Interesting Patterns in Normally Expanding Rulesets

For discussion of other cellular automata.
Post Reply
User avatar
Extrementhusiast
Posts: 1801
Joined: June 16th, 2009, 11:24 pm
Location: USA

Interesting Patterns in Normally Expanding Rulesets

Post by Extrementhusiast » January 11th, 2010, 12:12 am

Wow, that was a long title. Anyway, I have many oscillators and still lifes in various rulesets discovered by hand. Usually, spaceships are not mine.
B34678/S125 (probably already posted elsewhere):

Code: Select all

x = 314, y = 142, rule = B34678/S125
84bobo24bo6bo$83bo3bo22b3o4b3o$111bobo2bobo$83bo28b2o2b2o$83bo9bo18bob
2obo$92bo14bo2b3o4b3o2bo$83bo3bo3bo18b2o2b2o2b2o$84bobo3bo16bob3ob4ob
3obo$89bo18b4o6b4o$88bo3bobo13bo2bo6bo2bo$87bo3bo3bo13bo10bo$86bo22bo
10bo$95bo12b3o8b3o$94bo13b2o10b2o$93bo15b2o8b2o$92bo15bob2o2b2o2b2obo$
91bo18bo3b2o3bo$109bobo6bobo$60b4o27bo18bobob2obobo$92bob2o16bo4bo2$
41bobo18bo$40bo3bo18b2obo$61bobo$40bo20b4o2bo$40bo9bo11bob3o$49bo11bo$
40bo3bo3bo12bo3bo$41bobo3bo14b2o2bo$46bo16b2obo$45bo18bo$44bo3b2obo11b
2o$43bo8bo9b2o2$52bo7bo6bo$51bo10b4o$61bob2obo166bo15bo15bo$51bo8bo6bo
166bo15bo15bo$52bo9b4o169bo15bo15bo$236bo15bo15bo$52bo116bobo65bo15bo
15bo$48b2obo116bo3bo65bo15bo15bo$239bo15bo15bo$168bo9b2o4bo2bo52bo15bo
15bo$169bo7bo2bo3bo3bo52bo15bo15bo$170bo7b2o62bo15bo15bo$bobo167bo44b
2o25bo15bo15bo$o3bo167bo71bo15bo15bo$214bo30bo15bo15bo$o167bo3bo6bo34b
o31bo15bo15bo$o9bo158bobo8bo66bo15bo15bo$9bo171bo34b2o30bo15bo15bo$o3b
o3bo11b2o3b3o3b2o149bo66bo15bo15bo$bobo3bo14bo7bo152bo30bo35bo15bo15bo
$6bo14b3o5b3o152bo29bo36bo15bo15bo$5bo3bo4bo5bo2bo5bo2bo152bo66bo15bo
15bo$4bo4bo4bo5b3o2bobo2b3o153bo66bo15bo15bo$3bo18bobobobobo156bo66bo
15bo15bo$11b2o10bobobobo158bo66bo15bo15bo$22bo2b3o2bo158bo66bo15bo15bo
$14bo242bo15bo15bo$14bo10b3o230bo15bo15bo$24bo3bo230bo15bo15bo$23bob3o
bo230bo15bo15bo$23b2o3b2o231bo15bo15bo$24b2ob2o124b2obo105bo15bo15bo$
157bo105bo15bo15bo$25bobo236bo15bo15bo$157bo107bo15bo15bo$156bo109bo
15bo15bo$267bo15bo15bo$156bo111bo15bo15bo$157bo111bo15bo15bo$270bo15bo
15bo$157bo113bo15bo15bo$153b2obo115bo15bo15bo$273bo15bo15bo$274bo15bo
15bo$275bo15bo15bo$276bo15bo15bo$152bo3bo120b2o14b4o12b5o$153b2o2bo
119bo15bo15bo$153bo11bo127bo15bo$156bo8b2o126bo15bo$152bo2b2o6b2ob2o
141bo$153bo3bo6b2o$165bo11bo4bo$177bo4bo2$179b2o31b2o2$182bo27bo4bo$
182bo27bo4bo2$151b2o59b2o2$149bo33bo6bo5bo13bo4bo$149bo32bo5b2o6bob2o
10bo4bo$180bo8bo7bo$151b2o28bo5bo7b2obo13b2o$179bo6bo11bo$154bo23bo$
154bo2$151b2o$211bo2bo$210bob2obo$157bo53bo2bo$154b2o55bo2bo$155b3o52b
ob2obo$211bo2bo4$192bobo$191bo3bo2$195bo$194bo$193bo$192bo$191bo2$164b
2o25bo$192bob2o$154bo4bo2bo4bo$154bo4bo2bo4bo2$156b2o6b2o37bo$203bo9bo
8bo14bo$159bo2bo4bo24bo9bobo17bo14bo$159bo2bo4bo24bo8bo3bo6b3o6bobo4b
4o4bob2o3b2o4b2obo$190b2ob2o4b2o2bo2b2o2bob3obo2b2obob2o2b4o2b2obo5bo
5bob2o$164b2o26bo8bo3bo6b3o6bobo12bo7b2o$192bo9bobo17bo13bo$203bo9bo8b
o$203bo2$158b2o$159bo2$157b2o!
B3/S0123:

Code: Select all

x = 437, y = 240, rule = B3/S0123
56bob2o$56b2obo$54b2o4b2o$55bo5bo$54bo5bo$54b2o4b2o$56bob2o$56b2obo$
60b2o$61bo$60bo$60b2o$56bob2o$56b2obo66$403b2obo6b2obo8b2obobobobo$
403bob2o6bob2o8b2obobobobo$407b2o2b2o17bobob3o$407bo3bo13b6obo$408bo3b
o17b2ob2o$407b2o2b2o14b5o$403b2obo6b2obo15b3o$403bob2o6bob2o10b4o$407b
2o8b2o12b2o$407bo9bo9b3o$408bo9bo11b3o$407b2o8b2o8b2o$403b2obo6b2obo
12b4o$403bob2o6bob2o12bo2bo4$45bo3bo266b2o4b2obo$40bo2bo3bo3bo2bo261bo
5bob2o$40b15o262bo2b2o4b2o14b2o3bo$316b2o2bo5bo18bo$40b10obob2o266bo5b
o10bob7o$51bobo21bo15bo224b2o2b2o4b2o10bobo$40b8obobobo9bo3bo9bo2b2o3b
2o2bo226bo3bo5bo13bob5o$27bo2bob2o15bobob2o8b3o2bo7b2o5bo5b2o11bo214bo
3bo5bo12b2o$27b4obo7b6obobobobo12b2o10b11o13bo213b2o2b2o4b2o16b5o$3b2o
bo25bo14bobobobo9b2o13bo9bo11bobob2o214bo5bo11b7o$3bob2o6b2o12b4ob2o6b
4obobobobob2o11b2o8bobob5obobobo11bo213b2o3bo5bo16bobo$7b2o4bo18bo12bo
bobobobo9b2o13bobobo3bobo13bobo211bo3b2o4b2o12b5obo$7bo8bo10b2obobo7b
2obobobobobobo8bo2b3o9b2obobobobob2o14bo212bo4b2obo20bobo$8bo6b2o13bob
2o9bobobobobob2o8bo3bo10bobobobobobo15b2o32b2obo174b2o4bob2o14b7obo$7b
2o18b2obobo7b2obobobobobobo22bo13bo48bobo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o169bo$3b2obo23bobo10bobobobobobo85bob33o165bo3b2o$3bob2o23bob2o9bobob
obobob2o83b2o$b2o136bob33o$bo137bobo$2bo135b2obob31o$b2o136bobobo$3b2o
bo109bo20bobobobob29o$3bob2o111bo2bo2bo2bo9bobobobobo$111b2ob16o9bobob
obob27o$112bobo24bobobobobo$112bobob14o13bobobo2b24o$111b2obo22b7obobo
bo$95bobo14bobob14o15bobobobo2b20o$86bo2bo2bo2bobo14bobobo22b7obobobo$
86b10obobobo9b2obobob12o17bobo3bo2b18o$97bobobo10bobobo22b9ob4o$69bo
16b10obobob2o9bobo5b10o28b16o$30b2o39bo2bo22bobobo9b2ob5o20b14o20bo$
28bo25bo9b2ob10o9b10obobobo18b10o23bo4b14obobo$2b2obo6bo2bo2bo9b6ob2o
18bo9bobo29bobob2o8b9o19b15o2bo14bobo$2bob2o6b7o14bobo11b2obo3b2o9bobo
b8o9b10obobobo19b9o26bob12obob2o$6b2o20b4obobo12bobo13b2obo27bobobobo
9b7o21b17obo11bobobo$6bo5b3ob3o14bob2o9bobobob4o9bobob8o9b8obobobob2o
14bo2bobobobob2o27bobob7obobobo$7bo6bobo11b3o17bobobo12bobobo23bo3bobo
bo9b6o3bobobobobo10b17obobobo5bobobob2o$6b2o4b2o3b2o15b3o11bo5b2o8b2ob
obob6o9b6o2bo4bobo14bobobobobobobo28bobobobobobobobobo$2b2obo9bo12b2ob
o14bobo3bo12bobobo23bo3bobob2o8b4obobobobobobob2o9b17obobobobobobobobo
bo$2bob2o6b7o10bobob4o11bo5b2o9bobo5b4o9b8obobobobo12bo42bobobobobobob
obob2o$6b2o21bobo16bobobo11b2ob5o23bobobobo9b2obo24b17obobobobobobobob
obo$6bo5b7o9b2ob6o9bobobob4o17b4o9b10obobob2o9bo44bobobobobobobobobo$
7bo4bo2bo2bo17bo11bobo13b9o24bobobo10bo26b17obobobobobobobobob2o$6b2o
25b2o12b2obo3b2o17b4o9b10obobobo55bobobobobobobobobo$2b2obo49bo8b9o3bo
20bobob2o36b17obobobobobobobobobo$2bob2o48bo18b2o11b12obobo53bobobobob
obobobobob2o$66b6o27bobo37b5ob9obobobobobobobobobobo$66bo2bo16b12obob
2o52bobobobobobobobobobo$86bo2bo2bo6bo39b15obobobobobobobobobob2o$94b
2o3bo41bo2bo2bo2bo2bobo$153bobo7$2o3b2o29bo66bo7bo14bo$2o3b2o5b2obobob
obobo12bo18bo16bobo17bo12bobobo18bo2bo$13bobobobobobo11b2obo16b3o12b3o
bo13bo3bo3bo7b2obob2o11bob8o$2o3b2o6bobobobobob3o12bo5bo8b2o19bobo11b
3obobo10bobo14bobo$obobobo5b2obobo3bo13b4obobo13b2o12b3obobo15bob2o9bo
bob4obo9bob8o$2bobo8bobob3ob5o14bob2o9b3o18bo13b3obobo9b2obo4bobo8b2ob
o$b2obo8bobo19b4o17b2o12b2o2bo19bo10bo4bobo11bobob8o$5b2o5b2ob11o15b3o
9b2o31b5obob2o9bo4bob2o8bobobo$6bo6bo21b3obo17b3o10b2ob4o15bobo9b2ob2o
bobo11bo3b10o$5bo7bob11o13bob3o9b3o32bobobobo10bo4bobo11b2o$5b2o5b2obo
2bo3bo2bo9b3obo18b2o10b5o13bobobob2o7bobob4ob2o15bobobobo$6bo13bo16bob
5o9b2obo48bo6bo9b6obobobobo$5bo48bobob2o12bo31b2o3b2obo16bobobob2o$5b
2o34b3o8bo3bo55b2o8b8obobobo$41bo14bo55bo18bobobo$114bo7b10obob2o$122b
o2bo$128b2o250b2o$384bo2bo$358b2o4b2obo12b8o$358bo5bob2o10b3o$359bo2b
2o4b2o12b6o$358b2o2bo5bo9b4o$363bo5bo13b5o$358b2o2b2o4b2o8b5o$3b2obo
13bo337bo5b2obo14bob4o$3bob2o5bo2bo2bo340bo4bob2o8b6o$b2o9b8o338b2o2b
2o4b2o14b4o$bo360bo5bo9bobobo$2bo11bob6o336b2o3bo5bo8bobobob4o$b2o14bo
340bo3b2o4b2o7b2obobo$3b2obo12bo339bo4b2obo10bobobob4o$3bob2o7b2o342b
2o4bob2o10bobobo$7b2o5bobo2bo357b2obobob4o$7bo4bobo367bo3bo$8bo3bob8o
360bo5bo$7b2o10bo$3b2obo9b2o$3bob2o8$43bobobobobobobobobobobobobobob2o
$43bobobobobobobobobobobobobobobo$45bobobobobobobobobobobobobobo$41b5o
3bobobobobobobobobobobob2o$5bob2o38bobobobobobobobobobobobobo$5b2obo
21b2o11b5obobobobobobobobobobobobobo$3b2o26bo17bobobobobobobobobobobob
o$2bobo15bobobobob3o12b5obobobobobobobobobobo2bob4o$2bo17bobobobobo20b
obobo3bobobobobo2bobobo2bo$b2o13bobobobobobo2b2o12b7ob2ob3o5bobobobobo
bo$3b2obo9bobo8bobo24bo3bobobobobobobob2o$3bob2o8b2o2bobobobobobo13b
12obobobobobobobobobo$b2o4b2o8bobobobobo28bobobobobobobobobobo$bo5bo7b
3obobobobo17b10obobobobobobobobobob2o$2bo5bo5bo39bobobobobobobobobobo$
b2o4b2o5b2o27b10obobobobobobobobobobo$3b2obo47bobobobobobobobobob2o$3b
ob2o36b10obobobobobobobobobobo$44bo2bo2bo3bo19bo$42bo11bo6$3bob2o9bo$
3b2obo7b3o2bo2bo$7b2o10b6o$8bo7b3o$7bo12b5o$7b2o7b2o$5b2o14bob2o$6bo9b
2o$5bo14b5o$5b2o9b3o$3b2o14b6o$4bo9b3o2bo2bo$3bo12bo$3b2o!
Edit: Nathanial, could you move this topic to the "Other Cellular Automata" forum?
I Like My Heisenburps! (and others)

Sokwe
Moderator
Posts: 1493
Joined: July 9th, 2009, 2:44 pm

Re: Interesting Patterns in Normally Expanding Rulesets

Post by Sokwe » January 11th, 2010, 1:51 pm

The first has a lot of room for new spaceship discoveries:

c/2 orthogonal spaceships (periods 2-6):

Code: Select all

x = 380, y = 57, rule = B34678/S125
355b2o2$353bo$353bo2$2b2o351b2o2$5bo347bo4bo$5bo347bo4bo$242bo4bo$2b2o
238bo4bo107b2o2$o203bob4o2b4obo26b2o$o202b7o2b7o$204bob3o4b3obo29bo
122b4o$2b2o199bo2bobob2obobo2bo28bo121bob2obo$204bob2o6b2obo151b2o2b2o
$206bo8bo154bo2bo$205bobo6bobo$182b2o26b2o159b2o$149bo12bo15bo3b2o3bo
18bo3b2o3bo$148b3o10b3o$149bo12bo15bob2o2b2obo18bob2o2b2obo151b2ob4ob
2o$149bobob2o2b2obobo15b2o2b2o2b2o18b2o2b2o2b2o150bob8obo$150bo3b4o3bo
17b2o4b2o20b2o4b2o151b4ob2ob4o$151bobob2obobo19bo4bo22bo4bo153bobo4bob
o$151b2o2b2o2b2o207b2ob2ob2o$152b2o4b2o16bo5b2o5bo14bo5b2o5bo151bo4bo$
153b2o2b2o19bob6obo18bob6obo153bob2obo$127b2o6b2o17b4o18bob3o4b3obo14b
ob3o4b3obo153b2o$126b3o2b2o2b3o17b2o19b3o2bo2bo2b3o14b3o2bo2bo2b3o151b
ob2obo$126bobobo2bobobo16b4o19bo3bo2bo3bo16bo3bo2bo3bo154b2o$61bo9bo6b
obo3bo3bobo39bo2bo20bo2bo20bob2o2b2obo18bob2o2b2obo154bo2bo$63bo5bo57b
obo4bobo17bo2bo19b2o3b2o3b2o16b2o3b2o3b2o153bo2bo$61bobo5bobo6bo2bo2bo
2bo2bo36b3o4b3o15b3o2b3o18b3o4b3o18b3o4b3o152b3o2b3o$61b3ob3ob3o7b2obo
bobob2o38bo6bo15bobob2obobo18bo6bo20bo6bo111bo40bobob2obobo$62bobo3bob
o8b2o2bobo2b2o59bo12bo202bo12bo$64bo3bo11b2o5b2o16bo6bo15bo6bo15bo8bo
18bo6bo20bo6bo94b3o11bo5bo37bo8bo$63bo5bo11bobobobo16b3o4b3o13b3o4b3o
13bob2o4b2obo16b3o4b3o18b3o4b3o109bobo38bob2o4b2obo$4bo41bobo15bobobo
12b3ob3o17bobo2bobo15bobo2bobo16bobo2bobo19bobo2bobo20bobo2bobo64b3o
18bo8b3o14bo41bobo2bobo$3b3o76bo3bo19b2o2b2o17b2o2b2o18b2o2b2o21b2o2b
2o22b2o2b2o85b3o8bo15bo42b2o2b2o$3bo2bo39bobo16bobo15bobo20bob2obo17bo
b2obo18bob2obo21bob2obo22bob2obo65b3o17bo2bo23bo42bob2obo$5bobo5bobo
31bo18bo17bo16bo2b3o4b3o2bo7bo2b3o4b3o2bo8bo2b3o4b3o2bo11bo2b3o4b3o2bo
12bo2b3o4b3o2bo61bo20bobo5bobo10b2obobob2o33bo2b3o4b3o2bo$4bobob2o13bo
b2o5b2obo5bob2o5b2obo6bob2o5b2obo5bob2o5b2obo13b2o2b2o2b2o13b2o2b2o2b
2o14b2o2b2o2b2o17b2o2b2o2b2o18b2o2b2o2b2o59b2o7b2o14bobob2o20bo40b2o2b
2o2b2o$6bob2o5bo9bobo3bobo9bobo3bobo10bobo3bobo9bobo3bobo12bob3ob4ob3o
bo7bob3ob4ob3obo8bob3ob4ob3obo11bob3ob4ob3obo12bob3ob4ob3obo56b2o2bobo
2b2o16bob2o5bo11bo2bo2bo34bob3ob4ob3obo$6bobo2b4o8bo3b2ob2o3bo5bo3b2ob
2o3bo6bo3b2ob2o3bo5bo3b2ob2o3bo11b4o6b4o9b4o6b4o10b4o6b4o13b4o6b4o14b
4o6b4o56b3o7b3o15bobo2b4o54b4o6b4o$3bobob4o3bo9b3ob3ob3o7b3ob3ob3o8b3o
b3ob3o7b3ob3ob3o12bo2bo6bo2bo9bo2bo6bo2bo10bo2bo6bo2bo13bo2bo6bo2bo14b
o2bo6bo2bo34bo8bo12bob3o3b3obo12bobob4o3bo13bobobo36bo2bo6bo2bo$3bobob
ob2ob2o10b4o3b4o7b4o3b4o8b4o3b4o7b4o3b4o13bo10bo11bo10bo12bo10bo15bo
10bo16bo10bo33bo12bo14bobobo16bobobob2ob2o16bo39bo10bo$2bob2ob4ob2o12b
2obob2o11b2obob2o12b2obob2o11b2obob2o15bo10bo11bo10bo12bo10bo15bo10bo
16bo10bo34bo10bo12bo3bobo3bo12bob2ob4ob2o10bo11bo33bo10bo$4b3o17bo9bo
7bo9bo8bo9bo7bo9bo12b3o8b3o9b3o8b3o10b3o8b3o13b3o8b3o14b3o8b3o32b3o8b
3o11b3obobob3o14b3o17bob3o3b3obo32b3o8b3o$5b2ob2o2bo12bo3bo3bo9bo3bo3b
o10bo3bo3bo9bo3bo3bo13b2o10b2o9b2o10b2o10b2o10b2o13b2o10b2o14b2o10b2o
32b2o10b2o12bo2b3o2bo16b2ob2o2bo10bobo3b3o3bobo31b2o10b2o$6bo3b2obo13b
obobo13bobobo14bobobo13bobobo16b2o8b2o11b2o8b2o12b2o8b2o15b2o8b2o16b2o
8b2o34b2o8b2o14b2o3b2o18bo3b2obo11bob2o3b2obo34b2o8b2o$5b2obobobo12bob
2ob2obo9bob2ob2obo10bob2ob2obo9bob2ob2obo13bob2o2b2o2b2obo9bob2o2b2o2b
2obo10bob2o2b2o2b2obo13bob2o2b2o2b2obo14bob2o2b2o2b2obo32bob2o2b2o2b2o
bo12b2ob3ob2o16b2obobobo13b2ob3ob2o34bob2o2b2o2b2obo$5b3o2b3o12b3obob
3o9b3obob3o10b3obob3o9b3obob3o15bo3b2o3bo13bo3b2o3bo14bo3b2o3bo17bo3b
2o3bo18bo3b2o3bo36bo3b2o3bo15bob3obo17b3o2b3o14bob3obo37bo3b2o3bo$7bo
3bo14bo5bo11bo5bo12bo5bo11bo5bo15bobo6bobo11bobo6bobo12bobo6bobo15bobo
6bobo16bobo6bobo34bobo6bobo13bob2ob2obo18bo3bo14bob2ob2obo35bobo6bobo$
6bobobo16bobobo13bobobo14bobobo13bobobo17bobob2obobo13bobob2obobo14bob
ob2obobo17bobob2obobo18bobob2obobo36bobob2obobo16b5o19bobobo17b5o38bob
ob2obobo$8bo20bo17bo18bo17bo21bo4bo17bo4bo18bo4bo21bo4bo22bo4bo40bo4bo
19b3o22bo20b3o41bo4bo!
c/3 diagonal spaceships:

Code: Select all

x = 134, y = 97, rule = B34678/S125
128bo$126b2o$126bo$125bobo$125b2obo$126b4o3bo$123b2o3bobobo$116b2o4bo
3bob2ob2o$118bo3bobo4b2o$117bobo2b4obo$113b2ob3ob3obo2bo$13b2o99b8ob4o
$113bo2bobo2b3o$16bo95bo4bob2ob2o$16bo95b3ob3obobobo$107bo3b2o6bob3obo
$13b2o94bo2b4o3b2ob3obo$106bo2b3o7bob3o2bo$16bo90b2obob3o2bo4bo$16bo
90b3ob2ob2obobo2b2o$106b2obo3bobobobobobo$13b2o90bob3o4b2ob4o$105b3obo
bo2bobobo$104bo2b3o5b2o$102bo4bo2b5ob2o$102bo2b4obobob2o$100b3obo3b8o
2bo$99bo3b3o2bo2bobo2bo$98b3obob3obo2b2o$98bo2bobob3o2bo$93bo4bobob3ob
o$94bobo4bobobob3o$93bob3obob2obo2bo$95b3ob2o2bobobo$91bo4b2ob3o3b2o$
91bo3b4o4b3o$90bo2b3ob5o$88b3o4b2ob5o$87bo4bo3b3ob2o$87bobo2bobo2bo4bo
$85b4o8bo3bobo$83bobo4bobob2o$80bobo5bo9b2o$79bo6bo5bo3b2o$78bo3b3o9bo
bo$78b2ob3ob3o3bobo2bo$77b3obob2o3bo4b3o$78b2obo6bobo2bo$77bo2b2o6bo3b
2o$78bo8bobo$73b5obo7b3o2bo$73b4o4b2o5b2obo$71b7ob4o2b4o$70bobo4b2ob2o
3bo5bo$73b2obob2obobo2b3obo$69bo2bo4b4o3bob4o$70bo2bo2bobob2obobobo$
67bo4b6obob3o$68b3o3b3o4b3o$70b2obob2o2bob3o$69b2ob3ob2obob3o$68b3ob2o
2bobob2o$65bo3bobo2bo6bo$62bo2bo2bo3b4obo2bo$59bo2b8ob3obo2bo$57b3o2bo
b2obob2obo2bo$56bob3obobo2b3o6bo$55bob2o3bo6bo$55b3ob2o4bo2b4o$53b4o2b
obo2bo2b3o$54bo2bob5o5bo$54bob2o5bo2b5o$54bo2b3obob2o$56bo2bo3bobobo$
12bob2o39b4ob2ob3ob3o$11bo3bo38bobo2bobo4b3o$13bo39bobobobob3ob2obo$
11b2o42b2ob3obob2obo$9b3o36b2obo3b3obo4b3o$9bo4bo33b2o2bobo3bo2b4o$7b
4obo29bo3bo3bob2o3bo6bo$6bob2o3b2o6b2o19bobobob4ob2o$5bo2b2o2bo2bobo4b
o19b3o5b3o2bo$5b3o4bo2bo4bo22bo3bo2b4o$3b4obobo2b2obo2bo2bo17bo4b2o5bo
b2o$2bobobobobo7b2obo21bob3o4bob2o$7bob4o3bobo21bob3ob3obo$o3b4ob2o3b
5o21bo2bo2b4o2b2o$o3b2ob2o2b2ob3o23bo2bo4b2o$obo5b3o2bo2bo23b3obo2bo3b
2o$b2obo4bob3obo25b2o2b4ob2o$b4o3b2o2b3o23bo2b4o2bo3b3o$2b5ob2ob2o24bo
b2ob3o$3b3o6bo26bobo2b4obo$4b4o3bo25b2ob2o$5b2o31b2o2bo$7b3o29bobo!
c/4 orthogonal spaceship:

Code: Select all

x = 26, y = 28, rule = B34678/S125
o4bo$o4bo2$2b2o2$5bo$5bo4$19b3o$18b2ob2o$18b5o4$19b3o$19b3o$15b2o2bobo
2b2o$15b2o2bobo2b2o2$16b2o2bo2b2o$15bo3b3o3bo$17bo5bo$17b2obob2o$18bo
3bo$15bobob3obobo$17bo5bo!
-Matthias Merzenich

User avatar
Lewis
Posts: 320
Joined: March 17th, 2009, 5:26 pm
Location: UK
Contact:

Re: Interesting Patterns in Normally Expanding Rulesets

Post by Lewis » January 15th, 2010, 6:07 pm

B35/S0246

Code: Select all

x = 51, y = 33, rule = 0246/35
29b2o4b2o4bobo2b2ob2o$8b2o3bo3bo4bo5bo2bo2bo2bo2bob2o3bobo$2b
o3bo2bo2bobo2b3o4bo2bo2bo3bo2bo3bo5b2obo$6b2o5bo5bo3b2o3b2o5b
2o3b2o7bo$49b2o3$8bo17bo$bobo10bo4b2o4bobo$2bo3bobobo3bo3b3o4b
3o$bobo10bo3b2o5bobo$8bo15b2o$27bo3$46bobo$12b2o4bo4b2o4b2o2b
obo2bobo$6o5bo6b2o3b2o3b2o3b2o3b3o3bo2bo2bo$6o5bobo4bo4bo5bo4b
o11bobo$40bo3bo2bo2bo2$46bobo5$2b2o25b2o$2b2o16bo7b2o$6o4bo9b
ob2o5bo$6o3b2ob2o6b2o5bobo$2b2o8bo8bo5bo$2b2o23b2o$26b2o!

User avatar
calcyman
Posts: 2103
Joined: June 1st, 2009, 4:32 pm

Re: Interesting Patterns in Normally Expanding Rulesets

Post by calcyman » January 16th, 2010, 2:37 pm

Lewis:

A random blob in that rule resembles an amoeboid, outstretching pseudopodia and depositing oscillators in its vicinity. The amoeboid appears to undulate whilst slowly expanding; its expansion is quite slow, and the boundary occasionally retreats with surprising rapidity.

There is an amoeboid rule with spaceships of 16 different known velocities, if I remember correctly. By comparison, Life has 12 known velocities (but infinitely many have been proven to exist), and B36/S245 has 13 known velocities.
What do you do with ill crystallographers? Take them to the mono-clinic!

User avatar
calcyman
Posts: 2103
Joined: June 1st, 2009, 4:32 pm

B3/S0123 is omniperiodic

Post by calcyman » January 16th, 2010, 3:08 pm

Dean Hickerson proved that B3/S0123 is omniperiodic about 12 years ago. He exploited the fact that signals can travel in loops:

Code: Select all

x = 55, y = 55, rule = B3/S0123
30b2o$28bo$28bob2o$24bobobo$24bobo3b2o$22bobob2o$24bo5b2o2b2o$22bo3b2o
$21bo7bob5o$21bobo2b2obobo$17bobobobo5bobo2b2o$17bobobob5obo$15bobo11b
o4b4o$15bobo4b4o3b2obo5bobo$13bobob3o10bobob3o$15bo5bobo4bo5bo4b4o$13b
o3b4o7bobobobo$12bo16bo4bobobob5o$12bobo2b2o15bobobobo$6bobobobobo23bo
bo2b2o$6bobobobob5o19bo$8bo30bo3b4o$8bo4b2obo24bo5bobo$obobobob3o28bob
ob3o$obobobo6b2obo24bobo4b4o$8b6o3bo23bobo$b3o11b2o26bobobob3o$5bobobo
bo31bobobobo$3b3obobobo26b2o11b3o$11bobo23bo3b6o$3b4o4bobo24bob2o6bobo
bobo$9b3obobo28b3obobobobo$5bobo5bo24bob2o4bo$8b4o3bo30bo$16bo19b5obob
obobo$10b2o2bobo23bobobobobo$16bobobo15b2o2bobo$10b5obobobo4bo16bo$20b
obobobo7b4o3bo$12b4o4bo5bo4bobo5bo$18b3obobo10b3obobo$14bobo5bob2o3b4o
4bobo$17b4o4bo11bobo$25bob5obobobo$19b2o2bobo5bobobobo$23bobob2o2bobo$
19b5obo7bo$27b2o3bo$19b2o2b2o5bo$27b2obobo$23b2o3bobo$26bobobo$23b2obo
$26bo$23b2o!

Code: Select all

x = 128, y = 64, rule = B3/S0123
21boo14boo14boo14boo14boo$19bo15bo15bo15bo15bo$19boboo12boboo12boboo
12boboo12boboo$15bobobo11bobobo11bobobo11bobobo11bobobo$15bobo3boo4bo
3bobo3boo4bo3bobo3boo4bo3bobo3boo4bo3bobo3boo$13boboboobo8boboboo10bob
oboo10boboboo10boboboo$15bo5b4o3boobo5b4o3boobo5b4o3boobo5b4o3boobo5b
oobboo$13bo3boo9bo4boo9bo4boo9bo4boo9bo4boo$12bo7bob5obo7b7obo7bob5obo
7bob5obo7bob5o$12bobobboobobo5bobobboobobo5bobobboobobo5bobobboobobo5b
obobboobobo$6bobobobobo5bobobboobobo5bobobboobobo5bobobboobobo5bobobb
oobobo5bobobboo$6bobobobob5obo7bob5obo7bob5obo3bo3bob5obo7bob5obo$8bo
11bo4boo9bo4boo9bo3b3o9bo4b4o7bo4b4o$8bo4boobo3boobo5b4o3boobo5b4o3boo
bo5b4o3boobo3b6o3boobo5bobo$obobobob3o10boboboo10boboboo10boboboo10bob
obo11bobob3o$obobobo6boobobbo3bobo3boo4bo3bobo3boo4bo3bobo3boo4bo3bobo
3boo4bo5bo4b4o$8b6o3bo5bobobo11bobobo11bobobo11bobobo7bobobobo3bo$b3o
11boo10boboo12boboo12boboo12boboo5bo4bobobob5o$5bobobobo15bo15bo15bo
15bo13bobobo$3b3obobobo17boo14boo14boo14boo14bobobboo$11bobo79bo$3b4o
4bobo80bo3b4o$9bobobobo80bo5bobo$5bobo5bo80bobob3o$8b5obbo80bobo4b4o$
16bo79bobo$10boobbobo81bobobob5o$14bobobobo77bobobobo$10b5obobobo81bob
obboo$20bobo79bo$12b4o4bobo80bo3b4o$18b3obobo80bo5bobo$14bobo5bo80bobo
b3o$17b4o3bo80bobo4b4o$25bo79bobo$19boobbobo81bobobob5o$23bobobobo77bo
bobobo$19b5obobobo81bobobboo$29bobo79bo$21b4o4bobo80bobb5o$27b3obobo
80bo5bobo$23bobo5bo80bobobobo$26b4o3bo80bobo4b4o$34bo79bobo$28boobbobo
14boo14boo14boo14boo17bobobob3o$34bobobo13bo15bo15bo15bo15bobobobo$28b
5obobobo4bo5boobo12boobo12boobo12boobo10boo11b3o$34bo3bobobobo7bobobo
11bobobo11bobobo11bobobo5bo3b6o$30b4o4bo5bo4boo3bobo3bo4boo3bobo3bo4b
oo3bobo3bo4boo3bobo3bobboboo6bobobobo$36b3obobo11bobobo10boobobo10boob
obo10boobobo10b3obobobobo$32bobo5boboo3b6o3boboo3b4o5boboo3b4o5boboo3b
4o5boboo3boboo4bo$35b4o4bo7b4o4bo9b3o3bo9boo4bo9boo4bo11bo$43bob5obo7b
ob5obo3bo3bob5obo7bob5obo7bob5obobobobo$37boobbobo5boboboobbobo5bobob
oobbobo5boboboobbobo5boboboobbobo5bobobobobo$41boboboobbobo5boboboobbo
bo5boboboobbobo5boboboobbobo5boboboobbobo$37b5obo7bob5obo7bob5obo7bob
7o7bob5obo7bo$45boo4bo9boo4bo9boo4bo9boo4bo9boo3bo$37boobboo5boboo3b4o
5boboo3b4o5boboo3b4o5boboo3b4o5bo$45boobobo10boobobo10boobobo10boobobo
8boboobobo$41boo3bobo3bo4boo3bobo3bo4boo3bobo3bo4boo3bobo3bo4boo3bobo$
44bobobo11bobobo11bobobo11bobobo11bobobo$41boobo12boobo12boobo12boobo
12boobo$44bo15bo15bo15bo15bo$41boo14boo14boo14boo14boo!

And subsequently showed that any loop of period => 7 can be built using this method.


Here are oscillators of periods 8 and 9, since you don't have any in your collection:

Code: Select all

x = 128, y = 55, rule = B3/S0123
44boo$42bo$42boboo$38bobobo$38bobo3boo$36boboboo$38bo5boobboo$36bobb3o
$35bo7bob5o$35bobobboobo$31bobobobo5bobobboo$31bobobob5obo$29bobo11bo
4b4o$29bobo4b4o3boobo5bobo$27bobobobo10bobob3o$29bo5bobo4bo5bo4b4o$27b
o3b4o7bobobobo3bo$26bo16bo4bobobob5o$26bobobboo15bobobo$20bobobobobo
23bobobboo55bobboobbo$bboobo14bobobobob5o19bo$bboboo16bobboo26bo3b4o
51b12o$oo4boo14bo4boobo24bo5bobo35boboo8bo11bo$o5bo7bobobobob3o28bobob
3o39boobo8bobb8obobo$bo5bo6bobobobo6boobo24bobob7o31boo4boo4bobobo9bob
o$oo4boo12b8o3bo23bobobboo36bo5bo6bobobb6obobobo$bboobo9b3obboo7boo26b
obobob3o31bo5bo7bobobo7bobo$bboboo15bobobo31bobobobo33boo4boo4bobobobo
bboo5bo$oo4boo9b3obobobo26boo11b3o31boboo6bobobobobobo3bobobo$o5bo18bo
bo23bo3b7o37boobo8boboboboobbobobo$bo5bo9b4o4bobo24boboo6bobobobo34boo
6bobobo5bobobo$oo4boo15b3obobo28bobobobobobo35bo4bobobobo3boobbo$bboob
o13bobo5bo24boboo4bo42bo7bo11bo$bboboo16b5obbo30bo42boo6b6ob5o$26bo3bo
19b5obobobobo36boboo$24boobbobo23bobobobobo36boobo10b8o$28bobobobo15b
ooboobo$24b5obobobo4bo12boobbo58bobbo$34bobobobo7b6obo$26b4o4bo5bo4bob
o5bo$32b3obobo10b3obobo$28bobo3boboboo3b4o4bobo$31b4o4bo11bobo$39bob7o
bobo$33boobbobo5bobobobo$37boboboobbobo$33b5obo7bo$41boo3bo$33boobboo
5bo$39boboobobo$37boo3bobo$40bobobo$37boobo$40bo$37boo!
What do you do with ill crystallographers? Take them to the mono-clinic!

Sokwe
Moderator
Posts: 1493
Joined: July 9th, 2009, 2:44 pm

Re: Interesting Patterns in Normally Expanding Rulesets

Post by Sokwe » January 16th, 2010, 7:42 pm

calcyman wrote:A random blob in that rule (B35/S0246) resembles an amoeboid...
This rule does seem to have room for several new velocity discoveries. Here are some orthogonally traveling spaceships in this rule of speeds 2c/5, c/5, and c/6 respectively:

Code: Select all

x = 173, y = 151, rule = B35/S0246
167bo$167bo$166bobo$166bobo$165b5o$166b3o$164b2obob2o2$164b3ob3o$164bo
5bo$165b5o3$165b2ob2o$166b3o$166b3o$166b3o$162b3ob3ob3o$162bo3bobo3bo$
163bo2bobo2bo$164b2o3b2o$165b2ob2o$165bobobo$166b3o$166b3o$166b3o$165b
2ob2o2$165bobobo3$164b3ob3o$163bobo3bobo$163bobo3bobo$164b3ob3o$164b3o
b3o$164b3ob3o$165bo3bo2$166b3o$165b2ob2o$165b2ob2o$166b3o$165b2ob2o$
165bobobo$165bobobo$165b5o$165b5o$164b2o3b2o$165bobobo$164b2obob2o$
165bobobo$165bobobo$165bobobo$167bo$119bo6bo40bo$118bobo4bobo37b2ob2o$
84bo2bo30bobo4bobo38bobo$81bobo4bobo12b2o60b5o$83b2o2b2o11bo2b2o2bo11b
o6bo37b2o3b2o$82b2ob2ob2o11b6o10bo10bo34b2o5b2o$83bo4bo11b3o2b3o11bo6b
o36b2o5b2o$85b2o15bo2bo12b2o6b2o39bo$83b6o13b4o11b2o8b2o36bobobo$83bob
2obo10b4o2b4o8bo3bo2bo3bo37bobo$85b2o13b2ob2ob2o10b3o4b3o38b3o$85b2o
30b2o3b2o3b2o36bobobo$83b2o2b2o28b3ob4ob3o33bo4bo4bo$84bo2bo14bo2bo13b
8o38b2ob2o$83bob2obo13bo2bo14b2o2b2o37bo2bobo2bo$82b3o2b3o12bo2bo11bo
3bo2bo3bo34bo2b3o2bo$84b4o14bo2bo11bo10bo35bobobobo$83bo4bo13b4o12bobo
4bobo$102b4o12bo8bo37b2ob2o$83bob2obo9bo4b2o4bo7b4o4b4o36bobobo$83bob
2obo11b3o2b3o10b3o4b3o37bo3bo$102bo2bo12b2obo2bob2o39bo$84bo2bo10b2obo
4bob2o8b3o4b3o37bobobo$99b4o2b4o12bo2bo38b2obobob2o$99bobo4bobo10b2ob
2ob2o36b4ob4o$84b4o12b2o4b2o12bo4bo40b3o$117b3o6b3o34b3obob3o$84bo2bo
14bo2bo13b3o2b3o37bobobobo$83b6o12b6o10b2o8b2o$82bo2b2o2bo10bo2b2o2bo
10b2o6b2o36bo2bo2bo$118b2o6b2o35b3o3b3o$62b2o6b2o10b3o2b3o10b3o2b3o11b
2o4b2o35bo2b5o2bo$82bo2b2o2bo10bo2b2o2bo12bo4bo37bobo3bobo$64bo4bo12b
3o2b3o10b3o2b3o9bo10bo35bobobobo$63b2o4b2o13bo2bo14bo2bo11b5o2b5o37bob
o$63b2o4b2o47b2o6b2o36bobobobo$65bo2bo12bo2bo2bo2bo8bo2bo2bo2bo9bob2o
2b2obo37bo3bo$63b2o4b2o13bo2bo14bo2bo13bobo2bobo37b2o3b2o$46b2o15bo2b
2o2bo13bo2bo14bo2bo15b4o37bob2o3b2obo$46b2o16b2o2b2o10bo2bob2obo2bo6bo
2bob2obo2bo8bo2bo2bo2bo34bo3bobo3bo$45bo2bo17b2o14b8o10b8o10b2o6b2o35b
obo3bobo$45bo2bo32bob2o2b2obo8bob2o2b2obo54bo7bo$45bo2bo16b4o14bo4bo
12bo4bo10bob8obo36b2ob2o$64b6o14bo2bo14bo2bo13bob4obo36bobo3bobo$45bo
2bo17b2o14bo2b2o2bo10bo2b2o2bo10bob2o2b2obo36bob3obo$42bobo4bobo10b3ob
2ob3o9b3ob2ob3o8b3ob2ob3o8bobobo2bobobo37bobo$41bob8obo13b2o14bobo2bob
o10bobo2bobo12bo4bo40b3o$41b2obo4bob2o12bo2bo12bob2o2b2obo8bob2o2b2obo
11bob2obo$43bobo2bobo14bo2bo12bo3b2o3bo8bo3b2o3bo11b6o40bobo$44b6o14bo
4bo13bo4bo12bo4bo12b2o4b2o40bo$64b2o2b2o12bob4obo10bob4obo58bobo$44bob
2obo14b6o49b2o4b2o40bo$46b2o17bo2bo13bo6bo10bo6bo11bob4obo38b5o$42bo8b
o14b2o12b2o8b2o6b2o8b2o10b6o38b7o$66b2o13b3ob2ob3o8b3ob2ob3o11bo4bo40b
obo$42b2o6b2o14b2o17b2o16b2o16b4o$41bobo6bobo13b2o98b3o$41bob2o4b2obo
27bo2b2o2b2o2bo6bo2b2o2b2o2bo54b7o$43bo6bo14bo2bo11b3obo2bob3o6b3obo2b
ob3o53bob2ob2obo$44b2o2b2o31bo2b4o2bo8bo2b4o2bo11bo4bo37bobo3bobo$45b
4o14b2o4b2o11b3o2b3o10b3o2b3o13b4o38bobo3bobo$61bob3o2b3obo10bob2obo
12bob2obo13b2o2b2o39b2ob2o$46b2o14b2o6b2o48bo4bo39bobobo$5b5o34b6o12bo
bo4bobo10bo2b2o2bo10bo2b2o2bo56bob3obo$7bo38b2o13bo2bo4bo2bo46bo6bo37b
o5bo$7bo34b4o2b4o12bo4bo12bobo2bobo10bobo2bobo9bo2bob2obo2bo35bobobobo
$3bob5obo31b2o4b2o12bo6bo10bob2o2b2obo8bob2o2b2obo12bo2bo40bobobo$2o2b
2o3b2o2b2o29b2o2b2o11b3o6b3o8b2ob4ob2o8b2ob4ob2o9bo3b2o3bo38bobo$b3o7b
3o30b6o12bo8bo10bob4obo10bob4obo12b2o2b2o41bo$bob2o5b2obo30b2o2b2o12bo
bo4bobo11bob2obo12bob2obo14b4o40bo3bo$bo2b2o3b2o2bo31bo2bo15bob2obo12b
2o4b2o10b2o4b2o14b2o40b2o3b2o$2bobobobobobo32bo2bo17b2o13bo2b4o2bo8bo
2b4o2bo12b4o41b3o$3b2obobob2o34b2o17b4o12bo8bo8bo8bo10bobo2bobo36bo2bo
bo2bo$2bobobobobobo51bob2obo13bo4bo12bo4bo12bo2b2o2bo36b2obobob2o$bo
11bo29bo2b2o2bo13bob2obo11bobo4bobo8bobo4bobo12bo2bo$b2o3bobo3b2o29bob
4obo30b3o4b3o8b3o4b3o10b2o4b2o36b3obob3o$2bo9bo30b2o4b2o13bo4bo12bob4o
bo10bob4obo10bo8bo39bo$bobo2b3o2bobo49bobo2bobo11b2o4b2o10b2o4b2o10b2o
6b2o35bob2ob2obo$4bobobobo32b2ob2ob2o12bobo2bobo13bo2bo14bo2bo11bobo6b
obo37bobo$3b3o3b3o33bo2bo15bo4bo11bob2o2b2obo8bob2o2b2obo8b3o6b3o37bob
o$5b2ob2o31b2o2b4o2b2o10bo6bo10bob2o2b2obo8bob2o2b2obo9bo8bo38bobo$3bo
bo3bobo29b2o8b2o9bobo4bobo11bo4bo12bo4bo10b2obo4bob2o33bo3bobo3bo$2bob
o5bobo29bobo4bobo10b2o6b2o9b2o6b2o8b2o6b2o9b2o6b2o35bo2bobo2bo$4bo5bo
31bo8bo11bo6bo11bo6bo10bo6bo11bo6bo35bo9bo$4bo5bo30b2o8b2o9bo8bo9bo8bo
8bo8bo9bo8bo36bo5bo$4bo5bo33bo4bo11bo10bo7bo10bo6bo10bo7bo10bo35b2o3b
2o$5b2ob2o33bo6bo11b3o4b3o9b3o4b3o8b3o4b3o9b3o4b3o$6bobo34bo6bo113b3ob
3o$2bo2b2ob2o2bo30bo6bo15b2o17b2o16b2o17b2o38bo2b5o2bo$2b2ob2ob2ob2o
30bo6bo11bobo4bobo9bobo4bobo8bobo4bobo9bobo4bobo37bobobo$4bo5bo32b2o4b
2o12bob4obo11bob4obo10bob4obo11bob4obo35bobo2bo2bobo$3b2o5b2o32b2o2b2o
12bo3b2o3bo9bo3b2o3bo8bo3b2o3bo9bo3b2o3bo38bobo$2bo9bo29bo2b4o2bo11bob
o2bobo11bobo2bobo10bobo2bobo11bobo2bobo36bo2bobo2bo$3bo7bo30bo8bo12b2o
2b2o13b2o2b2o12b2o2b2o13b2o2b2o36b2ob2ob2ob2o$2b3o5b3o31bo4bo15b4o15b
4o14b4o15b4o40bobobo$b5o3b5o30b2o2b2o16b2o17b2o16b2o17b2o38b3o5b3o!
This rule seems ideal for David Eppstein's gsearch program, but I have been unable to get it to work properly. Does anyone have a working executable for gsearch?
calcyman wrote:Dean Hickerson proved that B3/S0123 is omniperiodic...
Does anyone have a list of two-state, totalistic, Moore-neighborhood cellular automata that have been proven to be omniperiodic?

Here are small oscillators of periods 8 and 17 in B3/S0123:

Code: Select all

x = 19, y = 36, rule = B3/S0123
8b2o$6bo4bo$6bob4o3$6bob4o$6bo4bo$8b2o10$2bobobobobobobobo$2bobobobobo
bobobo$2o4bobobobo4b2o$8bobo$2o6bobo6b2o$8bobo$3o5bobo5b3o$8bobo$8o3b
8o2$8o3b8o$8bobo$3o5bobo5b3o$8bobo$2o6bobo6b2o$8bobo$2o4bobobobo4b2o$
2bobobobobobobobo$2bobobobobobobobo!
Edit: c/5 diagonal spaceship in B35/S0246:

Code: Select all

x = 28, y = 28, rule = B35/S0246
21bobo$22bo$22bo$19b5o$19b2o3bo2bo$15bo8b3o$16b3o5bo2bo$13bo3b2o4b2o$
14bob2o5b2o$13bobo4b2o$13bo5b3o$13b3o3bobo$16bobo3bo$9bo6bo2bo$10bobo
3b3obo$10b4o$7b2o3bo$3b3o6b2o$4bobo2bo4bo$5bobo3bo$8bo2bo$2bo6bo$ob2o
4bobo$b3o5b2o$6o4bo$o2b4o$3b2o$2b2obo!
Edit 2: c/6 diagonal spaceship in B35/S0246:

Code: Select all

x = 30, y = 30, rule = B35/S0246
27bo2$24bobo$24bo4bo$25bo$24bo2bo$22bob2o$20b2obo2bo$20bo3bo$17bo3b3o$
21bo$15b4obo$15bo2bobo$15bob2o$14b5o$11b2o5bo$10b2o2bo$8bo3bo$6b2obobo
3bo$6bo3bo3bo$7b2o3b3o$3bo5b2o2bo$3b2o5bo2bo$2b2o3b2o$3bob4o$b2o3b3o$
2bo5bo$6o3bo$2ob3obo$bo!
-Matthias Merzenich

Sokwe
Moderator
Posts: 1493
Joined: July 9th, 2009, 2:44 pm

Re: Interesting Patterns in Normally Expanding Rulesets

Post by Sokwe » February 2nd, 2010, 5:34 am

I've been searching for p5 knightships in B35/S0246 with no luck. Here are some partial results:

Code: Select all

x = 84, y = 76, rule = B35/S0246
73b2ob3o3bo$73bo4bobobo$73bobobo2b2o$77bo2b2o$72bo2b3o2b3o$72b2o4bo$
73bo2b6o$74b2ob3o2bo$77b3ob2o$73bob2ob6o$73b4o2bo2bo$73bobo3b2obo$72bo
b2o3b3o$72b2o3bo2b2o$74bo2b2obo$73bobob4o$74b3o2b2o$77b2o$75bo2bo2bobo
$77b2o$75b2o2b2obo$75bob2ob2o$76b2o2bo$74b2obo$74bo2bo$75b2obobo$76b2o
4bo$75bo5bo$74b2ob2o2b2o$79b2o$74b2obobo$74bo4b2obo$73b2obobobo$74bobo
bob2o$74b5o$75b2ob2obo$75b2ob3o$76bob2o$76bo2bo$72b2obobobo$73b2obob3o
$73bo2bo2bo$73b6o$42bobo2b3o27bobobo$41bo2bo3b2o22bo4b2obo$42b3obobo
23bo4b2o2bo$41b7o26bo$41b4o27b4ob4o$42bobo3bo27b3ob2o$42b2o5bo26b2o2b
3o$44b2o2b2o22bob4obo$45bo2bo23bo4bo2bo$44b3o2bo23b2o5bo$45b4o25bob4o$
42b5o29bobo$45b4o26bobo$43bo2b2o26bo8bo$43b6o24b2obobobo$43bo30b3obobo
bo$45b2o26b6o3b2o$44bob3o23bo5bobobo$72bob3o$44b3obo25b2obo$44bo33bo$
46bo26bobo2b2o$42b5o28bob2o$41bob3o28b2o2bo$41bo4bo27bo4bo$2bo2bobo6b
2obo24bob3o27bobo3bo$bo3bobo5bob2o26bob3o27b3o$2b3o5bo2b3ob2o23bo3bo
27b2obobo$ob3obo6b4obo23bobob2o25bob2o3bo$3ob2o3b2o2bobo25b2ob3o26b2o
2bobobo$2ob2obobo2b2ob3obo23bob2o27b2o2bobobo$b4o2bob3o2bob3o23b2o30b
5o$12b2o3bo23b4o30b3o!
Also, here are some skinny or otherwise small spaceships (c/3 diagonal, c/4 diagonal, and 2c/5 orthogonal)

Code: Select all

x = 238, y = 178, rule = B35/S0246
234b2o2$234bo2$233b3o$230b2o4bo$232bob2o$230b2o4bo$230b2ob2o$231b4o2$
232b2o$233bo$233b2o$232bo$232bo$232b3o2$233b2o$235bo$232bob2o$231bo$
229b3ob2o2$230b2o$231b2o2bo$232b4o$233bobo$235bo$235bo$235b2o$235bo$
234b2o$234b3o$235b2o$233b2ob2o$236bo$231b2o$231b2o$232bobo$232bo$231bo
2bo$232bo$231bo$233bo$231b2obo$231bo2bo$231b3o$231b4o$232b3o$232b3o2$
232b2o$231b2o$231bo$230bob2obo$229b2ob2o$234bo$231b4o$233bo2$233b2o$
232b2o$230b3obo$230b4o$231b3o$230bo2bo2bo$230b2obo$231b2o2bo$231bo2b2o
$232bo2bo$232b5o$233bob2o$231bobobo$230bobo3bo$229bobo3b2o$232b5o$230b
3o$231bo$232bo$231b2o$230bobo$232bo$229bo$230b2o$229b2o$231bo$233b2o$
231b2obo$231bo3bo$232b2obo$232b3o$233b3o$231b4obo$234bobo$235bo$232bob
2o$231b3o$231b3o$230b2obo$231b3o2bo$234bobo$234b2o$233b2o$234bo$235b2o
$232b2o2bo$230bo4bo$230bo3bo2bo$232bo2bo$231bo4b2o$232bo3b2o$234b2o$
231b4obo$232bobo$233b3o$230bo2bo$232bo$232b3obo$231b2o2bobo$232bobobo$
233b3o2$232bo2bo$233bo$233b2o$232bob2o$229bobo2bobo$229bob2ob3o$231b2o
$230bo2b2o$208bo4bo17bobobo$206b3o2b2o19b3o$206bo2bo2bo19bo$206bo3bo
20b2o$204bo2b2obo21b5o$233bo$201bobob2o26b2o$202b2o30bob2o$198bo3b2o
32bo$199b2o31bob2o$197b3o31bo4bo$196bo2b2ob2o31bo$195bo2bo33b4o$26bo
167bo3bob2o30bo$26bo167bob2o32bobobo$24b2o167bob3o34bo2b3o$23bo2bo37bo
b2o126b2o36b2ob2o$23b2o166b3obo34b2ob4o$23b2o36b3ob2o32bo89bo3b2o35b2o
2bobo$8bo15bobo35bo35bo90bo2bo$3o4b2o14bobobo33bo4bobo31bo90b2o36bo3bo
$o4bobo12bobo35b2o3b2obobo28bobo91bo37bo2b2o$5bobo11bo39b2o2bo2bo31b2o
90bo39b4obo$b2o2bo14b3o35b6o31bo2bo87b3ob2o40b2o$o2b3o14b2ob2o32bo2bo
3bo29bo3bo28bo58bo43bo5bo$3b4o49b2o2bo3bo28b2obo28bo58bo46bob3o$2o2bob
o14bob2o32b2ob3o31b3obo87b2o44b3o$bo4b2o14bo31bo2bob2o30bo2bo2bo24b4o
60bo45b2o$2bo3bo15b3o28b5o32b5o88b2o48bobo$6bo15b2obo25b5o32b5o29b3o
55b4o49bobo$2b2obobo11bo4bobo24b2o35b2o33b2o55b2o50b2o$b2o3bo11bo4bobo
bo21bobobobo30bobobobo27bo60b2o49b2o$6o13bo3b3o24b3o2b2o30b3o2b2o25bo
2bo56bo49b2ob2o$3b2obo12bo3bo26bo2b3o31bo2b3o26b2o32b2o21b2obo$obob3o
12b2ob3o20bob3o3bobo26bob3o3bobo28bob2o29bobo20bo51b2ob2o$2o17bo2bo2bo
19bobob4obo27bobob4obo28b2o33bo2bo15b2o54bo2b2o$b4o5bo11bo2bo20bob2obo
31bob2obo34b4o25b2o2b2o14b2o55bo2b3o$2b2obob3o8b2o2b3o18bobobobo30bobo
bobo36bo2bo24b2o3bo15bo58bo2b2o$3b3o2bo11bo2bo19bobobobo30bobobobo65bo
18b3o58b2obo$3b2obo12b3o2bo16bobo2b2o2bo27bobo2b2o2bo36bo18bob3ob2o17b
3obo59bo2b2o$2bo3bobo10bo4b3o13b2obo5bo27b2obo5bo37b3o16bobobo3b2o14bo
b5o61bo$3bob3o10b2ob2o16bob7o28bob7o37bo21b2o21b2obo61b5o$b2obo13b3obo
19b2o35b2o63bo4bo19b3o61b2o$bobo2bobo10b2ob3o13b2obob3o29b2obob3o38bo
23b2ob2o17b2o63bo$b2ob4o2bo6b5obo14bobo3bo30bobo3bo37b2obo23b2ob2obo
14bobo63bo$3b2o4bo8b2o18b2obobo31b2obobo38bob3o24b4o15b2o63b3o$4bo3bo
10bobo17b3o34b3o42b4o24b2o80b5o!
-Matthias Merzenich

User avatar
ad_ca
Posts: 16
Joined: January 28th, 2010, 5:35 am
Contact:

Re: Interesting Patterns in Normally Expanding Rulesets

Post by ad_ca » February 4th, 2010, 1:46 am

I've been searching for p5 knightships in B35/S0246 with no luck.
You'll be famous if you find anything in this searches. According to Eppstein's DB, all currently known knightships [in rules without B0] have period >=11 and dimensions <=12, which means they've been mostly discovered naturally and/or with brute-force programs:

Code: Select all

Glider 1364, size 5x4, speed c/13, slope 2, rule B358/S0346
Glider 1968, size 5x5, speed 2c/23, slope 2, rules B36/S01347 to B368/S013478
Glider 2893, size 6x5, speed c/13, slope 2, rules B3/S01367 to B38/S013678
Glider 2947, size 6x5, speed 3c/23, slope 3/2, rules B345/S126 and B3458/S126
Glider 2956, size 6x5, speed 2c/25, slope 2, rule B34578/S358
Glider 2957, size 6x5, speed 3c/26, slope 3, rule B357/S024578
Glider 2975, size 5x6, speed 2c/41, slope 2, rule B348/S2567
Glider 3341, size 6x6, speed 2c/11, slope 2, rules B356/S02456 and B3567/S02456
Glider 10998, size 7x12, speed 4c/29, slope 4, rules B3/S12567 and B3/S125678

Axaj
Posts: 232
Joined: September 26th, 2009, 12:23 am

Re: Interesting Patterns in Normally Expanding Rulesets

Post by Axaj » February 5th, 2010, 5:43 pm

The first step to finding a spaceship in B017/S1?

Code: Select all

x = 27, y = 7, rule = B017/S1
2bo23bo$2bo23bo2$2bo$o3bo$o3bo$2bo!
Image

Sokwe
Moderator
Posts: 1493
Joined: July 9th, 2009, 2:44 pm

Re: Interesting Patterns in Normally Expanding Rulesets

Post by Sokwe » February 5th, 2010, 7:16 pm

ad_ca wrote:According to Eppstein's DB, all currently known knightships [in rules without B0] have period >=11 and dimensions <=12, which means they've been mostly discovered naturally and/or with brute-force programs
Indeed, I have not heard of any knightships being found directly. I've searched a few more rules, hoping to get lucky, but I haven't so far. Here are some partial results:

Code: Select all

x = 32, y = 40, rule = B35/S1246
22bobo5b2o$20b3ob2o4bo$30bo$21b2obo2bob3o$22b3obo2b2o$22bo2b4o2bo$22bo
b2ob3o$21bo2bo$21bobo5bo$2ob3o15bo3bo2b2o$2obob3o13bobo3b2o$2b3ob2o14b
2o2b6o$b2o19bo3b4o$4b2o16bobo3bo$b7o14b2ob2o$bo3b2o19bo$2b5o15bo4b2o$
2b2ob3o14b2ob2ob4o$2bob3obo14bobobob3o$b2o2b2obo11bo5bobo$2bob3o13b3o
2b2obo$2bobob2o13b2obo2b4o$2b2o2bobo14bob2o$2bobob3o12b2o4b3o$3b2ob2o
13bo4bobobo$3b2ob2o12b3o2bob2o$bo2bo15bob2ob2ob2obo$bobo17b2ob3o$3o3bo
15bo2b2o2bo$obo3bo13b2obo5bo$3b3o14bobobob2ob2o$2obob2o14bobo3bobo$bob
4o14bobo3b2o$bobo3bo12b4ob2obo$bo4bo15b2o$2b4o15bo4b2o$bob3obo15bob2ob
o$bobobo16bobobo$5ob2o13b5ob2o$b4o17b4o!

Code: Select all

x = 31, y = 24, rule = B357/S1358
22bobobobobo$21b2ob5obo$22bobo2b2o$21bo6bobo$22bob3o$22b3o4bo$obo2bo2b
o12bobo2bo$b2o2bo2bo13b5o$2b4o18bobobobo$3o2b3o15b8o$bo3bobo14b2ob2obo
$obo2b2o15b2o$3obobo16b3o2bo$2bo2bo17bobob2o$bob2obo15bo4bo$5b2o15bo3b
obo$b4o17bob2o2bo$3b3o16bob4o$3bo2bo16bobob2o$b4o19bobo$ob2obo16b2o4bo
$5o17bobo2bo$b5o16bobobo$6bo16b3o!
Axaj wrote:The first step to finding a spaceship in B017/S1?
Based on this idea, here is an 8c/16 spaceship:

Code: Select all

x = 16, y = 16, rule = B017/S1
obo5bobo$obo5bobo$13bo2$15bo$2bobo5bobo$2bobo5bobo3$2bobo5bobo$2bobo5b
obo$15bo2$13bo$obo5bobo$obo5bobo!
This also can be used to make small puffers:

Code: Select all

x = 15, y = 7, rule = B017/S1
o7bo$o7bo$12bo2$14bo$2bo7bo$2bo7bo!
Here is a breeder (since it breeds replicator-like patterns, I do not know what its growth rate is):

Code: Select all

x = 3, y = 7, rule = B017/S1
o$o$2bo$2bo2$o$o!
Edit: Here's a glide-symmetric spaceship in B017/S1

Code: Select all

x = 16, y = 21, rule = B017/S1
o7bo$o7bo$12bo2$14bo$2bo7bo$2bo2bobo2bo3$2bo7bo$2bo7bo2$10bobobo$2bo2b
obo5bobo$2bo$10bo2$8bo$o$o12bo$8bo!
-Matthias Merzenich

Post Reply