobobo$bb8o
7bobobobobo$9bo7bobobobobo$8bo3bo3bobbobobobo$9bo7bobobobobo$bb8o7bobo
bobobo$oo5bo6bo4bobobobo$6bo4bobbobobbobobobo$oo3bob3o3boo$bb3o5b4obb
11o!

--
Paul Tooke
paultooke@hotmail.com


From: "Paul Tooke" <paultooke@hotmail.com>
Date: Tue, 01 Aug 2000 13:18:13 -0000
Subject: [LifeCA] Just friends: Period 45 c/3 puffer

This produces a symmetric pair of dominoes every 45 generations.

x = 40, y = 25
31bo$29bobo$25boobb3o$27bobbo$25boo$29boo$b3o6b20o$obboobboo$b3oboo3bo
5bo$8b7obo7bo$38boo$3boo4boo12bo$3bo5bo12b3o$3boo4boo12bo$38boo$8b7obo
7bo$b3oboo3bo5bo$obboobboo$b3o6b20o$29boo$25boo$27bobbo$25boobb3o$29bo
bo$31bo!

--
Paul Tooke
paultooke@hotmail.com



From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Thu, 3 Aug 2000 16:05:03 -0700
Subject: [LifeCA] Re: Just friends: Period 30, speed c/5 rake

Paul Tooke said:

> Two copies of a wick modifying reaction convert the lines from a 
> single wickstretcher into the required configuration for the back end 
> reactions, producing a single engined sparker.  This reduces the size 
> of the rake somewhat.

Thanks!

Eight more puffers based on interacting sparks are shown below.  These
produce various combinations of dominoes, straight trominoes, and
gliders.  Most are p30, but the last two are p90 and p180.  I'm sure
there are many more combinations that I haven't tried yet.

Does anyone know of a simple collision of gliders, dominoes, and
trominoes that makes a c/3 wickstetcher?  If so, it shouldn't be
too hard to build a quadratic growth pattern.

x = 85, y = 468
16bo$18b15o2b3o2b4o$36bob2obobo$7bo12b3o3b2obobob2obo$9b8o6b2o10b2o2bo
5b2o$18b3obo6bo16bo$18bob2o19b2ob3o$6bo2b9o4b10o6b3ob2o2bo$38b2ob2o$
38bobo4bo$9b2o35b2o$7bo3bo26bobo4bo$11b2o25b2ob2o$11bob5o4b10o6b3ob2o
2bo$11bo6bob2o19b2ob3o$18b3obo6bo16bo$5b3ob8o6b2o10b2o2bo5b2o$8b2o10b
3o3b2obobob2obo$7bo28bob2obobo$7bo10b15o2b3o2b4o$3o13bo$o12bo$13bob14o
10bo$6b3o22bo2b2o$8bo7b4o3b2obobob2obo4bobo$o4b2obob6o4bo4b2obo2bo5b2o
2b2o$o6bo6bo4bo19bo$11bo5bo21b3o$11b5o2b10o11bo2bo$35bo4bo$7bo26bobo2b
o3bo$7bob2o29bo$34bobo2bo3bo$35bo4bo$8b8o2b10o11bo2bo$17bo21b3o$14bo4b
o19bo$7bob7o4bo4b2obo2bo5b2o2b2o$7bo8b4o3b2obobob2obo4bobo$31bo2b2o$
13bob14o10bo$13bo20$52bo$52bob14o10bo$70bo2b2o$16bo38b4o3b2obobob2obo
4bobo$16bob37o4bo4b2obo2bo5b2o2b2o$53bo4bo19bo$56bo21b3o$17b38o2b10o
11bo2bo$74bo4bo$73bobo2bo3bo$16bob2o59bo$16bo56bobo2bo3bo$74bo4bo$20b
35o2b10o11bo2bo$20bo35bo21b3o$17b2o34bo4bo19bo$14b3obob35o4bo4b2obo2bo
5b2o2b2o$3o3b3o4bobo2bo36b4o3b2obobob2obo4bobo$70bo2b2o$14bo37bob14o
10bo$21bo30bo$10bo12b15o2b3o2b4o$10bo30bob2obobo$14bo10b3o3b2obobob2ob
o$8bo3bob8o6b2o10b2o2bo5b2o$23b3obo6bo16bo$13bobo7bob2o19b2ob3o$15bob
6o4b10o6b3ob2o2bo$15b2o26b2ob2o$11bo3bo27bobo4bo$13b2o36b2o$43bobo4bo$
43b2ob2o$10bo2b10o4b10o6b3ob2o2bo$23bob2o19b2ob3o$23b3obo6bo16bo$13b9o
6b2o10b2o2bo5b2o$11bo13b3o3b2obobob2obo$41bob2obobo$23b15o2b3o2b4o$21b
o20$25bo$25bob14o3bo6bo$25b2o14bo3bob2obobo$11bo13bob4obo2b2obobob2obo
2bobobo$11bob12o2bo10bobo3bo3b7o$11b2o15bobobo5b3o11bo2bo$11bo28bo12b
2o$12b15o4b9o9bobo$11bo34bobobo4bo$11b2o$11bob2o40b2o$11bo$16bo29bobob
o4bo$15bob10o4b9o9bobo$15bo24bo12b2o$11bo16bobobo5b3o11bo2bo$11bobob
10o2bo10bobo3bo3b7o$25bob4obo2b2obobob2obo2bobobo$11bobo11b2o14bo3bob
2obobo$25bob14o3bo6bo$25bo$o5bo15bo$o5bo4bo10b16o2bo7bo$43b2o3bo$15bob
o7b3o2b4obob3o7bobo$15bob6o6b2o3bo2bo3bo8b2o$15bo7bo3bo17bo2bo$18bo30b
o$20b5o2b10o14bo$49b3o$15bo27bobo4bo$15b4o23b2ob2o2bo2bo$43bobo4bo$49b
3o$16b9o2b10o14bo$49bo$23bo3bo17bo2bo$15b8o6b2o3bo2bo3bo8b2o$15bo9b3o
2b4obob3o7bobo$43b2o3bo$22b16o2bo7bo$22bo20$26bo$28b15o2b3o2b4o$46bob
2obobo$14bo15b3o3b2obobob2obo$16b11o6b2o10b2o2bo5b2o$28b3obo6bo16bo$
28bob2o19b2ob3o$13bo2b12o4b10o6b3ob2o2bo$48b2ob2o$48bobo4bo$16b2o38b2o
$14bo3bo29bobo4bo$18b2o28b2ob2o$18bob8o4b10o6b3ob2o2bo$16bobo9bob2o19b
2ob3o$28b3obo6bo16bo$14bo3b9o6b2o10b2o2bo5b2o$16bo13b3o3b2obobob2obo$
46bob2obobo$b3o3b3o18b15o2b3o2b4o$26bo$23bo$23bob14o$19bo4bo16bob3o2bo
bo$2o4b2o4b2o12b5o2b2obobo4bo2bobobo$20b3o7bo5bobo2bo5bo3b2o$16bobo7bo
b3o6bo$19bobo4b2o23b2o$21bob15o14bo$44b3obob4o$17bo26bobo2bobo$17bob2o
22b2ob3obob3o$18bo25bobo2bobo$44b3obob4o$18b20o14bo$26b2o23b2o$18bo7bo
b3o6bo$17bob4o7bo5bobo2bo5bo3b2o$17bo8b5o2b2obobo4bo2bobobo$24bo16bob
3o2bobo$23bob14o$23bo20$21bo$21b16o2bo7bo$42b2o3bo$11bo12b3o2b4obob3o
7bobo$11b11o6b2o3bo2bo3bo8b2o$22bo3bo17bo2bo$48bo$12b12o2b10o14bo$48b
3o$42bobo4bo$11b4o26b2ob2o2bo2bo$11bo30bobo4bo$48b3o$16b8o2b10o14bo$
14bo33bo$11bo10bo3bo17bo2bo$11bob9o6b2o3bo2bo3bo8b2o$11bobo10b3o2b4obo
b3o7bobo$42b2o3bo$21b16o2bo7bo$21bo$17bo$17bob14o3bo6bo$17b2o14bo3bob
2obobo$2o4b2o5bo3bob4obo2b2obobob2obo2bobobo$11bob4o2bo10bobo3bo3b7o$
11b2o7bobobo5b3o11bo2bo$11b3obo16bo12b2o$15bob2o4b9o9bobo$16bo21bobobo
4bo$11bo$11bob2o32b2o$11b2o$11bo26bobobo4bo$12b7o4b9o9bobo$11bo20bo12b
2o$11b2o7bobobo5b3o11bo2bo$11bob4o2bo10bobo3bo3b7o$11bo5bob4obo2b2obob
ob2obo2bobobo$17b2o14bo3bob2obobo$17bob14o3bo6bo$17bo20$24bo$26b15o2b
3o2b4o$44bob2obobo$17bo10b3o3b2obobob2obo$19b6o6b2o10b2o2bo5b2o$26b3ob
o6bo16bo$26bob2o19b2ob3o$16bo2b7o4b10o6b3ob2o2bo$46b2ob2o$46bobo4bo$
19b2o33b2o$17bo3bo24bobo4bo$21b2o23b2ob2o$21bob3o4b10o6b3ob2o2bo$19bob
o4bob2o19b2ob3o$26b3obo6bo16bo$17bo3b4o6b2o10b2o2bo5b2o$19bo8b3o3b2obo
bob2obo$44bob2obobo$2o4b2o4b3o11b15o2b3o2b4o$24bo$21bo$21bob14o$16bo5b
o16bob3o2bobo$2b2o4b2o14b5o2b2obobo4bo2bobobo$17b4o7bo5bobo2bo5bo3b2o$
13bobo8bob3o6bo$16bobo5b2o23b2o$18bob16o14bo$42b3obob4o$14bo27bobo2bob
o$14bob2o23b2ob3obob3o$15bo26bobo2bobo$42b3obob4o$15b21o14bo$24b2o23b
2o$15bo8bob3o6bo$14bob5o7bo5bobo2bo5bo3b2o$14bo9b5o2b2obobo4bo2bobobo$
22bo16bob3o2bobo$21bob14o$21bo20$54bo$54b16o2bo7bo$75b2o3bo$43bo13b3o
2b4obob3o7bobo$43b12o6b2o3bo2bo3bo8b2o$55bo3bo17bo2bo$81bo$44b13o2b10o
14bo$81b3o$75bobo4bo$43b4o27b2ob2o2bo2bo$43bo31bobo4bo$81b3o$48b9o2b
10o14bo$46bo34bo$43b2o10bo3bo17bo2bo$38bo3bo3b9o6b2o3bo2bo3bo8b2o$43bo
bo11b3o2b4obob3o7bobo$37bobo4bo30b2o3bo$3o15b3o33b16o2bo7bo$38bo15bo$
39bo10bo$39b3o8bob14o$b3o15b3o17bo11bo16bob3o2bobo$40bo5bo6b5o2b2obobo
4bo2bobobo$40bo3b2ob3o7bo5bobo2bo5bo3b2o$46bo6bob3o6bo$48bo4b2o23b2o$
48bob15o14bo$71b3obob4o$44bo26bobo2bobo$44bob2o22b2ob3obob3o$45bo25bob
o2bobo$71b3obob4o$45b20o14bo$53b2o23b2o$45bo7bob3o6bo$44bob4o7bo5bobo
2bo5bo3b2o$44bo8b5o2b2obobo4bo2bobobo$51bo16bob3o2bobo$50bob14o$50bo
20$31bo$31b16o2bo7bo$52b2o3bo$24bo9b3o2b4obob3o7bobo$24b8o6b2o3bo2bo3b
o8b2o$32bo3bo17bo2bo$58bo$25b9o2b10o14bo$58b3o$52bobo4bo$24b4o23b2ob2o
2bo2bo$24bo27bobo4bo$58b3o$29b5o2b10o14bo$27bo30bo$24b2o6bo3bo17bo2bo$
19bo3bo3b5o6b2o3bo2bo3bo8b2o$24bobo7b3o2b4obob3o7bobo$18bobo4bo26b2o3b
o$14b2o15b16o2bo7bo$19bo11bo$27bo$27bob14o$28bo16bob3o2bobo$10bobo9bo
7b5o2b2obobo4bo2bobobo$bo18b2ob4o7bo5bobo2bo5bo3b2o$9b5o8bo7bob3o6bo$
2o9bo12bo5b2o23b2o$11bo12bob16o14bo$48b3obob4o$20bo27bobo2bobo$20bob2o
23b2ob3obob3o$21bo26bobo2bobo$48b3obob4o$21b21o14bo$30b2o23b2o$21bo8bo
b3o6bo$20bob5o7bo5bobo2bo5bo3b2o$20bo9b5o2b2obobo4bo2bobobo$28bo16bob
3o2bobo$27bob14o$27bo!

Dean Hickerson
dean@math.ucdavis.edu

From: David Bell <dbell@pcug.org.au>
Date: Fri, 4 Aug 2000 09:22:32 +1000 (EST)
Subject: [LifeCA] Just Friends: Creating c/3 wickstretcher

The c/3 wickstretcher can appear from a long double row of cells.
For example:

x = 12, y = 3
b11o$$12o!

Since impacts from gliders can make a row longer, I expect that it could
be built from gliders.  But it will probably be pretty large.  One thing
that might help is that if a row of cells has gaps, the gaps can be
"filled in" by gliders, so you aren't limited to adding cells at the
end of a row to make a long one.

BCNU,
-dbell-


From: David Bell <dbell@pcug.org.au>
Date: Fri, 4 Aug 2000 17:53:46 +1000 (EST)
Subject: Re: [LifeCA] Just Friends: Creating c/3 wickstretcher

A much simpler way to create the c/3 wickstretcher is to collide two
gliders into a period 26 oscillator:

x = 25, y = 17
bbo19bo$3o19b3o10$11bobo$11bobo$11b3o3$10b5o!


The period 26 oscillator is easily built by colliding a big glider into
a wall (and a longer wall also works).  So a wickstretcher and a few rakes
should easily be able to create a quadratic growth pattern from this
reaction.  The only problems are creating a forward rake from the backward
rake.  Maybe this can't be done in period 30, but should be easy in
period 60.

BCNU,
-dbell-


From: "Paul Tooke" <paultooke@hotmail.com>
Date: Fri, 04 Aug 2000 15:45:43 -0000
Subject: [LifeCA] Re: Just friends: Period 30, speed c/5 rake

A period 60 domino puffer based on c/5 sparker interactions:

x = 79, y = 42
44bo$44bob14o10bo$62bobboo$37bo9b4o3booboboboobo4bobo$37bob8o4bo4boobo
bbo5boobboo$45bo4bo19bo$48bo21b3o$38b9obb10o11bobbo$66bo4bo$65bobobbo
3bo$37boboo30bo$37bo27bobobbo3bo$66bo4bo$41b6obb10o11bobbo$41bo6bo21b
3o$37bo7bo4bo19bo$35boobob7o4bo4boobobbo5boobboo$38bo8b4o3booboboboobo
4bobo$36b3o23bobboo$oo10boo10boo18bob14o10bo$44bo$47bo$33boo12bob14o$
40b3o5bo16bob3obbobo$40bobo7b5obboobobo4bobbobobo$40bobob3o7bo5bobobbo
5bo3boo$40bo9bob3o6bo$44bo5boo23boo$44bob16o14bo$68b3obob4o$40bo27bobo
bbobo$40boboo23boob3obob3o$41bo26bobobbobo$68b3obob4o$41b21o14bo$50boo
23boo$41bo8bob3o6bo$40bob5o7bo5bobobbo5bo3boo$40bo9b5obboobobo4bobbobo
bo$48bo16bob3obbobo$47bob14o$47bo!

These puffers could possibly be made smaller by welding the sparkers 
together.  For example, the rake can be made narrower (and a bit 
longer) by eliminating some unnecessary parts.

x = 59, y = 31
11bo$11bobo$13b3o$13bobo8bo$13b3obboo4bob6o$11bobo18bo6bo3bo7boo$11bo
16bobb3o13b4oboo$20b5o3boboboboo4bobbo9bo$20bo21boobob5obobo$32bo9bobo
11boo$12bo3boob10o6bob5o5b4o3bo$12bo5bo16bo7b4o8bo$oo9bo30bo14bo$12boo
41b3o$o48bobo4bo$48booboobbobbo$49bobo4bo$11bo43b3o$10bo31bo14bo$10bo
5bo18bo7b4o8bo$10bo3boob12o6bob5o5b4o3bo$32bo9bobo11boo$17bo24boobob5o
bobo$17bob6o3boboboboo4bobbo9bo$8bo9bo9bobb3o13b4oboo$8bobo21bo6bo3bo
7boo$10b3obboo7bob6o$10bobo11bo$10b3o$8bobo$8bo!

On a different subject, here is another c/3 'ladder' wickstretcher 
with shorter vertical bars.

x = 30, y = 23
o$obo$3obboo$bobbo$5boo$boo9bo$bb6o5b3o$8b5o3boo$b7o14boo$12bo3bobo$bb
obobo13bo3bob3o$bboboboboobboob4o3bobboobbo$bbobobo13bo3bob3o$12bo3bob
o$b7o14boo$8b5o3boo$bb6o5b3o$boo9bo$5boo$bobbo$3obboo$obo$o!

--
Paul Tooke
paultooke@hotmail.com




From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Fri, 4 Aug 2000 17:47:02 -0700
Subject: [LifeCA] Just friends: Wickstretcher synthesis and ladder conversion

David Bell said:

> A much simpler way to create the c/3 wickstretcher is to collide two
> gliders into a period 26 oscillator:

Here's a collision between 4 gliders and a domino that makes the
wickstretcher:

x = 25, y = 11
10bo3bo$8b2o5b2o3$12bo$12bo3$o23bo$bo21bo$bo21bo!

I wonder if there's a 3 or 4-glider collision that can do this.


Paul Tooke said:

> On a different subject, here is another c/3 'ladder' wickstretcher 
> with shorter vertical bars.

Here's a 32c/185 conversion of the back end into a messy stable wick:

x = 37, y = 23
7bo$7bobo$7b3o2b2o$8bo2bo$12b2o$8b2o9bo$9b6o5b3o$3bo11b5o3b2o$bob12o
14b2o$o2bo15bo3bobo$bobobobobobobo13bo3bob3o$bobobobobobobob2o2b2ob4o
3bo2b2o2bo$bobobobobobobo13bo3bob3o$19bo3bobo$15o14b2o$15b5o3b2o$9b6o
5b3o$8b2o9bo$12b2o$8bo2bo$7b3o2b2o$7bobo$7bo!

I haven't found any way for the larger ladder to decay.

Dean Hickerson
dean@math.ucdavis.edu

From: David Bell <dbell@pcug.org.au>
Date: Sat, 5 Aug 2000 10:59:18 +1000 (EST)
Subject: [LifeCA] Just Friends: Period 60 forward and backward rakes

Here is a period 60 backward rake:

x = 76, y = 42
34bo$19b14obo$7bobobb3obo16bo$7bobobobbo4boboboobb5o9bo$5boo3bo5bobbob
o5bo7b5obo$20bo6b3obo8bo$5boo23boo$5bo14b21o$4b4obob3o$6bobobbobo26bo$
3b3obob3oboo23boobo$6bobobbobo27bo$4b4obob3o$5bo14b16obo$5boo23boo5bo
bbo$20bo6b3obo7bobo$5boo3bo5bobbobo5bo7b5o3boo$7bobobobbo4boboboobb5o$
7bobobb3obo16bo8bo$19b14obo7bo$34bo18bo$31bo21bo$16b14obo11bobo6boo$4b
obobb3obo16bo$4bobobobbo4boboboobb5o9bo5bo$bboo3bo5bobbobo5bo7b5o3bo3b
o$17bo6b3obo9bo$bboo23boo7bo$bbo14b18obo$b4obob3o24bo$3bobobbobo29bo
34bo$3obob3oboo25boobo34bo$3bobobbobo28boo33boo$b4obob3o29bo$bbo14b23o
$bboo23boo11bo$17bo6b3obo10boo$bboo3bo5bobbobo5bo7b7obo$4bobobobbo4bob
oboobb5o11bo$4bobobb3obo16bo$16b14obo$31bo!


Here is a period 60 forward rake built from the above and a reaction
with the sparker ship (which won't work with period 30):

x = 98, y = 61
95b3o$95bo$$34bo$7b4obb3obb15o$7boboboobo$14bobooboboboo3b3o10bo$4boo
5bobboo10boo6b6o$4bo16bo6bob3o$4b3oboo19boobo$4bobboob3o6b10o4b7obbo
50b3o$8booboo80bo$5bo4bobo$3boo33boo$5bo4bobo24bo3bo$8booboo23boo$4bo
bboob3o6b10o4b3obo$4b3oboo19boobo4bobo$4bo16bo6bob3o$4boo5bobboo10boo
6b5obo3bo$14bobooboboboo3b3o7bo52b3o$7boboboobo27bo48bo$7b4obb3obb15o
9bo$34bo8bo$31bo12bo9bo$4b4obb3obb15o22boo$4boboboobo26bo4bobo$11boboo
boboboo3b3o9bobo$boo5bobboo10boo6b6o3bo3bo$bo16bo6bob3o8boo$b3oboo19b
oobo6bo52b3o$bobboob3o6b10o4b5o54bo$5booboo$bbo4bobo29bo$oo34b4o36bo$
bbo4bobo64boo$5booboo$bobboob3o6b10o4b9o$b3oboo19boobo$bo16bo6bob3o$b
oo5bobboo10boo6b9o31bo15b3o$11bobooboboboo3b3o11bo5bo10b14obo15bo$4bob
oboobo37boobbo23bo$4b4obb3obb15o14bobo4bobooboboboo3b4o7bobo$31bo10boo
bboo5bobboboo4bo4b6obobo$45bo19bo4bo7bo$43b3o21bo6bo$42bobbo11b10obb6o
$44bo4bo$41bo3bobbobo27bo$44bo30boobo$41bo3bobbobo$44bo4bo$42bobbo11b
10obb9o$43b3o21bo$45bo19bo4bo$42boobboo5bobboboo4bo4b8obo$44bobo4boboo
boboboo3b4o9bo$49boobbo$45bo10b14obo$71bo!


BCNU,
-dbell-


From: David Bell <dbell@pcug.org.au>
Date: Sat, 5 Aug 2000 14:50:42 +1000 (EST)
Subject: [LifeCA] Just Friends: More rakes

Here is a period 30 backward big glider rake:

x = 100, y = 58
34bo$8bo6bo3b14obo$7boboboobo3bo14boo$7bobobobbobooboboboobbob4obo6bo$
5b7o3bo3bobo10bobb5obo$4bobbo11b3o5bobobo8boo$5boo12bo21bo$8bobo9b9o4b
8o$4bo4bobobo27bo$40boo$3boo32b3obo$41bo$4bo4bobobo$8bobo9b9o4b3o$5boo
12bo17bo$4bobbo11b3o5bobobo$5b7o3bo3bobo10bobb3oboo3bo$7bobobobboboobo
boboobbob4obo3bo5bo$7boboboobo3bo14boo$8bo6bo3b14obo8boo$34bo$$31bo$5b
o6bo3b14obo9bobo11bo$4boboboobo3bo14boo21b3o$4bobobobbobooboboboobbob
4obo4bo5bo$bb7o3bo3bobo10bobb3o3bo3bo$bobbo11b3o5bobobo7bo61boo$bboo
12bo17bo31bo32bo$5bobo9b9o4b3obo29b3o29boobo$bo4bobobo22bo$38bo58bo$oo
33boobo48boo$37boo38bo10bo$bo4bobobo27bo36b3o7boobo$5bobo9b9o4b8o$bboo
12bo21bo47bo$bobbo11b3o5bobobo8boo31bo$bb7o3bo3bobo10bobb5obo5bo7bobb
16o8bo$4bobobobbobooboboboobbob4obo6bo5bo3boo29bo$4boboboobo3bo14boo
11bobo7b3obob4obb3o7bobbobo$5bo6bo3b14obo9boo8bo3bobbo3boo6b4obo$31bo
12bobbo17bo3bo7bo$43bo30bo$41bo14b10obb5o$41b3o$42bo4bobo27bo$40bobbo
bbooboo23b4o$42bo4bobo$41b3o$41bo14b10obb9o$43bo$44bobbo17bo3bo$41boo
8bo3bobbo3boo6b8o$43bobo7b3obob4obb3o9bo$44bo3boo$44bo7bobb16o$70bo!


Here is a period 60 forward big glider rake (which there is bound to be
a much smaller version of):

x = 203, y = 82
198b3o$198bo$200bobo$200bo4$98bo$72bo6bo3b14obo$71boboboobo3bo14boo$
71bobobobbobooboboboobbob4obo6bo90b3o$69b7o3bo3bobo10bobb5obo90bo$68bo
bbo11b3o5bobobo8boo92bobo$69boo12bo21bo92bo$72bobo9b9o4b8o$68bo4bobobo
27bo$104boo$67boo33boobo$105bo$68bo4bobobo22bo$72bobo9b9o4b3obo92b3o$
69boo12bo17bo92bo$68bobbo11b3o5bobobo9bo90bobo$34bo34b7o3bo3bobo10bobb
3obobo90bo$7b4obb3obb15o38bobobobbobooboboboobbob4obo$7boboboobo56bobo
boobo3bo14boo4bobo$14bobooboboboo3b3o10bo30bo6bo3b14obo15bo$4boo5bobb
oo10boo6b6o58bo13b3o$4bo16bo6bob3o62bo$4b3oboo19boobo36bo6bo3b14obo9bo
$4bobboob3o6b10o4b7obbo25boboboobo3bo14boo9bo86b3o$8booboo55bobobobbob
ooboboboobbob4obo5bo90bo$5bo4bobo53b7o3bo3bobo10bobb6obo3bo86bobo$3boo
33boo25bobbo11b3o5bobobo101bo$5bo4bobo24bo3bo24boo12bo19bobo$8booboo
23boo31bobo9b9o4b5obo$4bobboob3o6b10o4b3obo27bo4bobobo24boo35bo$4b3ob
oo19boobo4bobo60bo3bo29b3o$4bo16bo6bob3o31boo35boo$4boo5bobboo10boo6b
5obo3bo$14bobooboboboo3b3o7bo26bo4bobobo115b3o$7boboboobo27bo26bobo9b
9o4b9obbo84bo$7b4obb3obb15o9bo23boo12bo111bobo$34bo8bo21bobbo11b3o5bob
obo99bo$31bo12bo9bo11b7o3bo3bobo10bobb7o$4b4obb3obb15o22boo14bobobobbo
booboboboobbob4obo8bo$4boboboobo26bo4bobo22boboboobo3bo14boo62bo$11bob
ooboboboo3b3o9bobo29bo6bo3b14obo60b3o$boo5bobboo10boo6b6o3bo3bo50bo$bo
16bo6bob3o8boo$b3oboo19boobo6bo151b3o$bobboob3o6b10o4b5o153bo$5booboo
180bobo$bbo4bobo29bo53b3o94bo$oo34b4o36bo$bbo4bobo64boo18boo$5booboo
81bo4bo83bo$bobboob3o6b10o4b9o53bo85b3o$b3oboo19boobo61bo3bo16bo11bo
11bo11bo11bo11bo11bo$bo16bo6bob3o59bo3boo13bo3bo11bo11bo11bo11bo11bo
11bo$boo5bobboo10boo6b9o47boobbo3bo13bo14bo11bo11bo11bo11bo11bo$11bob
ooboboboo3b3o11bo30bo16bo4bo16bo$4boboboobo32bo7bobb16o6bo9bo3bo4bo$4b
4obb3obb15o14bo3boo37booboobboo$31bo11bobo7b3obob4obb3o8bobbo9bo$41boo
8bo3bobbo3boo6b7o16b3o$44bobbo17bo3bo8bo$43bo30bo$41bo14b10obb5o$41b3o
$42bo4bobo27bo$40bobbobbooboo23b4o$42bo4bobo$41b3o$41bo14b10obb9o$43bo
$44bobbo17bo3bo$41boo8bo3bobbo3boo6b8o$43bobo7b3obob4obb3o9bo$44bo3boo
$44bo7bobb16o$70bo!


Here is a period 60 glider duplication reaction:

x = 129, y = 58
33bo$7bo10b14obo$11boobbo$6bobo4bobooboboboo3b4o9bo$4boobboo5bobboboo
4bo4b8obo$7bo19bo4bo$5b3o21bo$4bobbo11b10obb9o$6bo4bo$3bo3bobbobo$6bo
30boobo$3bo3bobbobo27bo$6bo4bo$4bobbo11b10obb6o$5b3o21bo6bo50bobo$7bo
19bo4bo5boo47bo$4boobboo5bobboboo4bo4b6obob3o$6bobo4bobooboboboo3b4o7b
obbobo$11boobbo111boo$7bo10b14obo94bo$33bo13bobo78bo$30bo$4bo10b14obo
15boobo$8boobbo24bo4bo6bo$3bobo4bobooboboboo3b4o15bobo39bobo$boobboo5b
obboboo4bo4b9o7bo40bo$4bo19bo4bo8bobo24bo$bb3o21bo8bobo25bobo$bobbo11b
10obb6obo69boo$3bo4bo97bo$o3bobbobo29bo66bo$3bo32boobo$o3bobbobo28bo$
3bo4bo$bobbo11b10obb11o44bobo$bb3o21bo56bo$4bo19bo4bo8bo$boobboo5bobbo
boo4bo4b10obo32bo$3bobo4bobooboboboo3b4o11bo5b4obb3obb15o12boo$8boobbo
32boboboobo31bo$4bo10b14obo21bobooboboboo3b3o7bobo5bo$30bo11boo5bobboo
10boo6b4obo$42bo16bo6bob3o7bo$42b3oboo19boobo4bo$42bobboob3o6b10o4b3ob
o$46booboo23boo$43bo4bobo24bo3bo$41boo33boo$43bo4bobo$46booboo$42bobb
oob3o6b10o4b7obbo$42b3oboo19boobo$42bo16bo6bob3o$42boo5bobboo10boo6b6o
$52bobooboboboo3b3o10bo$45boboboobo$45b4obb3obb15o$72bo!


Here is a period 120 forward glider rake:

x = 104, y = 74
101b3o$101bo11$78bo$52bo7bobb16o$52bo3boo$51bobo7b3obob4obb3o9bo$34bo
14boo8bo3bobbo3boo6b8o$19b14obo17bobbo17bo3bo$7bobobb3obo16bo17bo$7bob
obobbo4boboboobb5o9bo7bo14b10obb9o$5boo3bo5bobbobo5bo7b5obo7b3o45b3o$
20bo6b3obo8bo9bo4bobo39bo$5boo23boo16bobbobbooboo23b4o$5bo14b21o9bo4bo
bo27bo$4b4obob3o35b3o$6bobobbobo26bo8bo14b10obb5o$3b3obob3oboo23boobo
9bo30bo$6bobobbobo27bo10bobbo17bo3bo6boo$4b4obob3o35boo8bo3bobbo3boo6b
5o3bo3bo$5bo14b16obo13bobo7b3obob4obb3o7bobo$5boo23boo5bobbo11bo3boo
26bo4bobo$20bo6b3obo7bobo10bo7bobb16o13bo$5boo3bo5bobbobo5bo7b5o3boo
33bo11bobo$7bobobobbo4boboboobb5o$7bobobb3obo16bo8bo$19b14obo7bo49bo$
34bo18bo$31bo21bo$16b14obo11bobo6boo$4bobobb3obo16bo$4bobobobbo4bobob
oobb5o9bo5bo$bboo3bo5bobbobo5bo7b5o3bo3bo$17bo6b3obo9bo$bboo23boo7bo
53boo$bbo14b18obo$b4obob3o24bo54bo$3bobobbobo29bo34bo$3obob3oboo25boob
o34bo$3bobobbobo28boo33boo$b4obob3o29bo$bbo14b23o$bboo23boo11bo$17bo6b
3obo10boo$bboo3bo5bobbobo5bo7b7obo31bo15boo$4bobobobbo4boboboobb5o11bo
4b4obb3obb15o$4bobobb3obo16bo14boboboobo35bo$16b14obo20bobooboboboo3b
3o8bo$31bo10boo5bobboo10boo6b4o3bo$42bo16bo6bob3o$42b3oboo19boobo4bobo
$42bobboob3o6b10o4b3obo$46booboo23boo$43bo4bobo24bo3bo$41boo33boo$43bo
4bobo$46booboo$42bobboob3o6b10o4b7obbo$42b3oboo19boobo$42bo16bo6bob3o$
42boo5bobboo10boo6b6o$52bobooboboboo3b3o10bo$45boboboobo$45b4obb3obb
15o$72bo!


There are also many glider turning reactions which I won't bother
showing here.

BCNU,
-dbell-


From: David Bell <dbell@pcug.org.au>
Date: Sat, 5 Aug 2000 21:11:01 +1000 (EST)
Subject: [LifeCA] Just Friends: Quadratic growth pattern

Here is a relatively simple quadatic growth pattern which conveniently
results from the impact of backward big gliders into the sparker ship:

x = 119, y = 58
33bo$7bo7bobb16o$7bo3boo$6bobo7b3obob4obb3o9bo50bo$4boo8bo3bobbo3boo6b
8o23b4obb3obb15o$7bobbo17bo3bo31boboboobo$6bo64bobooboboboo3b3o10bo$4b
o14b10obb9o21boo5bobboo10boo6b6o$4b3o54bo16bo6bob3o$5bo4bobo48b3oboo
19boobo$3bobbobbooboo23b4o20bobboob3o6b10o4b7obbo$5bo4bobo27bo24booboo
$4b3o55bo4bobo$4bo14b10obb4obo23boo33boo$6bo29bo25bo4bobo24bo3bo$7bobb
o17bo3bo5b3o24booboo23boo$4boo8bo3bobbo3boo6b5oboboo18bobboob3o6b10o4b
3obo$6bobo7b3obob4obb3o30b3oboo19boobo4bo$7bo3boo26bobo19bo16bo6bob3o
21bobo$7bo7bobb16o27boo5bobboo10boo6b4oboo3bo9bobo$33bo37bobooboboboo
3b3o7bo5bo4boo4bo4boo$50bo13boboboobo29bo$30bo17boo14b4obb3obb15o10boo
$4bo7bobb16o7bo52bo$4bo3boo28bo65bo$3bobo7b3obob4obb3o77bo$boo8bo3bobb
o3boo6b5o3b3o20bo40boobo$4bobbo17bo3bo7bo21boo42bo$3bo30bo68bo$bo14b
10obb5o60bo$b3o90bo$bbo4bobo27bo34bo18boobo$obbobbooboo23b4o32boo20bo$
bbo4bobo82bo$b3o78bo$bo14b10obb9o46bo$3bo76boobo$4bobbo17bo3bo40bo10bo
$boo8bo3bobbo3boo6b8o17b14obo10bo$3bobo7b3obob4obb3o9bo5bobobb3obo16bo
5b3o$4bo3boo33bobobobbo4boboboobb5o7bobo$4bo7bobb16o10boo3bo5bobbobo5b
o7b3obobo$30bo25bo6b3obo9bo$41boo23boo5bo$41bo14b16obo$40b4obob3o$42bo
bobbobo27bo$39b3obob3oboo23boobo$42bobobbobo26bo$40b4obob3o$41bo14b21o
$41boo23boo$56bo6b3obo8bo$41boo3bo5bobbobo5bo7b5obo$43bobobobbo4bobob
oobb5o9bo$43bobobb3obo16bo$55b14obo$70bo!


BCNU,
-dbell-


From: "Alan Hensel" <alanh@mindspring.com>
Date: Sat, 5 Aug 2000 13:15:15 -0400
Subject: [LifeCA] Just Friends gallery online


Since there has been so much discussion of the "Just Friends" rule 
recently, and most list members (like me) are too lazy to download a 
program capable of non-totalistic rules and set it all up, I have 
created an "easter egg" hack of my Life applet:

http://www.mindspring.com/~alanh/life/justfriends.html

Hit the "Open" button to see most of the patterns discussed recently. I 
haven't gotten around to converting the few that were given in MCell 
format.

WARNING: If you discover anything new with my applet, beware that there 
is no "save" mechanism whatsoever. If you really get into this rule, 
please move to a real Life program.

The "easter egg" is the ability to specify the rules as "justfriends".

Alan


From: "Alan Hensel" <alanh@mindspring.com>
Date: Sat, 5 Aug 2000 13:15:30 -0400
Subject: [LifeCA] Just Friends: XL glider


David Bell wrote:
> Here are two related period 6 c/6 diagonal gliders.  The second one
> shows a tag-along for the smaller glider.  I haven't been able to
> extend this.
>
> ..............OO.
> OO..............O
> ..O.........OOO..
> ..............O..

Surely you've done it since you wrote that?

 .*......................
 .*......................
 **.*....................
 ...*....................
 .....*..................
 ...*.*..................
 .......*................
 .....***................
 ........................
 .......**.*.............
 ........................
 .........**.*...........
 ............*...........
 ...........**.*.........
 ..............*.........
 ................*.......
 ..............*.*.......
 ..................*.....
 ................***.....
 ........................
 ..................**.*..
 ........................
 ....................**.*
 .......................*
 ......................**

Alan


Date: Tue, 8 Aug 2000 08:34:41 +1000 (EST)
From: David Bell <dbell@supreme.pcug.org.au>
Subject: Just Friends: Wick burning rakes

Here is a period 480 backward rake which uses a wick-burning reaction:

x = 330, y = 115
107b4o$112b3obbobo$107boo3bobbobobo86b3o8bo$104boboobbo5bo3boo34b3o8bo
44boo3bo$104boobbo50bobboo43boo7bobo$107bo12boo35b3obo4bobo41bo8boo$
105bobboo11bo34bobbo5boobboo31bobbo8bobbo10b3o8bo$113b3obob4o29bobo12b
o34boo14bo15boo3bo$113bobobbobo34boo10b3o33boobboo11bo8boo7bobo$112boo
b3obob3o30bobboo8bobbo47b3o11bo8boo$76bo36bobobbobo42bo4bo43bobo4bo4bo
bbo8bobbo$76bobo34b3obob4o39bobobbo3bo39booboobbobbobboo14bo57b8obb4o$
80bo25bo14bo46bo5bo37bobo4bo5boobboo11bo54boo5boboobobo$89bo10bo7b3o9b
oo3bo36bobobbo3bo4bo41b3o19b3o53b7obo$80bobboo4bob3o6bob5o4b5o9bobo35b
o4bo9bo26bo14bo13bobo4bo54bobbo3boobbo5boo$76bobo11bo10bo6bobo9boo5b3o
25bo11bobbo8bo8bo10bo6b4o8bo14booboobbobbo52bobb4o11bo$76bo17bobbo7b4o
bb5obobo7bobo8bo10bo6b4o7b3o8bo3boo4b5o6b6o5b4o3bo16bobo4bo55bo4bo6boo
b3o$85bob3o3bobo3boo4bobbobo5bobo8b3obboo4bob3o6bob5o4b4o3bo8bo16b4o
10boo10boo19b3o55bobbo4b3oboobbo$85bo7bobo7bobbo4b4o10bobo18bo10bo7boo
bboo3bo19bobo11b7obobo6boobboo11bo63booboo$81bo23bo19bo29boo3b5obobo
16b4o3b3oboboo4bobo9bo7boo14bo65bobo4bo$81bobob13o36b5o3boboboboo4bo
28bo8bo4bo4boob3obb4oboo7bobbo8bobbo74boo$81bobo50bo7bobb3o4boo3bobb4o
16bo33boo16bo8boo63bobo4bo$81b3o62bo7bo22b3o3b13o33boo7bobo65booboo$
126bo3boob13o88boo3bo66b3oboobbo$126bo5bo46bo48b3o8bo58b3o7b3ob3o$125b
o53bo120boob5o6bo$126boo174bobo4bo3boo$299bo6boo$302bobo6bo$130bo97b
73o5boobo$130bo171b3o3bo$130bo94boo74bo$226bo55bobo$226bo56bo4b3o$126b
oo154bobobboobo$125bo53bo107bo3b13o$126bo5bo46bo107b3o14bo7bo$126bo3b
oob13o144bobo7bobb3o4boo3bobb4o$80bobo63bo7bo22b3o3b13o96b5o3boboboboo
4bo$134bo7bobb3o4boo3bobb4o16bo33boo67bo29boo3b5obobo$79boobob14o36b5o
3boboboboo4bo28bo8bo4bo4boob3obb4oboo66bobo18bo10bo7boobboo$81b3o21bo
19bo29boo3b5obobo16b4o3b3oboboo4bobo9bo68b3obboo4bob3o6bob5o4b4o3bo$
85bo7bobo7bobbo4b4o10bobo18bo10bo7boobboo3bo19bobo11b7obobo66bobo8bo
10bo6b4o7b3o$85bob3o3bobo3boo4bobbobo5bobo8b3obboo4bob3o6bob5o4b4o3bo
8bo16b4o10boo10boo64b3o25bo11bobbo$76bo17bobbo7b4obb5obobo7bobo8bo10bo
6b4o7b3o8bo3boo4b5o6b6o5b4o3bo65bobo35bo4bo$76bobo11bo10bo6bobo9boo5b
3o25bo11bobbo8bo8bo10bo6b4o8bo64bo36bobobbo3bo$80bobboo4bob3o6bob5o4b
5o9bobo35bo4bo9bo26bo14bo105bo$89bo10bo7b3o9boo3bo36bobobbo3bo4bo41b3o
99bobobbo3bo$80bo25bo14bo46bo5bo37bobo4bo101bo4bo$76bobo34b3obob4o39bo
bobbo3bo39booboobbobbo90bobboo8bobbo$76bo36bobobbobo42bo4bo43bobo4bo
93boo10b3o$112boob3obob3o30bobboo8bobbo47b3o8boo79bobo12bo$113bobobbob
o34boo10b3o33boobboo11bo9bo83bobbo5boobboo$113b3obob4o29bobo12bo34boo
14bo11bo20bo63b3obo4bobo$105bobboo11bo34bobbo5boobboo31bobbo8bobbo33bo
b14o50bobboo$107bo12boo35b3obo4bobo41bo8boo31bo16bob3obbobo35b3o8bo$
104boobbo50bobboo43boo7bobo25bo9b5obboobobo4bobbobobo$104boboobbo5bo3b
oo34b3o8bo44boo3bo26bob5o7bo5bobobbo5bo3boo14bo$107boo3bobbobobo86b3o
8bo27bo8bob3o6bo31b15obb3obb4o$112b3obbobo134boo23boo34boboobobo$o106b
4o134b21o14bo7bo10b3o3booboboboobo$o271b3obob4o8b6o6boo10boobbo5boo$bo
243bo26bobobbobo17b3obo6bo16bo$244boboo23boob3obob3o14boboo19boob3o$
244bo27bobobbobo7bobb7o4b10o6b3oboobbo$272b3obob4o35booboo$248bob16o
14bo36bobo4bo$248bo5boo23boo9boo33boo$246bo7bob3o6bo22bo3bo24bobo4bo$
240bo3boob4o7bo5bobobbo5bo3boo11boo23booboo$240bo5bo7b5obboobobo4bobbo
bobo13bob3o4b10o6b3oboobbo$233boo4bo12bo16bob3obbobo13bo4boboo19boob3o
$234bo4b3o9bob14o30b3obo6bo16bo$234bo16bo34b3ob6o6boo10boobbo5boo$289b
oo8b3o3booboboboobo$288bo26boboobobo$288bo8b15obb3obb4o$277bo17bo$277b
3o18bo$286boo12b15obb3obb4o$318boboobobo$286bo5bo9b3o3booboboboobo$
286bo3boob6o6boo10boobbo5boo$300b3obo6bo16bo$293bo6boboo19boob3o$238bo
bo54b5o4b10o6b3oboobbo$240bo79booboo$255bo34bo29bobo4bo$255b3o32b4o34b
oo$320bobo4bo$320booboo$291b9o4b10o6b3oboobbo$300boboo19boob3o$300b3ob
o6bo16bo$241boo15bo31b9o6boo10boobbo5boo$242bobbobo10bob14o10bo5bo11b
3o3booboboboobo$246bo4b3o22bobboo37boboobobo$245bobobboobo7b4o3boobobo
boobo4bobo14b15obb3obb4o$250bo3b7o4bo4boobobbo5boobboo10bo$250b3o6bo4b
o19bo$253bobo6bo21b3o$255b6obb10o11bobbo$280bo4bo$251bo27bobobbo3bo$
251boboo30bo$279bobobbo3bo$280bo4bo$252b9obb10o11bobbo$262bo21b3o$259b
o4bo19bo$251bob8o4bo4boobobbo5boobboo$251bo9b4o3booboboboobo4bobo$276b
obboo$258bob14o10bo$258bo!


This can be made into an arbitrarily large period rake by increasing
the length of the wick.

It might be possible to make such a wick-burning rake without any use of
impacting gliders.  The perturbing sparker ship which stops the burning
wick from destroying the wickstretcher can be positioned to cause the
wick to leave other types of debris.  When the burning wick reaches that
debris, another passing sparker ship might be able to re-ignite it.
Note that this can still be an arbitrarily large period rake because the
wick can burn at two different speeds.


PS: To Alan:

Wow, thanks for the super-long gliders.  I still had not discovered that!
I don't know how I missed it.  I thought I had tried the obvious thing.

BCNU,
-dbell-


Date: Tue, 8 Aug 2000 03:14:08 -0700
From: Dean Hickerson <dean@math.ucdavis.edu>
Subject: Just Friends: p480 rake from David Bell

David Bell asked me to post this for him, because he's temporarily
unable to access the Life list.

Dean Hickerson
dean@math.ucdavis.edu

--------------------   Start of David Bell's message   ---------------

Here is a period 480 backward rake which uses a wick-burning reaction:

x = 330, y = 115
107b4o$112b3obbobo$107boo3bobbobobo86b3o8bo$104boboobbo5bo3boo34b3o8bo
44boo3bo$104boobbo50bobboo43boo7bobo$107bo12boo35b3obo4bobo41bo8boo$
105bobboo11bo34bobbo5boobboo31bobbo8bobbo10b3o8bo$113b3obob4o29bobo12b
o34boo14bo15boo3bo$113bobobbobo34boo10b3o33boobboo11bo8boo7bobo$112boo
b3obob3o30bobboo8bobbo47b3o11bo8boo$76bo36bobobbobo42bo4bo43bobo4bo4bo
bbo8bobbo$76bobo34b3obob4o39bobobbo3bo39booboobbobbobboo14bo57b8obb4o$
80bo25bo14bo46bo5bo37bobo4bo5boobboo11bo54boo5boboobobo$89bo10bo7b3o9b
oo3bo36bobobbo3bo4bo41b3o19b3o53b7obo$80bobboo4bob3o6bob5o4b5o9bobo35b
o4bo9bo26bo14bo13bobo4bo54bobbo3boobbo5boo$76bobo11bo10bo6bobo9boo5b3o
25bo11bobbo8bo8bo10bo6b4o8bo14booboobbobbo52bobb4o11bo$76bo17bobbo7b4o
bb5obobo7bobo8bo10bo6b4o7b3o8bo3boo4b5o6b6o5b4o3bo16bobo4bo55bo4bo6boo
b3o$85bob3o3bobo3boo4bobbobo5bobo8b3obboo4bob3o6bob5o4b4o3bo8bo16b4o
10boo10boo19b3o55bobbo4b3oboobbo$85bo7bobo7bobbo4b4o10bobo18bo10bo7boo
bboo3bo19bobo11b7obobo6boobboo11bo63booboo$81bo23bo19bo29boo3b5obobo
16b4o3b3oboboo4bobo9bo7boo14bo65bobo4bo$81bobob13o36b5o3boboboboo4bo
28bo8bo4bo4boob3obb4oboo7bobbo8bobbo74boo$81bobo50bo7bobb3o4boo3bobb4o
16bo33boo16bo8boo63bobo4bo$81b3o62bo7bo22b3o3b13o33boo7bobo65booboo$
126bo3boob13o88boo3bo66b3oboobbo$126bo5bo46bo48b3o8bo58b3o7b3ob3o$125b
o53bo120boob5o6bo$126boo174bobo4bo3boo$299bo6boo$302bobo6bo$130bo97b
73o5boobo$130bo171b3o3bo$130bo94boo74bo$226bo55bobo$226bo56bo4b3o$126b
oo154bobobboobo$125bo53bo107bo3b13o$126bo5bo46bo107b3o14bo7bo$126bo3b
oob13o144bobo7bobb3o4boo3bobb4o$80bobo63bo7bo22b3o3b13o96b5o3boboboboo
4bo$134bo7bobb3o4boo3bobb4o16bo33boo67bo29boo3b5obobo$79boobob14o36b5o
3boboboboo4bo28bo8bo4bo4boob3obb4oboo66bobo18bo10bo7boobboo$81b3o21bo
19bo29boo3b5obobo16b4o3b3oboboo4bobo9bo68b3obboo4bob3o6bob5o4b4o3bo$
85bo7bobo7bobbo4b4o10bobo18bo10bo7boobboo3bo19bobo11b7obobo66bobo8bo
10bo6b4o7b3o$85bob3o3bobo3boo4bobbobo5bobo8b3obboo4bob3o6bob5o4b4o3bo
8bo16b4o10boo10boo64b3o25bo11bobbo$76bo17bobbo7b4obb5obobo7bobo8bo10bo
6b4o7b3o8bo3boo4b5o6b6o5b4o3bo65bobo35bo4bo$76bobo11bo10bo6bobo9boo5b
3o25bo11bobbo8bo8bo10bo6b4o8bo64bo36bobobbo3bo$80bobboo4bob3o6bob5o4b
5o9bobo35bo4bo9bo26bo14bo105bo$89bo10bo7b3o9boo3bo36bobobbo3bo4bo41b3o
99bobobbo3bo$80bo25bo14bo46bo5bo37bobo4bo101bo4bo$76bobo34b3obob4o39bo
bobbo3bo39booboobbobbo90bobboo8bobbo$76bo36bobobbobo42bo4bo43bobo4bo
93boo10b3o$112boob3obob3o30bobboo8bobbo47b3o8boo79bobo12bo$113bobobbob
o34boo10b3o33boobboo11bo9bo83bobbo5boobboo$113b3obob4o29bobo12bo34boo
14bo11bo20bo63b3obo4bobo$105bobboo11bo34bobbo5boobboo31bobbo8bobbo33bo
b14o50bobboo$107bo12boo35b3obo4bobo41bo8boo31bo16bob3obbobo35b3o8bo$
104boobbo50bobboo43boo7bobo25bo9b5obboobobo4bobbobobo$104boboobbo5bo3b
oo34b3o8bo44boo3bo26bob5o7bo5bobobbo5bo3boo14bo$107boo3bobbobobo86b3o
8bo27bo8bob3o6bo31b15obb3obb4o$112b3obbobo134boo23boo34boboobobo$o106b
4o134b21o14bo7bo10b3o3booboboboobo$o271b3obob4o8b6o6boo10boobbo5boo$bo
243bo26bobobbobo17b3obo6bo16bo$244boboo23boob3obob3o14boboo19boob3o$
244bo27bobobbobo7bobb7o4b10o6b3oboobbo$272b3obob4o35booboo$248bob16o
14bo36bobo4bo$248bo5boo23boo9boo33boo$246bo7bob3o6bo22bo3bo24bobo4bo$
240bo3boob4o7bo5bobobbo5bo3boo11boo23booboo$240bo5bo7b5obboobobo4bobbo
bobo13bob3o4b10o6b3oboobbo$233boo4bo12bo16bob3obbobo13bo4boboo19boob3o
$234bo4b3o9bob14o30b3obo6bo16bo$234bo16bo34b3ob6o6boo10boobbo5boo$289b
oo8b3o3booboboboobo$288bo26boboobobo$288bo8b15obb3obb4o$277bo17bo$277b
3o18bo$286boo12b15obb3obb4o$318boboobobo$286bo5bo9b3o3booboboboobo$
286bo3boob6o6boo10boobbo5boo$300b3obo6bo16bo$293bo6boboo19boob3o$238bo
bo54b5o4b10o6b3oboobbo$240bo79booboo$255bo34bo29bobo4bo$255b3o32b4o34b
oo$320bobo4bo$320booboo$291b9o4b10o6b3oboobbo$300boboo19boob3o$300b3ob
o6bo16bo$241boo15bo31b9o6boo10boobbo5boo$242bobbobo10bob14o10bo5bo11b
3o3booboboboobo$246bo4b3o22bobboo37boboobobo$245bobobboobo7b4o3boobobo
boobo4bobo14b15obb3obb4o$250bo3b7o4bo4boobobbo5boobboo10bo$250b3o6bo4b
o19bo$253bobo6bo21b3o$255b6obb10o11bobbo$280bo4bo$251bo27bobobbo3bo$
251boboo30bo$279bobobbo3bo$280bo4bo$252b9obb10o11bobbo$262bo21b3o$259b
o4bo19bo$251bob8o4bo4boobobbo5boobboo$251bo9b4o3booboboboobo4bobo$276b
obboo$258bob14o10bo$258bo!

This can be made into an arbitrarily large period rake by increasing
the length of the wick.

It might be possible to make such a wick-burning rake without any use of
impacting gliders.  The perturbing sparker ship which stops the burning
wick from destroying the wickstretcher can be positioned to cause the
wick to leave other types of debris.  When the burning wick reaches that
debris, another passing sparker ship might be able to re-ignite it.
Note that this can still be an arbitrarily large period rake because the
wick can burn at two different speeds.

--------------------   End of David Bell's message   -----------------

From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Thu, 10 Aug 2000 15:27:09 -0700
Subject: [LifeCA] Just friends: c/14 wickstretcher and 2c/7 ladder conversion

Here's a c/14 device that can add 3 lines to an existing one.  Two
copies of it can support each other, so we also get a c/14 6-line
wickstretcher:

x = 86, y = 32
b85o2$2b4o2$3b3o2$6b2o2$3b3o9$b3o2$4b2o2$4o2$b3o2$2b4o2$3b3o2$6b2o2$3b
3o!

Here's a way to lengthen one of Paul's ladders, at 2c/7.  The version
shown here changes a length-3 ladder to length 5.  Unfortunately,
we first need to add another line (at c/3), and another line is left
behind, so I don't see a way to get arbitrarily long ladders from this.

x = 57, y = 24
16b3o$19b3o5bo$15bo6b2o3bobo$13bo5bo7b3o2b2o$22b2o4bo2bo$b9o9b3o10b2o$
11b8o9b2o9bo$10o19b6o5b3o$10bo24b5o3b2o$bobobobo2b25o14b2o$bobobobo2bo
28bo3bobo$bobobobobobobobobobobobobobobobobo13bo3bob3o$bobobobobobobob
obobobobobobobobobob2o2b2ob4o3bo2b2o2bo$bobobobobobobobobobobobobobobo
bobo13bo3bob3o$39bo3bobo$35o14b2o$35b5o3b2o$29b6o5b3o$28b2o9bo$32b2o$
28bo2bo$27b3o2b2o$27bobo$27bo!

Dean Hickerson
dean@math.ucdavis.edu

From: Jason Summers <jason@med-web.com>
Date: Fri, 11 Aug 2000 21:52:13 -0500
Subject: [LifeCA] Just Friends: oscillators

Here are a few Just Friends oscillators that I don't think have been posted
yet. These occurred naturally from random disturbances in an agar, except for
the second p19 which is a trivial bisection of one of Dean's. The first p19
and the p10 are also bisections of known oscillators, but slightly less
trivial.

x = 70, y = 105
15bobb6o$15bo$15bo$15bo27bo$15bo25boboobbo$15bobb3obbo15bobobobobobo$
15bo7bo15bobobobobobo$15bo7bo15bo3bo3bo$15bo7bo$15bo7bo$15bobb3obbo8$
15bobb3obbo$15bo7bo$15bo7bo24bobbo$15bo7bo15bo11bo$15bo7bo15bobobo5bo$
15bobb3obbo25bo$15bo7bo17bobo3bobo$15bo7bo17bobobobo$15bo7bo19bobo$15b
o7bo21bo$15bobb3obbo8$15bobb3obbo$15bo7bo$15bo7bo$15bo7bo16boo5boo$15b
o7bo$15bobb3obbo15b3o5b3o$23bo19b3o$23bo16boo5boo$23bo19b3o$23bo18bo3b
o$15b6obbo8$8bo6bobb3obbo$8bo6bo7bo$8bo6bo7bo$8bo6bo7bo$8bo6bo7bo25bo$
8bo6bo7bo16bo9boo$8bo6bo7bo16bobobobboo$8bo6bo7bo16bo9bo$8bo6bo7bo18bo
bo3bobo$8bo6bo7bo18bobobobo$8bo6bobb3obbo20bobobo$46bo8$8bo6bobb3obbo$
8bo6bo7bo$8bo6bo7bo$8bo6bo7bo$8bo6bo7bo$8bo6bobb3obbo19boo20bobo$8bo
14bo19bo$8bo14bo17bobo4b5o12b5o$8bo14bo17bobobobobo$8bo14bo17bo3bobobo
bo13b3o$8bo6b6obbo23bobobo10bo$49bo12bo8$6obbo6bobb3obbo$8bo6bo7bo$8bo
6bo7bo$8bo6bo7bo18boo$8bo6bo7bo$obb3obbo6bobb3obbo17b5o$o14bo7bo25boo$
o14bo7bo18b4o$o14bo7bo25b3o$o14bo7bo21b3o$obb6o6bobb3obbo25boo$47bo$
47bo!

From: "Paul Tooke" <paultooke@hotmail.com>
Date: Mon, 14 Aug 2000 15:11:10 -0000
Subject: [LifeCA] Just friends: Period 2 oscillators

We don't appear to have seen many period 2 oscillators yet, so here 
are a few more examples.

x = 78, y = 76
42bo$32bo6boobo17bo3bo11bo$28boobbo11bo15bo3bo8boobo$3bo26boo12bo16boo
12bo$boboboo22bobboo6bobobo16bo13bo$oo38boboo17bobo10bobo$6boo20bo14bo
19boo$boobobo20boo15bo16bobo$4bo22bo12bobobo15boo12bobo$40boboo17bobo
11bo$26bo16bo19boo10bo$25boo17bo16bobo10bobo$25bo14bobobo15boo$40boboo
17bobo$oo5boo15bo18bo19boo9bobo$bb3o18boo19bo16bobo11bo$bbo3bo16bo16bo
bobo15boo13bo$4b3o33boboo17bobo10bobo$oo5boo13bo20bo19boo$22boo20bo16b
obo$23bo16bobobo15boo12bobo$40boboo17bobo11bo$22bo20bo19boo10bo$22boo
20bo16bobo10bobo$o6boo14bo16bobobo15boo$o3b3o33boboo17bobo$boo3bo15bo
20bo19bo10bobo$bo19boo21bo17boo11bo$bo5bo9boobbo18bobobo15bo3bo10bo$7b
o32bobbo16bo3bo9bobo$bbo3boo10bobboo17bobbo$bb3o3bo9bo23boboo$oo6bo33b
o31boboo$74bo11$54bo$29bo24bo4boo$4bo24boo24boo$3booboobboobboobboobb
oobboo27bobbo4boo$8boobboobboobboobboobbo23bobbobb3o$4bo3bo3bo3bo3bo3b
o3bo23bo4b3obbo4boo$4bo48boo4bobb3o$5boobboobboobboobboobboo26bobbo4b
3obbo4boo$5bobboobboobboobboobboobbo21bobbobb3o4bobb3o$4bo3bo3bo3bo3bo
3bo3bo21bo4b3obbo4b3obbo4boo$4bo46boo4bobb3o4bobb3o$5boobboobboobboobb
oobboo24bobbo4b3obbo4b3obbo$5bobboobboobboobboobboobbo19bobbobb3o4bobb
3o4bobbo$4bo3bo3bo3bo3bo3bo3bo19bo4b3obbo4b3obbo4boo$4bo44boo4bobb3o4b
obb3o4bo$5boobboobboobboobboobboo22bobbo4b3obbo4b3obbobbo$5bobboobboo
bboobboobboobbo17bobbobb3o4bobb3o4bobbo$4bo3bo3bo3bo3bo3bo3bo17bo4b3o
bbo4b3obbo4boo$4bo42boo4bobb3o4bobb3o4bo$5boobboobboobboobboobboo20bo
bbo4b3obbo4b3obbobbo$5bobboobboobboobboobboobbo18bobb3o4bobb3o4bobbo$
4bo3bo3bo3bo3bo3bo3bo20b3obbo4b3obbo4boo$4bo40boo4bobb3o4bobb3o4bo$5b
oobboobboobboobboobboo26b3obbo4b3obbobbo$5bobboobboobboobboobboobbo20b
oo4bobb3o4bobbo$4bo3bo3bo3bo3bo3bo3bo28b3obbo4boo$4bo48boo4bobb3o4bo$
5boobboobboobboobboobbooboo31b3obbobbo$bboo24bo28boo4bobbo$3bo61boo$
61boo4bo$67bo!

--
Paul Tooke
paultooke@hotmail.com


From: "Alan Hensel" <alanh@mindspring.com>
Date: Sat, 19 Aug 2000 19:16:46 -0400
Subject: [LifeCA] Non-Totalistic Rule Notation Extension Proposal


Having been excited enough by David Bell's "Just Friends" rule to add 
the "justfriends" easter egg to my applet, I decided to find a way to 
express all symmetric non-totalistic rules in a simple, comprehensible 
way that I could type on one line. (At least for my applet.)

(It has been particularly conspicuous that "Just Friends" patterns have 
been posted with no "rule = " part in the header.)

I decided not to concern myself with asymmetric rules, unless it turns 
out that there is some interesting property that asymmetry gives. It 
seems to me that it would only mean that there are patterns that only 
work in certain orientations. Bummer.

I count 51 unique neighborhoods. The maximum number for any particular 
neighborhood count is 13 for 4 neighbors. I decided to use letters of 
the alphabet to identify them (excluding b and s).

The table I came up with is here:
http://www.mindspring.com/~alanh/life/neighbors.html#table

The applet button on that page takes you to a version of my applet that 
implements this notation.

In this notation, "Just Friends" is 12/2-a, or B2-a/S12.

Is this the proper standards body to submit it to? ;-)

 ---

Here are my first explorations into the non-totalistic world:

If you modify the Life rules to exclude survival on 2 neighbors of 
opposite edges,

  B3/S2-i3

blinkers fail because their middle drops out, but a "T" shape becomes a 
very common c/5 orthogonal glider, which coexists with the regular 
glider. It makes the universe slightly less active though, and I'm not 
sure what is the best way to fix it. The nice thing about non-
totalitarian rules is that you can apply fairly subtle tweaks.

Some of the tweaks I've tried:

  B2i34et/S2-i3 -- has a common p10 oscillator
  B2i3/S2-i3

I also investigated what the specific non-totalian rules are that 
support the regular Life glider. Using my notation, it comes out like 
this:

   do: Binjl S2ea3nrj
don't: B1e2aec4n5n S14k

Naturally, just satisfying the minimum requirements forms a boring 
death universe. While spicing it up, I made an interesting mistake, and 
included something from the "don't" list, and the regular Life glider 
turned into a c/9 glider traveling in a direction orthogonal to the one 
intended! That rule was B2-ak3injl/S2ea3nrj. (The mistake was letting 
2ec be included in the birth list.)

Here is a universe with a wild replicator: B2-ca3-e/S1c2-a3jck
 .o.oo
 o...o
 .o.oo

I found that universe while investigating universes in which this is a 
glider:
 .o        oo
 o.  <-->  o.
 .o        oo

The requirements for that are:

   do: B2e3i S1c2ce
don't: B12c3e5i S2a4u

Only non-totalitarian rules can support this glider.

 ---

Anway, sorry for rambling. I have been very quiet on this list for a 
long time, though. I'm interested to see the reaction to this rule 
notation proposal. I'm willing to shift letters around if better 
mnemonics are found.

BTW, this feature of the applet is still unadvertised. It will be a 
part of version 0.41d :-)

Alan


From: Dean Hickerson <dean@math.ucdavis.edu>
Date: Mon, 21 Aug 2000 19:42:04 -0700
Subject: [LifeCA] Just Friends is omniperiodic

I've partially modified the drifter searcher to handle the Just Friends
rule.  It would be difficult to change the part that grows the stable
background so that it could handle nontotalistic rules, so I just changed
the part that evolves the drifter; the program uses B2/S12 for the
background rule.  Anything that the program finds will work in Just
Friends, but there are probably interesting things that it can't find.

After a couple of days of searching, the program has found components
that yield a proof of omniperiodicity: a 27-gen 90 degree turn and a
23-gen flip.  Here are a couple of examples of loops made from these.
First, 4 copies of the turn give a p108 oscillator; by inserting
additional drifters this could also have period 18, 27, 36, or 54:

x = 38, y = 38
16bo$16bob2o$16bo$16bo2b7o$16bo9b2o$13b2obob3o$7b4o5bo7bob3o$15b2ob3ob
obo6bo$8bo2b2o3bo5bobob4obo$6bobo7bobobo10bo$4bobobo3b2o2bobobo3b2o5bo
$4bobobo7bo3bo8bo$3bo6bobob2o4bo2b3obobo$3bo2b3obobo4b2obo6bo4bo$3bo8b
ob3o4bobobo6bo$3bo3b2o11bo2bobo4bo$3bo10bo5bo2bo2b4ob7o$3bobobob5ob2o
7bo$bobobobo16bo2b2obobo3bo$bo3bobob2o2bo16bobobobo$13bo7b2ob5obobobo$
7ob4o2bo2bo5bo10bo$7bo4bobo2bo11b2o3bo$5bo6bobobo4b3obo8bo$5bo4bo6bob
2o4bobob3o2bo$8bobob3o2bo4b2obobo6bo$8bo8bo3bo7bobobo$6bo5b2o3bobobo2b
2o3bobobo$6bo10bobobo7bobo$6bob4obobo5bo3b2o2bo$6bo6bobob3o2bo$9b3obo
7bo5b4o$17b3obob2o$10b2o9bo$12b7o2bo$21bo$18b2obo$21bo!

Next, a p292 loop with 4 turns and 8 flips; periods 73 and 146 can
also be obtained.

x = 64, y = 64
38bo4b2o$38bobo4b4o$35bo2bobob2o$20bo2bo10b2o8bo2bo$13b6obo2bo13b6obo
2bo$11b2o9bo13bo9bo$18b3obob3o3bo5bo5b3obob2o$10b3obo7bo4b2obo2bo2bobo
7bo5b4o$7bo6bobob3o2bo6bo2bo4bobob3o2bo$7bob4obobo5bo3b2o2bobo2b2obobo
5bo3b2o2bo$7bo10bobobo7bobobo7bobobo7bobo$7bo5b2o3bobobo2b2o3bobobo2b
2o3bobobo2b2o3bobobo$9bo8bo3bo7bobobo7bobobo7bobobo$9bobob3o2bo4b2obob
o5bo3b2o2bo4b2obobo6bo$6bo4bo6bob2o4bobob3ob2o6bob2o4bobob3o2bo$bo4bo
6bobobo3bo2bobo7bo4b2obo3b3obo8bo$bob2o3bo4bobo2bo5bo5b3obob3o3bo11b2o
3bo$bo3b3ob4o2bo2bo5bo9bo13bo10bo$bo12bo10b6obo2bo10b2ob5obobobo$o2b2o
bobob3obo7b2o8bo2bo19bobo$obo3bobo14bo2bobob2o17bo2b2obobob2o$2bobobob
ob7o9bobo4b4o11b2o$4bo21bo4b2o11bo6b4ob3o$b2obo3b2o5bo27b2o5bo4bo3b2o$
4bo8bobo30b3obo6bo$3obo2b3obobo2bo28bo6bo4bo$4bo6bo4bo24b3obo2b3obobo
2bo$5b3obo6bo4bo23bo8bobo$2b2o5bo4bo3b2obo20b2obo3b2o5bo$3bo6b4ob3o3bo
23bo$7b2o12bo21bobobobob7o$9b4obobob2o2bo18bobo3bobo$14bobo3bobo18bo2b
2obobob4o$6b7obobobobo21bo12b2o$18bo23bo3b3ob4o6bo$7bo5b2o3bob2o20bob
2o3bo4bo5b2o$7bobo8bo23bo4bo6bob3o$6bo2bobob3o2bob3o24bo4bo6bo$6bo4bo
6bo28bo2bobob3o2bob3o$6bo6bob3o30bobo8bo$3b2o3bo4bo5b2o27bo5b2o3bob2o$
5b3ob4o6bo11b2o4bo21bo$14b2o11b4o4bobo9b7obobobobo$3b2obobob2o2bo17b2o
bobo2bo14bobo3bobo$6bobo19bo2bo8b2o7bob3obobob2o2bo$4bobobob5ob2o10bo
2bob6o10bo12bo$4bo10bo13bo9bo5bo2bo2b4ob3o3bo$4bo3b2o11bo3b3obob3o5bo
5bo2bobo4bo3b2obo$4bo8bob3o3bob2o4bo7bobo2bo3bobobo6bo4bo$4bo2b3obobo
4b2obo6bo2b3obobo4b2obo6bo4bo$4bo6bobob2o4bo2b2o3bo5bobob2o4bo2b3obobo
$5bobobo7bobobo7bobobo7bo3bo8bo$5bobobo3b2o2bobobo3b2o2bobobo3b2o2bobo
bo3b2o5bo$7bobo7bobobo7bobobo7bobobo10bo$9bo2b2o3bo5bobob2o2bobo2b2o3b
o5bobob4obo$16bo2b3obobo4bo2bo6bo2b3obobo6bo$8b4o5bo7bobo2bo2bob2o4bo
7bob3o$14b2obob3o5bo5bo3b3obob3o$17bo9bo13bo9b2o$16bo2bob6o13bo2bob6o$
16bo2bo8b2o10bo2bo$20b2obobo2bo$15b4o4bobo$19b2o4bo!

Finally, a p384 loop with 4 turns and 12 flips; this also gives periods
24, 32, 48, 64, 96, 128, and 192:

x = 88, y = 64
38bo4b2o17bo4b2o$38bobo4b4o13bobo4b4o$35bo2bobob2o15bo2bobob2o$20bo2bo
10b2o8bo2bo10b2o8bo2bo$13b6obo2bo13b6obo2bo13b6obo2bo$11b2o9bo13bo9bo
13bo9bo$18b3obob3o3bo5bo5b3obob3o3bo5bo5b3obob2o$10b3obo7bo4b2obo2bo2b
obo7bo4b2obo2bo2bobo7bo5b4o$7bo6bobob3o2bo6bo2bo4bobob3o2bo6bo2bo4bobo
b3o2bo$7bob4obobo5bo3b2o2bobo2b2obobo5bo3b2o2bobo2b2obobo5bo3b2o2bo$7b
o10bobobo7bobobo7bobobo7bobobo7bobobo7bobo$7bo5b2o3bobobo2b2o3bobobo2b
2o3bobobo2b2o3bobobo2b2o3bobobo2b2o3bobobo$9bo8bo3bo7bobobo7bobobo7bob
obo7bobobo7bobobo$9bobob3o2bo4b2obobo5bo3b2o2bobo2b2obobo5bo3b2o2bo4b
2obobo6bo$6bo4bo6bob2o4bobob3o2bo6bo2bo4bobob3ob2o6bob2o4bobob3o2bo$bo
4bo6bobobo3bo2bobo7bo4b2obo2bo2bobo7bo4b2obo3b3obo8bo$bob2o3bo4bobo2bo
5bo5b3obob3o3bo5bo5b3obob3o3bo11b2o3bo$bo3b3ob4o2bo2bo5bo9bo13bo9bo13b
o10bo$bo12bo10b6obo2bo13b6obo2bo10b2ob5obobobo$o2b2obobob3obo7b2o8bo2b
o10b2o8bo2bo19bobo$obo3bobo14bo2bobob2o15bo2bobob2o17bo2b2obobob2o$2bo
bobobob7o9bobo4b4o13bobo4b4o11b2o$4bo21bo4b2o17bo4b2o11bo6b4ob3o$b2obo
3b2o5bo51b2o5bo4bo3b2o$4bo8bobo54b3obo6bo$3obo2b3obobo2bo52bo6bo4bo$4b
o6bo4bo48b3obo2b3obobo2bo$5b3obo6bo4bo47bo8bobo$2b2o5bo4bo3b2obo44b2ob
o3b2o5bo$3bo6b4ob3o3bo47bo$7b2o12bo45bobobobob7o$9b4obobob2o2bo42bobo
3bobo$14bobo3bobo42bo2b2obobob4o$6b7obobobobo45bo12b2o$18bo47bo3b3ob4o
6bo$7bo5b2o3bob2o44bob2o3bo4bo5b2o$7bobo8bo47bo4bo6bob3o$6bo2bobob3o2b
ob3o48bo4bo6bo$6bo4bo6bo52bo2bobob3o2bob3o$6bo6bob3o54bobo8bo$3b2o3bo
4bo5b2o51bo5b2o3bob2o$5b3ob4o6bo11b2o4bo17b2o4bo21bo$14b2o11b4o4bobo
13b4o4bobo9b7obobobobo$3b2obobob2o2bo17b2obobo2bo15b2obobo2bo14bobo3bo
bo$6bobo19bo2bo8b2o10bo2bo8b2o7bob3obobob2o2bo$4bobobob5ob2o10bo2bob6o
13bo2bob6o10bo12bo$4bo10bo13bo9bo13bo9bo5bo2bo2b4ob3o3bo$4bo3b2o11bo3b
3obob3o5bo5bo3b3obob3o5bo5bo2bobo4bo3b2obo$4bo8bob3o3bob2o4bo7bobo2bo
2bob2o4bo7bobo2bo3bobobo6bo4bo$4bo2b3obobo4b2obo6bo2b3obobo4bo2bo6bo2b
3obobo4b2obo6bo4bo$4bo6bobob2o4bo2b2o3bo5bobob2o2bobo2b2o3bo5bobob2o4b
o2b3obobo$5bobobo7bobobo7bobobo7bobobo7bobobo7bo3bo8bo$5bobobo3b2o2bob
obo3b2o2bobobo3b2o2bobobo3b2o2bobobo3b2o2bobobo3b2o5bo$7bobo7bobobo7bo
bobo7bobobo7bobobo7bobobo10bo$9bo2b2o3bo5bobob2o2bobo2b2o3bo5bobob2o2b
obo2b2o3bo5bobob4obo$16bo2b3obobo4bo2bo6bo2b3obobo4bo2bo6bo2b3obobo6bo
$8b4o5bo7bobo2bo2bob2o4bo7bobo2bo2bob2o4bo7bob3o$14b2obob3o5bo5bo3b3ob
ob3o5bo5bo3b3obob3o$17bo9bo13bo9bo13bo9b2o$16bo2bob6o13bo2bob6o13bo2bo
b6o$16bo2bo8b2o10bo2bo8b2o10bo2bo$20b2obobo2bo15b2obobo2bo$15b4o4bobo
13b4o4bobo$19b2o4bo17b2o4bo!

By adding more flips to these, we can get any track length of the form
292+92n gens, and oscillators of period P for any P>=13 that's not
divisible by 23.  To get periods divisible by 23, we need to use more of
the 27-gen turns; I haven't built such an oscillator.

The stators of all of these can probably be reduced.


Also, here's a drifty p12 that the program found; it also works as a p6:

x = 12, y = 12
3bo$3bobo$3bobobo$7bob3o$2b2o3bo$9b2o$b2o$8b2o$3obo$4bobobo$6bobo$8bo!

Dean Hickerson
dean@math.ucdavis.edu
