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'Life Digits'

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

'Life Digits'

Postby Lewis » June 7th, 2009, 8:44 am

Has anything been done regarding patterns from strings of digits, since the first 2 posts at http://pentadecathlon.com/lifeNews/restricted_patterns/ ?

The LifeWiki also sems to be missing a page on this, would it be worthwhile creating one?
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Lewis
 
Posts: 316
Joined: March 17th, 2009, 5:26 pm
Location: UK

Re: 'Life Digits'

Postby Nathaniel » June 7th, 2009, 9:01 am

Lewis wrote:Has anything been done regarding patterns from strings of digits, since the first 2 posts at http://pentadecathlon.com/lifeNews/restricted_patterns/ ?

The LifeWiki also sems to be missing a page on this, would it be worthwhile creating one?


This is actually on my personal to-do list for the wiki right now, as quite a few of these are known. Here's the "integer constructions" that come packed with Golly:

x = 809, y = 458, rule = B3/S23
14$12b3o12b3ob3o60b2o13b3ob3o46b2o15bobob3ob3ob3ob3obobob3obob3o33b2o
13bobobob3ob3ob3ob3obobob3ob3obobobobo37bo16bob3ob3obobob3ob3ob3ob3ob
3ob3obobobo25bo16bob3ob3ob3ob3obobobob3obobob3obobob3ob3ob3obob3ob3o
15b2o13bob3ob3ob3ob3ob3ob3ob3ob3obob3ob3o43b3o14bo$29bobobo59bo2bo14bo
bo48bo16bobo3bobo5bo3bobobo3bobobo34bo2bo12bobobobobobobobo3bobobobo3b
o3bobobobobo36bobo15bobobobobobobo3bo3bobobobobobobobo3bobobo24bobo15b
o3bobo5bo3bobobobobo3bobobobobobobobobobobobobobobo3bo14bo2bo12bobobo
3bobo5bobobobobobo5bobobo3bo62bo$27b3ob3o59bo2bo12b3ob3o47b3o13bobob3o
b3ob3o3bob3o3bobob3o32bobo13bob3ob3obobob3ob3ob3o3bob3obobob3o35bo2bo
15bob3ob3ob3ob3ob3ob3obobob3ob3ob3obo24bobo15bob3ob3o3bob3ob3obob3ob3o
bobob3obobobobobobobob3ob3o14bo2bo12bob3ob3ob3ob3obobob3ob3o3bobob3ob
3o41bo5bo12bo$27bo5bo60b2o15bobobo50bo12bobo3bo3bobo5bo3bo3bobobobo33b
o14bo3bo3bobobo3bo3bo3bo3bo3bobobo3bo36b2ob2o13bobobo3bo3bobo3bo3bobob
obobobo3bo3bobo25bob2o13bo3bobobo3bo3bo3bobo3bo3bobobo3bobobobobobobob
obobo3bo15b2o13bobobobo5bo3bobobobobobobo3bobobobobobo41bo5bo12bo$27b
3ob3o75b3ob3o49b2o12bobob3ob3ob3o3bo3bo3bobob3o30b3o15bo3bob3ob3ob3ob
3o3bo3bob3obobo3bo38bo2bo12bob3ob3o3bob3ob3ob3ob3ob3ob3o3bobo27bobo12b
ob3ob3o3bob3o3bobob3o3bob3o3bob3ob3ob3obob3ob3o30bob3ob3ob3ob3ob3ob3ob
3o3bobob3ob3o41bo5bo12bo$242bo96bobo82bo2bo86b4o$340bo84b2o86bo4bo98b
3o$513b2o2b2o8$676b3ob3o$676bobobobo$676b3obobo$678bobobo$676b3ob3o2$
612b2o$612b2o2b2o$616b2o7$13b2o12b3ob3o59b2o14b3ob3ob3o42bo16bob3ob3ob
3ob3ob3ob3ob3ob3o34b2o12b3ob3ob3ob3obobob3ob3ob3obobob3ob3ob3ob3ob3o
24b2o14b3ob3obobob3ob3ob3o47bo14b3ob3ob3obob3ob3obobob3ob3ob3ob3obobob
o26b2o2b2o12bob3ob3ob3obob3ob3ob3ob3obobobobo64b3ob3o$13b2o14bobobo58b
o2bo13bobobo5bo41bobo15bobobo3bobo3bobo3bobo3bobo3bo33bobo12bo5bo3bo3b
obobobo3bobo3bobobobobobo5bo3bobo25bo2bo15bo3bobobobo5bo3bo46bobo13bo
3bo3bobobobobobobobobo3bobobobobo3bobobobo26bo4bo12bo3bo3bobobobobo5bo
3bo3bobobobobo64bo5bo$29bobobo59bo2bo12b3ob3o3bo42bobo14bob3o3bob3ob3o
3bob3ob3ob3o32bobo13b3o3bob3ob3obobob3ob3ob3obobob3ob3o3bo3bob3o23b2ob
o13b3ob3ob3ob3ob3o3bo47b2o13b3ob3ob3obobobobobob3ob3ob3ob3ob3obob3o27b
4o13bob3ob3ob3obob3ob3ob3ob3obobob3o64b3o3bo$29bobobo60b2o13bobo3bo3bo
44bo14bobobo3bo3bo3bo3bo3bobobobo33bobo14bobo3bo3bo3bobobobobobobobo3b
obobobo3bo3bo3bobobo24bob2o14bobo5bobobo3bo3bo62bobo3bobobobobobobobo
3bo3bo3bo3bo3bobo3bo44bobo3bo5bobo3bobo5bo3bobobo3bo64bobo3bo$29bob3o
75b3ob3o3bo44bobo12bob3o3bob3ob3o3bob3ob3ob3o31bo16b3o3bob3ob3obobob3o
b3ob3obobob3ob3o3bo3bob3o24bo2bo12b3ob3o3bob3ob3o3bo45b4o13b3ob3ob3obo
b3ob3o3bob3ob3ob3ob3obo3bo27b4o13bob3ob3ob3obob3ob3ob3ob3obobo3bo64b3o
3bo$165b2o75b2o96b2o80bo4bo85bo3bo$422b2o2b2o85b2o5$616b2o$616b2o2b2o$
620b2o2$676b3ob3ob3ob3o$678bo3bobobo3bo$676b3ob3obobo3bo$678bobo3bobo
3bo$676b3ob3ob3o3bo7$615bo$614bobo$614bobo$615bo$13bo13b3ob3ob3ob3o53b
o13bob3ob3ob3obob3o34b2o15b3obob3ob3ob3ob3ob3ob3ob3ob3ob3obobobobo14b
2o16bobob3ob3obob3ob3ob3ob3obob3ob3ob3o37b2o13bobobobob3ob3ob3ob3ob3o
37b2o5b2o12b3ob3ob3ob3ob3ob3ob3o47b2o15b3obob3obob3ob3ob3obob3ob3o70b
3ob3o$12bobo14bobobobobobo54bobo12bo3bo3bobo3bobo36bobo16bobobobobobob
obobo3bo3bobobobo3bobobobobobobo14bobo15bobo3bobo3bobobobobobo3bo3bobo
bobo5bo36bo2bo12bobobobo3bo3bobobobobo3bo37bo7bo14bobo3bobobo5bo3bobob
o47b2o17bobobo3bobobobobobo3bo3bobo48b2o7b2o15bobobo$13bo13b3ob3obobob
3o51bobo13bob3o3bob3obob3o35bobo13b3obob3obobob3ob3ob3obobobobo3bobobo
bobob3o15b2o15bobob3ob3obobobobobob3ob3obob3ob3o3bo36bob2o12bob3obo3bo
b3obobobobob3o38b3ob3o15bob3ob3ob3ob3ob3ob3o51bo14bobob3obobobobobob3o
bo3bob3o45bo2bo5bo2bo14bob3o$29bo3bobobobobo50bobo14bobo5bo3bobo3bo36b
obo14bobobobobobobobobobo3bobobobobo3bobobobobo3bo17b2o13bobobo5bobobo
bobobo3bobobobo3bo3bo3bo33b2obo15bo3bobo3bobo3bobobobobo42bobo17bobobo
bobobobo3bobo3bobo47b5o14bobobobobobobobobobobobo3bobobo46b2o7b2o15bob
obo$27b3ob3ob3ob3o51bo15bob3o3bob3obob3o37b2o12b3obob3ob3ob3ob3ob3ob3o
b3o3bob3obobo3bo17bobo12bobob3ob3obob3ob3ob3ob3obob3ob3o3bo33bo2bo15bo
3bobo3bob3ob3ob3ob3o41bo18bob3ob3ob3ob3ob3ob3o46bo19bobob3obob3ob3ob3o
bo3bob3o72bob3o$246bo90b2o174bobob2o96bo$514b2ob2o95bobo$614bobo$615bo
7$676b3obobobob3obobo$676bobobobobo3bobobo$676b3ob3obo3bob3o$678bo3bob
o3bo3bo$676b3o3bobo3bo3bo11$13bo13b3obobo59b2o14bob3obobob3ob3ob3obobo
bobo24bo16b3ob3ob3ob3ob3obobob3obobob3ob3ob3ob3o20b2o12bob3ob3obob3ob
3ob3ob3ob3obob3o42bo15bobob3ob3obob3ob3o46b2o16bobobobob3ob3ob3ob3obob
3o44b2o2b2o12b3ob3obobobob3ob3ob3ob3obob3obob3obob3o38b2o16b3obob3ob3o
$12bobo14bobobo59bobo13bobo3bobo3bo3bobo3bobobobo23bobo17bo3bobobobobo
bo3bobo3bobobobobo3bo3bobobo17bo2bo13bobobo3bobobobobo3bobo3bobo3bobob
o40b5o13bobo3bobobobo3bo3bo45bo2bo15bobobobo3bobobo3bo3bobobobo44bo4bo
14bobo3bobobobobobobobobobobobo3bobobobobobobo38bobo17bobobobobobo$12b
2o13b3ob3o60bobo12bob3ob3ob3ob3ob3obobob3o24b2o17bob3obobobobob3ob3o3b
obobobobob3ob3ob3o16bobobo13bob3o3bobobobob3ob3ob3ob3obobobo39bo5bo12b
obob3obobobob3ob3o45bo2bo15bob3obob3obobo3bob3obobobo45b4o13b3ob3ob3ob
obobob3obobob3obob3obobobobob3o39b2o17bobobobob3o$27bo5bo61b2o12bo3bo
3bobo5bo3bobobo3bo26b2o15bobo3bobobobobobo3bo3bobobobobobo3bo3bobo17b
2ob2o12bobobo3bobobobo3bobobo3bobobobobobo40b5o13bobo3bobobobo3bobo48b
2ob2o13bo3bobobo3bobo3bo3bobobobo62bo5bo3bobobobobobobobobobobo3bobobo
bobobobo41b2o15bobobobobobo$27b3o3bo75bob3o3bob3ob3ob3obobo3bo26bobo
14bob3ob3ob3ob3o3bo3bobobob3ob3ob3ob3o34bob3o3bobob3ob3ob3ob3ob3obob3o
42bo15bobob3ob3obob3ob3o48bo2bo12bo3bobob3ob3o3bob3obob3o45b4o13b3ob3o
3bobob3ob3ob3ob3obob3obob3obob3o34b2o5bobo14bobob3ob3o$165bo258bo2bo
85bo4bo93bobo5b2o$425b2o86b2o2b2o94b2o$615b2o$615bobo$616b2o6$676bob3o
b3ob3ob3ob3obob3ob3ob3ob3ob3ob3obobob3obobob3obobobobo$676bobobobo3bo
3bobobobobobobobobo3bobobo3bo3bobobobobobobo3bobobobobo$676bob3ob3ob3o
b3ob3obobobobobob3ob3o3bob3obobobobob3ob3obobob3o$676bobobo3bo3bo3bobo
bobobobobobobo5bo3bo3bobobobobo3bo3bobobo3bo$676bob3ob3ob3ob3ob3obob3o
b3ob3ob3o3bob3obobob3o3bob3obobo3bo11$12b2o13bob3ob3o57bo15b3ob3ob3ob
3ob3ob3ob3o27bo2bo12bobobob3ob3ob3ob3ob3ob3obobobobobo26bo2bo12b3ob3ob
ob3ob3ob3obob3o52bo15b3ob3ob3ob3ob3ob3ob3ob3ob3ob3obobobob3ob3o15b2o
15bobob3obob3ob3o59b2o13bobob3ob3ob3ob3ob3ob3obo56b2o16bob3ob3ob3o$11b
o2bo12bobo5bo56bobo16bobo3bo5bo3bo3bobo29b4o12bobobo3bo3bobo3bo5bobo3b
obobobobo26b4o14bo3bobobobobobo3bobobobo50b5o15bo3bo3bobobobobo3bobo3b
obo3bobo3bobobo3bo3bo15bo3bo12bobo3bobobobo3bo59bobo12bobobo5bo3bobo3b
o3bobobo55bo2bo15bobo5bo3bo$12b2o13bob3ob3o57bobo13b3ob3ob3o3bob3o3bob
3o43b3obob3o3bob3ob3o3bob3ob3obob3o42b3ob3obobobob3ob3obob3o49bo5bo12b
3ob3o3bob3ob3ob3ob3ob3ob3ob3ob3obob3ob3o16b4o12bobob3obob3ob3o61bo12b
3ob3o3bob3ob3ob3ob3obo55bobo16bob3o3bob3o$27bobobo3bo59bo13bo5bo3bo3bo
3bo3bobobo29b2o14bobobo5bo3bobobo3bobobo3bobo3bo26b4o14bo3bobobobobobo
3bobobobo50bob3o13bo3bo5bo3bobobobo5bobobobo5bo3bobo3bobo34bobo3bobobo
bo3bo57b4o15bobobo3bobo5bobobobobobo53b2obo3bo13bobobo3bobo$27bob3ob3o
59b2o12b3ob3ob3o3bob3o3bob3o29b2o14bobob3o3bob3ob3o3bob3o3bobo3bo26bo
2bo12b3ob3obob3ob3ob3obob3o51b2o15b3ob3o3bob3ob3ob3ob3ob3ob3ob3o3bobob
3ob3o16b4o12bobob3obob3ob3o57bo18bob3o3bob3ob3ob3ob3obo52bo2bo3bobo12b
ob3o3bob3o$423bo3bo83b2obob2o94bobo3bo2bo$423b2o86bo2bob2o95bo3bob2o$
512b2o102bobo$615bo2bo$616b2o21$13b2o12b3obob3o59b2o12b3ob3obob3obobob
ob3ob3ob3ob3ob3obobobobo9b2o12bob3ob3obobob3obobob3obo40b2o12bobobobob
3ob3ob3obobob3ob3o48b2o14b3ob3obobobobobob3ob3ob3obobob3ob3ob3ob3obo
16b2o2b2o12b3obobob3obobobob3ob3ob3obobob3ob3obobobob3ob3ob3obob3o8b2o
b2o13bob3ob3ob3obob3ob3ob3ob3ob3ob3ob3ob3obo36b2o16bob3ob3ob3ob3ob3obo
$12bobo12bo3bobo62bo12bo5bobobobobobobobobobo3bo3bobo3bobobobobo9bo13b
obobobobobobobo3bobo3bobo39bobo12bobobobo3bo3bobo3bobobo5bo48bobo15bo
3bobobobobobo3bobo3bo3bobo3bobo3bo3bobobo16bo4bo14bobobobobobobobo3bo
3bobobobobobo3bobobobobobo3bo5bobo3bo8b2ob2o13bo3bobobobobobobobobobob
o5bo3bobobo3bobo3bo35bo2bo15bobo5bobo3bo3bo3bo$12b2o13b3obob3o59bo13b
3ob3obobobob3obobobob3ob3obobob3obobob3o6b2obo13bobobob3ob3ob3ob3ob3ob
o39b2o13bob3obob3ob3ob3ob3ob3ob3o50bo13b3ob3obob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3obo17b4o13b3ob3obobob3obob3ob3obobob3ob3ob3obob3ob3ob3o3bobob3o
26bob3ob3obobobobobobobob3o3bob3ob3o3bob3obo35bo2bo15bob3ob3ob3ob3ob3o
bo$29bobobobo56bobo16bobo3bobobo3bobobobobobo3bobobo3bobobo3bo5bo2bo
14bobobobobo3bobobo3bobo3bo37b2o15bo3bobobo3bo5bo3bo3bobo52b2o12bo5bob
o3bo3bo3bo3bo3bo3bo3bo3bobobobobobo36bo3bobobo3bobobo3bo3bobo3bo3bo3bo
bo3bo3bobobo3bobobo10b5o13bo3bobobobobobobobobobobobo3bobo3bobo3bo3bob
o36b2ob2o13bobobo3bo3bobobobobobo$27b3obob3o56b2o15b3ob3obob3o3bobob3o
b3ob3ob3ob3obobo3bo6b2o15bob3ob3o3bob3o3bob3obo36bobo15bo3bobob3ob3ob
3o3bob3ob3o47b2obo13b3ob3obo3bo3bob3ob3ob3o3bob3ob3ob3ob3obo19b2o13b3o
3bob3o3bobob3ob3ob3o3bob3ob3obo3bob3ob3o3bobob3o7bo5bo12bob3ob3ob3obob
3ob3ob3o3bob3ob3o3bob3obo38bo2bo12bob3ob3ob3ob3ob3obo$242b2o94bo2bo82b
o2bo84bobo2b2o99bo2bo$339b2o84b2o86b2o104b2o$609b2o$608bo2bo$608bo2bo$
609b2ob2o$611bo2bo$611bo2bo$612b2o17$13bo13b3obobob3o56b2o13bob3ob3ob
3ob3ob3o31b2o16b3ob3ob3obobob3ob3ob3ob3ob3ob3ob3o21b2ob2o12bobob3obob
3obobob3ob3ob3ob3o47b2o13b3ob3ob3ob3obob3o49bo14bobobob3ob3obob3ob3ob
3ob3obobob3o35b2o15b3ob3ob3ob3ob3ob3ob3ob3ob3ob3obobobobo32bo7bo15bobo
b3ob3ob3o$12bobo14bobobo3bo57bo13bobo5bo3bobobobo34bo16bo3bo3bo3bobobo
bobo3bo3bobo3bobo5bo22bob2o12bobo3bobo3bobobo3bobo3bo3bobo46bo2bo14bob
obobobo3bobobobo48bobo13bobobobobobobobo3bobobobobo3bobobobobo34bobo
15bo5bobobobobo3bobobo3bobobo3bobobobobobobo30b3o7b3o13bobo3bobobobobo
$11bobo13b3ob3ob3o56bo14bob3o3bo3bob3ob3o32bobo14b3ob3ob3ob3obobob3ob
3ob3ob3ob3ob3o22bo15bobob3obo3bobobob3ob3ob3ob3o47b3o12b3ob3obobo3bobo
b3o48bo2bo12b3obobobob3obob3ob3ob3ob3obobobobo34bo4bo12b3ob3obobob3ob
3ob3ob3ob3ob3obobobobob3o29bo13bo12bobob3obobobobo$12bo14bo5bo3bo56bob
o12bo3bo3bo3bo3bobobo33bobo15bo3bo3bo3bobobo3bo3bo3bo3bo3bo3bo23b3o12b
obo3bobo3bobobo3bo3bobobo3bo64bobobobobo3bobobobo49b3o14bobobobobobobo
3bobobobobo3bobobobobo35b5o12bobo3bobobobobo3bobobo3bobobo3bobobobobo
3bo29b2o11b2o12bobo3bobobobobo$27b3o3bob3o57b2o12bob3o3bo3bob3ob3o34bo
bo12b3ob3ob3o3bob3ob3ob3ob3ob3ob3ob3o25bo12bobob3obo3bobobob3ob3ob3ob
3o47b3o12b3ob3ob3o3bobob3o66bobob3ob3obob3ob3ob3ob3obobob3o52b3ob3ob3o
b3ob3ob3ob3ob3ob3ob3obobo3bo56bobob3ob3ob3o$165bo173bo2bo82b3o86b5o$
340b2o82bo2bo85bo4bo$424bobo86bobo$425bo88b2o3$607b2o11b2o$607bo13bo$
608b3o7b3o$610bo7bo16$13bo13b3ob3ob3ob3o53b2o12bobob3obob3ob3ob3ob3ob
3ob3ob3obobo13bo15bob3ob3ob3ob3ob3obob3obob3ob3obobob3obobobobobo13bo
12bobobob3ob3ob3obobob3obobob3obobobobo36bo17bobobob3obobob3obobob3ob
3ob3ob3o33b2o13bob3ob3ob3ob3obob3ob3ob3ob3ob3ob3ob3ob3ob3obo15b2o3b2o
12b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3obob3o$11bo2bo12bobobo3bobobo
55bo13bobo3bobobobobobo3bobo3bobo3bobobobobo12bobo14bobo3bo5bobobo3bob
obobobo3bo3bobobobo3bobobobobo11b3o12bobobobobo3bobo3bobo3bobobobo3bob
obobo35bobo16bobobobobobobobo3bobobo3bobo3bo3bo32bo2bo12bobobobobo3bo
3bobo3bobobobo3bo3bobobobobo5bobobobo15bobobobo12bo5bobobobobobobobobo
bobobobobobobobobobobobobobobobobo$11bo2bo12b3ob3ob3ob3o50b2obo13bobob
3obobobob3ob3ob3obobob3obobob3o11bobobo13bob3ob3ob3ob3ob3obob3obob3ob
3ob3ob3ob3obob3o10bo15b3obobobo3bob3ob3ob3ob3ob3obobob3o35bobo16b3obob
obob3ob3ob3ob3obobo3bob3o32b3o13bob3obobob3o3bobob3obobob3ob3ob3ob3ob
3ob3obobobo17bobo14b3ob3obobob3obobobobobobobobobobobobob3obobobobobob
obo$12bo14bobobobo3bobobo50bobo14bobobo3bobobobobo3bo3bobobobo3bobo3bo
12bo2bo13bo3bo3bobo5bobo3bo3bobobo3bo5bobobo3bobo3bo10b2o16bobobobo3bo
3bo3bobo5bo3bobobo3bo36b2ob2o15bobobobo3bobobo3bo3bobobo3bobo32b2o16bo
bobobobo3bo3bobobo3bobobobobobo3bobobobobo3bobobobo16b2ob2o13bobo3bobo
bobobobobobobobobobobobobobobobobobobobobobobobo$27b3ob3ob3ob3o67bobob
3obob3ob3ob3ob3ob3ob3ob3o3bo15b2o12bob3ob3ob3ob3ob3obob3obob3ob3o3bob
3o3bobo3bo11bo16bobob3o3bob3o3bob3o3bob3obobo3bo39bobo14bobob3o3bob3o
3bob3ob3o3bob3o31bob2o13bob3ob3ob3o3bobob3ob3ob3ob3ob3ob3ob3ob3ob3obo
17bobo14b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3obob3o$245bobo92bobo80bo
2bo85bobobobo$246b2o93bo82b2o86b2o3b2o19$611bo5bo$611bo5bo$611b2o3b2o
2$607b3o2b2ob2o2b3o$11b2o14b3ob3ob3obo52b2o15b3ob3ob3ob3ob3ob3ob3obobo
b3ob3o17b2o12b3obob3ob3obobob3obobob3ob3ob3ob3o23b2o15bob3ob3ob3ob3ob
3ob3obob3obobobob3ob3o35b2o13b3ob3ob3obob3ob3ob3obobobob3ob3obobo26bo
15b3ob3ob3ob3ob3ob3ob3obobobob3ob3obobob3ob3ob3ob3o10b2o4b2o12bob3ob3o
b3ob3ob3ob3ob3ob3ob3obob3ob3ob3ob3o23bobobobobobo14b3o$11bo17bobo5bobo
52bo18bobobo3bobobo3bobobobobobobobo3bo18bobo12bobobo3bobo3bobobo3bobo
3bo3bobo5bo23bo3bo12bobobobobobo5bobobo3bobo3bobobobobo3bo36bo2bo14bob
o5bobo3bobobo3bobobobobo5bobobo26b3o13bo3bo3bo3bobobo3bobo3bobobobobob
o3bobobobobo3bobo3bobo10bo3bo2bo12bobobobobo3bobobo3bobobo3bo3bobobobo
bobo3bo3bobobo25b2o3b2o16bobo$14bo12b3ob3o3bobo53bobo15bobobob3obobob
3obobobobob3ob3ob3o16bo14b3obob3ob3ob3ob3ob3ob3ob3ob3o3bo24b4o12bobobo
bobob3ob3ob3ob3obo3bobob3ob3ob3o34b3o15bob3ob3obob3ob3ob3obobobob3o3bo
b3o29bo12b3ob3ob3ob3ob3obobob3ob3obob3o3bobobobobob3ob3ob3o11b6o13bob
3obobob3obobob3obobob3ob3ob3obob3o3bob3obobo48bobo$13b2o14bobobo3bobo
56bo14bobobobo3bobobo3bobobobo3bo3bo3bo17bo15bobobo5bo3bobobo3bo3bobo
3bobo3bo40bobobobobobobo3bobobobo3bo3bobo3bo3bobobo52bobobobo3bo3bo3bo
bo3bobobobobo3bo3bo26b3o13bobobobobobo3bo3bobobo3bo3bobo3bo3bobobobobo
3bo3bo3bo30bobobobobo3bobobo3bobobo3bo3bobobobobobo3bobo3bobo25b2o3b2o
16bobo$27b3ob3o3bobo55b2o14bob3ob3ob3ob3ob3ob3o3bob3ob3o14b3o14b3obob
3ob3o3bob3o3bob3ob3ob3o3bo24b2o14bob3ob3ob3ob3ob3ob3obo3bobo3bob3ob3o
34b3o15bob3ob3obob3ob3ob3obobobob3o3bo3bo25bo16b3ob3ob3ob3ob3ob3ob3o3b
obob3o3bobobob3ob3ob3ob3o11b6o13bob3ob3ob3ob3ob3ob3ob3ob3ob3obob3o3bob
3ob3o23bobobobobobo14b3o$162bo81b2o92bo2bo82b3o84bo3bo2bo88b3o2b2ob2o
2b3o$339b2o86bo83b2o4b2o$424b3o184b2o3b2o$424bo186bo5bo$611bo5bo16$
620bo$619bobo3$619b3o$13b2o12bob3ob3obob3ob3o49b2o12b3ob3ob3ob3obobob
3ob3ob3ob3ob3o16b2o13bobobobobobob3ob3ob3obobob3ob3ob3obobobob3ob3ob3o
5b2o17bob3ob3ob3obobob3ob3ob3ob3o46b2o14bob3ob3ob3ob3ob3ob3ob3o37bo18b
ob3ob3ob3ob3ob3ob3ob3obob3o37b2o3b2o12bob3ob3ob3obob3ob3obob3ob3ob3obo
49b3o12bobobobobob3obobob3obob3ob3ob3ob3ob3obobobob3ob3obobobobobobob
3obob3ob3obo$11bo2bo12bobobobo3bo3bobo50bobo12bobo3bo3bobobobobo3bo3bo
bobo3bobo18bobo12bobobobobobobobo3bobobobobobobobo3bo3bobobobobobo3bob
o5bobo16bo3bo3bo3bobobobo3bobobo5bo46bo2bo12bobobobobo3bobobo3bobobo3b
o36bobo17bobobobobo3bo3bobobo3bobo3bobo39bobobobo12bobobobobobobobobob
obobobobobobobobobobo50bo13bobobobobobo3bobobobobobobobobo3bo3bobobobo
bobo3bobobobobobobobobo3bobo3bo3bobo$11b2o14bob3ob3obo3bob3o48bo14b3ob
3ob3obobob3ob3ob3ob3ob3ob3o18bo12bobobob3obobobob3ob3ob3obobob3ob3obob
obobobob3ob3o7bo16bob3o3bo3bob3ob3obobob3ob3o47b3o12bob3obobob3obobob
3ob3ob3o36bo2bob2o13bob3ob3ob3ob3obobob3ob3obob3o39bobo14bob3obobobobo
bobobobobobobobobobob3obo64bob3ob3ob3ob3ob3obobobobobob3ob3obobob3obob
3ob3obob3ob3obo3bobo3bo3bobo$27bobobobobobo3bobobo49bo13bobo3bo3bobobo
3bobo5bo3bo3bo3bo17bo13bobobo3bobobobobo5bo3bobobobobo3bobobobobobobob
obobo7b3o14bobo5bo3bo3bo3bobobo3bo3bo62bobobobobo3bobobo3bobobo3bo37bo
bobobo12bobobo3bo3bo3bobobo3bo3bobo3bo39bobo14bobobobobobobobobobobobo
bobobobobobobobo64bo3bo3bo3bo3bobobobobobobobo3bo3bobobo3bobobo5bobo3b
o3bobo3bobo3bo3bobo$27bob3ob3obo3bob3o50bo12b3ob3ob3ob3o3bob3ob3ob3ob
3ob3o14bobo14bobobo3bobob3ob3ob3o3bob3ob3ob3obobobob3ob3ob3o10bo13bob
3o3bo3bo3bob3ob3ob3ob3o47b3o12bob3ob3ob3ob3ob3ob3ob3o38b2o3bo12bob3ob
3ob3ob3ob3ob3ob3obob3o38b2ob2o13bob3ob3ob3obob3ob3obob3ob3ob3obo50bo
13bo3bo3bob3o3bob3obob3ob3ob3ob3ob3o3bobob3ob3obo3bo3bobo3bobo3bo3bobo
$95b2o65b2o81bobo91bo2bo81b3o87bobo102b3o$246bo92b2o83bo89bobo102b3o$
512bobobobo$512b2o3b2o$619bobo$620bo20$13b2o12b3obobobob3ob3ob3ob3ob3o
b3obobobobo27bo13bobobobob3ob3o38b2ob2o12b3ob3obob3ob3ob3ob3ob3ob3ob3o
b3ob3obo18b2o14b3ob3ob3obobobobob3ob3ob3ob3ob3ob3ob3obob3ob3obobob3ob
3o8bo3b2o12bobob3ob3ob3obob3ob3ob3ob3ob3ob3ob3ob3obobo17b2o13bobobobob
3ob3ob3ob3ob3ob3ob3obobobo30bobobobo13b3ob3ob3obob3ob3ob3ob3obobobobo
41bobo22bob3ob3ob3ob3ob3ob3ob3ob3ob3obobob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3obobob3ob3obob3o$13bo15bobobobobobobo5bobo3bo5bobobobobo26bobo
12bobobobo3bobo41bobo15bo3bobo3bo3bobobobo3bo5bobobobo3bobobo17bo2bo
15bobobobo3bobobobo3bo3bo3bo3bo3bobobobobobo3bobo3bobobobobobo7bobobob
o12bobo3bobobo3bobo3bobobo3bobobo3bobobobo3bobobobo16bo2bo12bobobobobo
bobobobobobobobobo3bo3bobobobo29bob2ob2obo14bobobo3bobobobobobobobo3bo
bobobobo39bo3bo22bobobobobo3bo3bobo5bo3bo3bobo3bobo3bobobobo3bo3bo3bo
3bo5bobo3bo3bo3bo3bobo3bobo3bobobo$14bo12b3ob3obob3ob3o3bob3ob3ob3obob
ob3o25bobo13b3ob3o3bob3o39bo2bo12b3ob3obo3bob3ob3ob3ob3o3bobobob3ob3ob
o18b2obo14bob3ob3obob3obob3ob3ob3ob3ob3obobob3obob3ob3ob3obobob3o7bobo
bo14bobob3obobob3obo3bob3o3bobobob3obobob3ob3ob3o15bo2bo13b3obobobobob
obob3obobobobob3ob3obobobo29bo7bo14bobobob3obobobobobobobob3obobob3o
32b2o5bo26bob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o3bobobob3ob3ob3ob3ob3ob3ob3o
b3ob3ob3ob3o3bob3obob3o$13b2o14bo3bobo3bo3bo3bobobo3bobo3bobo3bo24bobo
16bo3bo3bobobo40b2o15bo3bobo3bobo3bobobobo3bo3bobobobobobobobo21bo14bo
3bobobobo3bobobo3bo5bo3bo3bobobobobobobo5bo3bobobobobo8b2ob2o13bobo3bo
bobobo3bo3bo3bo3bobobobo3bobobobo3bo3bo15b3o16bobobobobobobobobobobobo
bo3bo3bobobobo30b7o15bobobo3bobobobobobobobo3bobobo3bo32b2o4bo4bo8b2o
12bo3bobobo3bobo3bobo3bobo3bo5bo3bo3bobobobobobobobobobobobobobo3bobob
obobobobobo3bo3bobobobobobo$27b3o3bobob3ob3o3bob3ob3ob3obobo3bo24b2o
17bo3bo3bob3o55b3ob3obo3bob3ob3ob3ob3o3bob3ob3ob3obo18b3o15bob3ob3obo
3bobob3ob3ob3ob3ob3ob3ob3obob3ob3o3bob3ob3o26bobob3ob3ob3obo3bob3o3bob
3ob3ob3ob3ob3o3bo34bobobob3ob3ob3ob3ob3ob3ob3obobobo52bob3ob3obob3ob3o
b3ob3obobo3bo39bo12b2o12bob3ob3ob3ob3ob3ob3ob3ob3ob3o3bo3bob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3o3bo3bob3obob3o$244bo178b3o85b7o89bo3bo$423bo2bo
83bo7bo90bobo$424bo2bo82bob2ob2obo$425b2o84bobobobo20$593b2o2b2o4bo2b
2o12b2o$593b2ob2o6b2obo12b2o$13bo13b3ob3o59bo15b3obobob3ob3ob3obo35bo
13b3ob3obob3obobobob3obobobo38b2o12bob3ob3ob3ob3ob3ob3ob3ob3obobob3ob
3obobob3ob3ob3obobobob3o9b2o13b3ob3obobobob3ob3obob3obobob3ob3obobobob
ob3o14bo19b3ob3ob3ob3obob3ob3obob3ob3ob3ob3o114bobo6bo27b3ob3ob3ob3ob
3obobob3ob3ob3obob3o$12bobo12bo3bobo59b3o15bobobobobobo3bobobo34bobo
14bobo3bo3bobobobo3bobobobo36bo2bo12bobo3bo5bobo3bobobo3bo3bo3bobobo5b
obobobobobo3bo3bobobobobo5b2obo2bo12bo3bobobobobo3bo3bobobo3bobo3bo3bo
bobobobo3bo13bobo18bo3bo3bobobobobobobobo3bobobobo3bobobobo115b2o4b3o
29bobobo3bo3bobobobobo3bo3bo3bobobobo$11bo2bo12b3obobo62bo12b3ob3ob3ob
3ob3obo33bo2bo14bob3obob3obob3o3bobob3o35bob2o13bob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3o3bobobobobob3ob3obob3ob3o6bobo2bo12b3obobob3obob3ob3obob3ob
3ob3ob3obobob3o3bo13bo2bob2o14b3ob3ob3obobobob3ob3obobobob3ob3ob3o151b
3ob3o3bob3obobobobob3ob3ob3obobobo$12b2o13bobobobo59b3o13bo5bo3bobobob
obobo33bobo15bobobobo3bobo3bo3bobo3bo35bo16bobobobobo3bo3bo3bobobobobo
bobo3bobobo3bobobobobobobobobobo3bobobo6bo2b2o13bobobobo3bobobo5bobo3b
o3bobo5bobobo3bo3bo14bobobobo13bobobobo3bobobobo3bobobobobobobobo3bo3b
o115b2o4b3o29bo3bo3bo3bobobobobo3bo3bo3bobobobo$27b3ob3o59bo15b3o3bob
3ob3ob3obo32b2ob2o14bob3obob3obo3bo3bobo3bo36b3o13bob3ob3ob3ob3ob3ob3o
b3ob3o3bob3o3bobobob3ob3ob3obo3bob3o5b2o17b3ob3o3bobob3ob3obob3o3bob3o
b3obobo3bo3bo15b2obo2bo12b3ob3ob3ob3obob3ob3obob3ob3ob3ob3o114bobo6bo
27b3ob3o3bob3ob3obobob3ob3ob3obob3o$246bo178bobo168b2o6b2obo12b2o$426b
o170b2o4bo2b2o12b2o22$593b2o2b2o4bo2b2o12b2o$593b2ob2o6b2obo12b2o$13b
2o12b3ob3ob3o54b2o15bob3ob3obob3obob3ob3o31b2o12bob3ob3ob3ob3ob3ob3ob
3obobobob3obobo23b2o13b3ob3ob3ob3ob3ob3obobobob3ob3obo42b2o12bobobobob
3obobob3obobob3ob3ob3obobobob3ob3obo17b2ob2o12bobobob3ob3ob3ob3ob3obob
3ob3o122bobo6bo27b3ob3obobob3obob3ob3obobob3ob3ob3obob3o$12bobo12bo3bo
bo3bo55bo15bobobobobobobobobo3bobobo32bo12bobobobo3bobo3bobobobo3bobob
obobobo3bobo23bobo14bobobobobo3bo3bobo3bobobobo3bobobo38b2obobo12bobob
obo3bobobo3bobobobo5bo3bobobobobobo3bobo17bo3bo12bobobobobobobo3bobobo
3bobo3bo3bo123b2o4b3o29bo3bobobobobobo3bobobobobo3bo3bo3bobobobo$11bob
o13b3ob3o3bo55bobo13bob3obobobob3obob3ob3o29b3o13bob3ob3ob3o3bobobob3o
bobobobobob3ob3o25bo12b3ob3ob3ob3ob3ob3ob3obob3ob3obo38b2obo14bob3obob
3ob3o3bob3ob3o3bob3ob3obob3o3bobo18b3o13b3obobobob3ob3obobob3obob3ob3o
159b3ob3obobobobobob3obobobobob3ob3ob3obobobo$12bo16bobobo3bo56bobo12b
obobobobobo3bobo3bobobo29bo15bobobo3bobobo3bobobo3bobobobobobobobo3bo
21b4o15bobobo3bobo5bo3bo3bobobobobobobo41bo14bo3bobobo5bo3bo3bo3bo3bo
3bo3bobobobo3bobo36bobobobobobo3bobobo3bobo3bobo125b2o4b3o29bo3bobobob
obobo3bobobobobo3bo3bo3bobobobo$27b3ob3o3bo57b2o12bob3ob3obob3obob3ob
3o27bobo15bob3ob3ob3o3bob3ob3ob3obobobob3o3bo21bo16b3ob3ob3ob3ob3ob3o
3bobob3ob3obo41bobo12bo3bobob3o3bo3bo3bob3o3bob3o3bobob3o3bobo18b3o15b
obob3ob3ob3ob3ob3obob3ob3o122bobo6bo27b3ob3obobob3obob3ob3obobob3ob3ob
3obob3o$161b2o81bo96b2o80bo3bo165b2ob2o6b2obo12b2o$243b2o178b2ob2o165b
2o2b2o4bo2b2o12b2o24$11bo15bob3ob3obobob3ob3ob3o44bo12bob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3o11b2o2b2o12b3obob3ob3ob3ob3ob3obob3ob3obo30bo13b3ob3o
b3ob3ob3ob3obob3obobob3ob3obo37b2o13bobobob3obob3ob3ob3obobob3obobob3o
bob3ob3obo15b2o17b3ob3ob3ob3ob3ob3obob3ob3obo$11b3o13bobobobobobobobo
3bo5bo42b3o12bobobo3bo3bo3bobobo3bobo3bo3bobo3bo11bobo2bo14bobobo3bobo
bobobobo3bobobobo3bobo29bobo14bo3bo3bo3bobobobo3bo3bobobobo3bobobo36bo
2bo12bobobobobobo3bo3bobo3bobobo3bobo3bobobobobo3bo15bobo16bo3bo3bobo
3bobobobo3bobobo3bobo$14bo12bobobob3ob3ob3ob3o3bo41bo15bob3ob3ob3ob3ob
obo3bob3ob3obobob3o13bobo13b3obob3ob3obobob3o3bobobobob3obo28bo2bo12b
3o3bo3bob3obobob3obo3bob3ob3ob3obo36b4o12b3obobobobo3bob3ob3ob3ob3ob3o
b3obob3ob3obo17bo2b2o12b3ob3ob3o3bob3ob3obob3o3bobo$13b2o12bobobobobo
3bo3bo3bo3bo40bobo14bo3bo3bo3bo3bobobo3bobobo3bobobo3bo13b2o14bo3bo3bo
3bobobo3bo3bobobobo3bobo27bob2o13bo5bo3bo3bobobo3bobo3bo3bobobobobobo
54bobobobobo3bo3bobobo3bo3bo3bobo3bo3bobobobo15bobobobo12bobo3bobobo3b
o3bobobobo3bo3bobo$27bob3ob3o3bob3ob3o3bo41b2o14bob3ob3ob3ob3ob3o3bob
3ob3ob3ob3o29b3obob3ob3ob3ob3o3bobob3ob3obo26bobo15b3o3bo3bob3ob3ob3ob
o3bo3bob3ob3obo36b2o16bobob3obo3bob3ob3o3bob3o3bob3obob3ob3obo15b2o2bo
14b3ob3ob3o3bob3ob3obob3o3bobo$242bobo93bo2bo83bobo$243bo95b2o85b2o24$
12b2o13b3ob3ob3ob3ob3ob3ob3ob3obobob3obobobob3ob3obobobo6bo16bob3ob3ob
3obobob3ob3ob3ob3ob3obobobobo11b2o12bobobob3obobob3ob3ob3ob3ob3ob3ob3o
b3o22bo13b3ob3obob3ob3o60b2o2b2o12bobobob3obobobobob3ob3ob3ob3ob3ob3ob
3ob3obo20bo13bob3ob3ob3obobob3ob3obob3obobobo$12bo14bo3bobobo3bo5bo3bo
bobo3bobobo3bobobobo3bobo3bobobo5bobo15bobo3bobobobobobo3bobo3bobobobo
bobobobobobo10bobo12bobobo3bobobo3bo3bobo5bo3bobobo3bo3bo21bobo14bobo
3bobobobobo60bobo2bo12bobobobo3bobobobo3bobobobobo3bobobobobobo3bobobo
19bobo12bo3bobo3bo3bobo3bo3bobo3bobobobo$13bo13b3obobob3ob3ob3o3bobobo
b3ob3o3bob3obob3ob3obob3o6bo2b2o12bob3ob3ob3ob3ob3ob3ob3ob3obobobobob
3o10bo14bob3o3bob3ob3ob3ob3ob3ob3obobob3ob3o20bo2bo14bob3obobobob3o62b
2o14bob3ob3ob3ob3ob3obobob3ob3ob3ob3ob3ob3obo18bo2bo12bob3ob3ob3ob3ob
3o3bobo3bobob3o$14bo12bobobobobobo3bobo5bobobobo5bo3bo3bobo3bobobobo3b
o7b2obo12bo3bo3bo3bo3bo3bo3bo3bo3bobobobobo3bo9b2o14bo3bo3bo3bo3bobo5b
o3bobo3bobobo5bo19bob2o15bobobobobobo3bo62bo15bo3bobobo3bo3bo3bobobo3b
obo3bobobobobobobobobo14b2o2bobo13bo3bo3bo3bo3bobo5bobo3bobo3bo$13b2o
12b3ob3ob3ob3ob3o3bob3ob3o3bo3bo3bobob3ob3obo3bo23bob3ob3ob3o3bob3ob3o
b3ob3ob3obobo3bo9bo15bo3bo3bo3bob3ob3ob3ob3ob3ob3ob3ob3o18bobo17bob3ob
ob3ob3o60bobo15bo3bob3o3bo3bob3ob3ob3ob3ob3ob3ob3ob3obo14bobob2o14bob
3ob3ob3o3bob3o3bobo3bobo3bo$164bo76bo2bo92b2o83bo$163b2o77b2o176bobo$
420b2o!


I might even add what number syntheses are known to the synthesis box on the pattern sidebar (I'd have to rename it from "Glider synthesis" to just "Synthesis" of course, and then list the different types of syntheses). Thoughts on that?
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Re: 'Life Digits'

Postby Lewis » June 7th, 2009, 9:38 am

Do you know how the syntheses for each object were found? The smaller ones (numbers <100) were most likely found by hand, but the larger numbers seem too complex to be found without computer searches etc.

I might even add what number syntheses are known to the synthesis box on the pattern sidebar (I'd have to rename it from "Glider synthesis" to just "Synthesis" of course, and then list the different types of syntheses). Thoughts on that?

That sounds like a good idea. Would we just put the lowest number that creates that pattern alone in the synthesis box, or all known numbers that produce the object by itself?
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Re: 'Life Digits'

Postby dvgrn » June 7th, 2009, 10:24 am

> Has anything been done regarding patterns from strings of digits, since the
> first 2 posts at http://pentadecathlon.com/lifeNews/restricted_patterns/ ?

Not too much, to my knowledge. Recent results are mostly catalogued on Dean Hickerson's Web page, which has moved to

http://radicaleye.com/DRH/digits.html

There was some discussion this March about finding an integer that produced not just unlimited growth, but a quadratic growth rate. But most quadratic-growth patterns aren't exactly easy to construct with the kind of slow-salvo recipes that Dean Hickerson figured out how to produce from integers. Here's the most constructible one I know of, Mitchell Riley's 38-cell switch-engine breeder from July 2006, as a glider recipe:
#C 21 gliders in two perpendicular salvos = quadratic growth
x = 255, y = 64, rule = B3/S23
137bo$138boo$137boo8$112bo$110bobo$111boo$252bobo$252boo$253bo$$120bo$
112bo5bobo$110bobo6boo$111boo128bo$241bobo8bobo$241boo9boo$253bo$$120b
o$118bobo$bbo116boo$obo238bo$boo238bobo$182bobo56boo$182boo$183bo3$
101bo$99bobo$100boo$219bobo$219boo$220bo$$109bo$107bobo$108boo$208bo$
65bo142bobo$63bobo142boo$64boo$185bobo$185boo$186bo$$73bo$71bobo$72boo
$174bo$174bobo$34bo139boo$32bobo$33boo$147bo$147bobo$147boo!

Seems vaguely possible that an integer could be coaxed to produce something like this, but it would be quite an effort. There's only one degree of freedom for each of the components -- where you construct the glider/LWSS determines when you have to build it, and vice versa. That doesn't leave a lot of leeway.

However, it's certainly possible to use an integer to build a 'seed' pattern for the above, as slowly as necessary, and then trigger the seed with one final glider. Here's a suboptimal sample -- I'm sure this could be reduced quite a bit:
#C 5 beehives and 75 blocks produce a quadratically expanding
#C population when hit by a trigger glider
x = 221, y = 173, rule = B3/S23
148boo$148boo3$143boo$143boo3$159boo$159boo$177bo$154boo20bo$154boo9b
oo9b3o$165boo$$153boo5boo$153boo5boo$$167boo$159boo6boo$159boo3$171boo
4boo$171boo4boo4$174boo$170boobboo5boo$170boo9boo4$178boo$174boobboo5b
oo$174boo9boo$$109boo$109boo$113boo67boo$113boobboo59boobboo$117boo59b
oo4$174boo$174boo4$178boo$178boo9$149boo$149boo4$153boo$153boo9$124boo
$124boo$$193boo24boo$193boo24boo$128boo$128boo$$184boo$87boo95boo33boo
$87boo130boo$$210boo$185boo23boo$91boo92boo$91boo$206boo$206boo5$219b
oo$161boo56boo$161boo10boo$173boo35boo$210boo$$161boo41boo$141boo18boo
41boo$141boo4$132boo70boo$132boo70boo$$127boo66boo$127boo66boo$133boo$
133boo57boo$192boo$$127boo$101boo24boo$101boo$118boo54boo29boo$118boo
54boo29boo$96boo72boo$96boo68boobboo24boo$166boo28boo$114boo31boo13boo
$114boo31boo13boo3$151boo$139bo11boo$138bobo$138bobo$129boo8bo$117boo
4boo4boo34boo4boo$117boo4boo40boo4boo$$133boo$121bo11boo$107boo11bobo$
107boo11bobo$121bo$$111boo$99bo11boo$98bobo$98bobo$99bo4$78boo$78boo3$
82boo$70bo11boo$69bobo$69bobo$70bo3$9boo$9boo3$13boo$bo11boo$obo$obo$b
o!

Building all the blocks and beehives one at a time is a tedious but not too terribly painful exercise, given the tools described on the 'digits' Web page. Most of the job could even be automated with an integer-making utility -- maybe a Golly script?
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Re: 'Life Digits'

Postby knightlife » June 7th, 2009, 11:28 am

I might even add what number syntheses are known to the synthesis box on the pattern sidebar (I'd have to rename it from "Glider synthesis" to just "Synthesis" of course, and then list the different types of syntheses). Thoughts on that?


Is the following "synthesis" or is it just a "glider precursor"?

#C glider precursor is the number 5
#CXRLE Pos=-3,-4
x = 4, y = 8, rule = B3/S23
4o$o$o$3o$3bo$3bo$o2bo$b2o!

I tried different fonts until the digit 5 yielded a glider, but I would call the pattern a precursor, not synthesis. Don't get me wrong, I am fascinated with the standard life digits and how patterns can be engineered from them (synthesis) but what about the letters? Nobody came up with letters because they realized it would be hard to chose a standard font, and you could go crazy trying to find a standard font for letters.

Synthesis is the process of creating from basic elements, so are the digits of the "life digits" font really basic elements? In a sense they are because they are about as basic as you can get when trying to find the simplest set of digits.

Actually, it would be a lot of fun to engineer patterns by spelling words :)
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Re: 'Life Digits'

Postby DivusIulius » June 7th, 2009, 12:26 pm

Hmm... For nostalgy reasons, mostly, hereby, I suggest the ZX Spectrum font http://www.urbanfonts.com/fonts/ZX_Spectrum.htm as a potential candidate.

Just kidding... or not.

Something to begin with: the 26 Capital Letters

#CXRLE Pos=1,1
x = 206, y = 6, rule = B3/S23
b4o3b5o4b4o3b4o4b6o2b6o3b4o3bo4bo3b5o7bo2bo3bo3bo7bo4bo2bo4bo3b4o3b5o
4b4o3b5o4b4o3b7obo4bo2bo4bo2bo4bo2bo4bo2bo5bob6o$o4bo2bo4bo2bo4bo2bo3b
o3bo7bo7bo4bo2bo4bo5bo9bo2bo2bo4bo7b2o2b2o2b2o3bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo10bo4bo4bo2bo4bo2bo4bo3bo2bo4bo3bo6bo$o4bo2b5o3bo7bo4bo2b5o3b5o
3bo7b6o5bo9bo2b3o5bo7bob2obo2bobo2bo2bo4bo2bo4bo2bo4bo2bo4bo3b4o6bo4bo
4bo2bo4bo2bo4bo4b2o6bobo6bo$6o2bo4bo2bo7bo4bo2bo7bo7bo2b3o2bo4bo5bo4bo
4bo2bo2bo4bo7bo4bo2bo2bobo2bo4bo2b5o3bobo2bo2b5o8bo5bo4bo4bo2bo4bo2bo
4bo4b2o7bo6bo$o4bo2bo4bo2bo4bo2bo3bo3bo7bo7bo4bo2bo4bo5bo4bo4bo2bo3bo
3bo7bo4bo2bo3b2o2bo4bo2bo7bo2bobo2bo3bo3bo4bo5bo4bo4bo3bo2bo3bob2obo3b
o2bo6bo5bo$o4bo2b5o4b4o3b4o4b6o2bo8b4o3bo4bo3b5o3b4o3bo4bo2b6o2bo4bo2b
o4bo3b4o3bo8b4o3bo4bo3b4o6bo5b4o5b2o5bo2bo3bo4bo5bo4b6o!


Each ZX Spectrum font letter fits inside a 8 x 8 square. The external bits are normally empty...

OOOOOOOO
OXXXXXXO
OXXXXXXO
OXXXXXXO
OXXXXXXO
OXXXXXXO
OXXXXXXO
OOOOOOOO


... except for letters I T and Y, that use the final column. Therefore in the code above, letter A starts at column 0 and ends at column 7, letter B starts at column 8 and ends at column 15, ..., letter Z starts at column 200 and ends at column 207.

I ignore their fate. :lol:
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Re: 'Life Digits'

Postby knightlife » June 7th, 2009, 1:27 pm

How about the ultimate in simplicity, restricting digits to the simplest possible "0" and "1"----- a blinker would be a "1" and the smallest square (3x3) that can have a hole in it would be a "0". Being stuck with binary is overly restrictive and uninteresting although it might be interesting to prove that nothing of interest can be done with it. :)

The standard "life digits" however, can produce some results in binary.

dual pulsars -- 1100011101
escaping gliders -- 1011100011011110

Here is a challenge:
Using the standard "life digits" what is the smallest number base that can produce infinite growth?

Ternary anyone?
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Re: 'Life Digits'

Postby Lewis » June 7th, 2009, 1:54 pm

What program was used to find the digits for the small patterns on http://radicaleye.com/DRH/digits.html , and if it isn't available anywhere on the web, are there any other programs (or scripts for Golly) that will do the same job?
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Re: 'Life Digits'

Postby DivusIulius » June 25th, 2009, 4:59 am

knightlife wrote:Here is a challenge:
Using the standard "life digits" what is the smallest number base that can produce infinite growth?

Binary: the 16-"bit" string is "0011001000100011" is minimal.
http://infinitegrowth.wordpress.com/2009/06/25/life-digits/
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Re: 'Life Digits'

Postby DivusIulius » June 26th, 2009, 5:10 am

knightlife wrote:Ternary anyone?

The 11-trit string 21011121122 is minimal (it produces a block-laying switch engine).
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Re: 'Life Digits'

Postby knightlife » July 5th, 2009, 11:14 pm

I did a search of the binary digits for the smallest pattern that generates (non-glider) spaceships.
I was interested in the possibilities of engineering new patterns, as done with the normal base ten "life digits".
To do this requires a pattern starting and ending with 0's that can be embedded in a "sea of 1's".
The ones quickly die out and the embedded patterns take over.
Strings of 0's turn into burning fuses, not too useful for construction.
The smallest (non-glider) spaceship generating binary pattern that starts and ends with zero is surprisingly small indeed - 000011000
It generates an LWSS traveling parallel to the string of digits and a lot of other debris (unfortunately).

The following shows two such patterns embedded in a string of binary digits which is basically a "sea of 1's".
The two ends of the string are terminated with a 01010 pattern to eliminate debris at the ends:

x = 259, y = 5, rule = B3/S23
3obob3obob3obobobobobobobobobobobobobobobobobobobobob3ob3ob3ob3obobob
3ob3ob3obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobob3ob3ob3obobob3ob3ob3ob3obobobobobobobob
obobobobobobobobob3obob3obob3o$obobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobo$3obob3obob3obobobobobobobobob
obobobobobobobobobobobob3ob3ob3ob3obobob3ob3ob3obobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
b3ob3ob3obobob3ob3ob3ob3obobobobobobobobobobobobobobobobob3obob3obob3o
!


The two LWSS's collide to generate two gliders cleanly.
I am not sure that universal construction can actually be done with binary digits, but life is full of surprises. :)
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Re: 'Life Digits'

Postby DivusIulius » July 8th, 2009, 4:03 pm

Minimum numbers:

Base 02: 16-digits: 0011001000100011
Base 03: 11-digits: 21011121122
Base 04: 10-digits: 0023321310
Base 05: 08-digits: 40101123
Base 06: 07-digits: 0253033
Base 07: 07-digits: 0051165
Base 08: 07-digits: 140732
Base 09: 07-digits: 140732
Base 10: 06-digits: 140732

How about 154299? http://pentadecathlon.com/lifeNews/restricted_patterns/

Well, definitively, the smallest number which shows infinite population growth is not 154299. :)
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Re: 'Life Digits'

Postby knightlife » July 10th, 2009, 10:20 am

DivusIulius wrote:

Well, definitively, the smallest number which shows infinite population growth is not 154299.


Nice work. It seems that switch engines are not that hard to come by (154299 is less than 10% bigger than 140732).
It makes me wonder what the second smallest binary digits number to produce infinite growth is, after 0011001000100011.
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Re: 'Life Digits'

Postby DivusIulius » July 10th, 2009, 6:31 pm

It makes me wonder what the second smallest binary digits number to produce infinite growth is, after 0011001000100011.


After 0011001000100011 (16 digits), I found that the third smallest is 001010010001001100 (18 digits).

Note that 1100010001001100 (the mirror image of the smallest one) is the second smallest. :|
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