Faster ladders in Life without Death
Life without Death is a cellular automaton with the same rule for creating new live cells as Conway's Game of Life, but in which no live cell ever dies. Despite the inability to create oscillators or spaceships (both of which require some cells to die sometimes) it has interesting dynamics due to the existence of ladders, patterns that grow at speed \( c/3 \) (that is, one unit of growth for every three time steps of the cellular automaton). Typical random seeds end up with from one to four chaotic regions spreading diagonally from the starting region, spewing ladders on both sides of them so that one ends up with a pattern in which the four quarters of the pattern (as split on roughly diagonal lines) are striped by axis-parallel ladders, separated by the chaotic regions. The chaotic regions separating the striped quarters tend to grow wider, but slowly as the pattern grows, and the boundary of the chaotic regions keeps pace with the ladders (probably in a self-limiting way: there is a pattern that grows at speed \( 2c/3 \) along the side of a ladder and then erupts in chaos at the tip, so if the chaotic growth regions ever fell too far behind they would catch up using this mechanism).
Patterns of this type can be simulated to hundreds of thousands of time steps using the Hashlife algorithm embedded into Golly.
But as it turns out there is another ladder, one that can grow more quickly (the text below is a pattern format that can be copied and pasted into Golly):
x = 26, y = 15, rule = B3/S012345678 obobobobobobobobobobo$23o$3ob3ob3ob3ob3ob3o$26o$26o$ob3ob3ob3ob3ob3ob 3o$3ob3ob3ob3ob3ob3obo$25o$3ob3ob3ob3ob3ob3obo$ob3ob3ob3ob3ob3ob3o$26o $26o$3ob3ob3ob3ob3ob3o$23o$obobobobobobobobobobo!
Rather than growing at speed \( c/3 \), it grows at speed \( 4c/9 \). I've only seen this once out of many chaotic starting seeds, but if it happens once it should happen more than once. My suspicion is that most chaotic patterns should have a shape that eventually comes to be dominated by these faster ladders, but that even hundreds of thousands of steps isn't enough to see this domination.
ETA: animated gif by Simpsons contributor, who set this all off by starting a Wikipedia article on LwoD.
ETA2, 6/13: Already discovered in October 2000 by Dean Hickerson, who also found ladders of speeds \( 4c/10 \) and \( 4c/13 \). Dean's patterns:
#C 4c/9 x = 258, y = 20, rule = B3/S012345678 246bo6bo$245b4o2b4o$245b3ob2ob3o$230bo2b3o7b14o$228b4ob3o7b4ob4ob4o$ 221b2ob14o4b16o$220b7ob5ob4o2b2obob3ob2ob3obo$207b2ob2o9b3ob4ob10ob17o $60bo145b6o7b8ob4ob3obob3ob4ob4ob4o$59b3ob3o90b3o3b3o32bo2b3ob4ob3o7b 4ob16ob17o$4bo5bo10bo6bo28b10o2b2ob2o82b3obob3o31b3ob15o2b10ob5ob4ob3o bob3ob2ob3obo$3b3obob3o8b3ob2ob3o9bo9bo7b4ob5ob6o8b2ob2o16b2ob2o16b2ob 2o16b2ob2o4b13o16bo11b8ob5ob4ob3obob3ob4ob10ob17o$b13o4b14o6b3ob3o2b4o 5b9ob4ob3o8b6o15b6o15b6o15b6o3b4ob3ob4o15b3ob3o6bob3ob4ob10ob10ob4ob3o bob3ob4ob4ob4o$b4ob3ob4o4b4ob4ob4o4b8ob2ob3o6bob3ob4ob8o6b3ob4ob3o2bo 6b3ob4ob3o2bo6b3ob4ob3o2bo6b3ob4ob14o5b3ob2o3b7o5b9ob4ob3obob3ob4ob16o b17o$15o2b16o3b4ob3ob8o3b15ob4o4b14ob3o3b14ob3o3b14ob3o3b10obob3obob3o bo4b8ob4ob3obo5b4ob16ob10ob5ob4ob3obob3ob2ob3obo$bob3obob3obo4bob3ob2o b3obo3b9ob3ob4o4b4ob5ob9o3b4ob5ob8o2b4ob5ob8o2b4ob5ob8o2b4ob4ob15o3b4o b16ob10ob5ob4ob3obob3ob4ob10ob17o$15o2b16o3bob3ob12o2b9ob4ob3obo3b9ob 4ob3ob11ob4ob3ob11ob4ob3ob11obob4ob3ob4o3b9ob5ob4ob3obob3ob4ob10ob10ob 4ob3obob3ob4ob4ob4o$b4ob3ob4o4b4ob4ob4o3b9ob2ob3obo4bob3ob4ob9o3bob3ob 4ob8o2bob3ob4ob8o2bob3ob4ob8o2bob3ob4ob14o3bob3ob4ob10ob10ob4ob3obob3o b4ob16ob17o$b13o4b14o3b18o3b21o3b87o4b85o$3bo2bobo2bo8bo2bo2bo2bo7bo2b o2bo2bo2b2o5bo2bo2bo2bo2bobo2b2o7bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo6bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobo!
#C 4c/10 x = 274, y = 13, rule = B3/S012345678 224bo11b2o8bob3o4bo4b3ob3o$140bo3bo11b2o42bo10b3o8b4o7b6o5b6ob2ob3obob 3ob3o$129bo3bo5b3ob3obob3ob2ob5o26b3o9b3o8b4o7b6o2bo2b8ob9ob15obob3o$ 128b3ob4o2bob15ob4ob2o24b3o4bo3b4o3b2o2b5o2b3ob6ob4ob6ob4ob6ob3obob3ob 2ob8o$9bo11bo3bo19bo39bo33bob3o3b4ob3ob6ob2ob3obob3ob9o17b3obob4ob4obo b4ob4obob4ob4obob4ob4obob4ob4obob15ob4ob2obo$6bob4o2b3o2b4ob3o15bob4o 2b3o4b4o4b4o3b3o3b3o2b4obo24bo3b6ob2obob8ob4ob15obob4o11bo5b13ob11ob 11ob11ob11ob6ob2ob3obob3ob9o$3b7ob2ob3obob3ob4o2bo8b7ob2ob3ob2ob4ob2ob 4obob3obob3ob2ob7o13bo6b3ob7ob7ob2ob7ob3obob3ob2ob10o8b4o3bob2ob6ob11o b11ob11ob11ob9ob15obob4o$3b2ob4ob15obob3o7b2ob4ob37ob4ob2o11b4ob2obob 4ob5ob7ob5obob15ob4ob2obo6b2ob5o2b9ob4ob6ob4ob6ob4ob6ob4ob6ob4ob6ob3ob ob3ob2ob10o$b9ob3obob3ob2ob9o4b9ob3obob4ob2ob4ob2ob3obob3obob3ob9o6b2o b4ob7ob2obob4ob5ob3ob6ob2ob3obob3ob10o3b9o3b4obob4ob4obob4ob4obob4ob4o bob4ob4obob4ob4obob15ob4ob2obo$b4obob15ob4ob2obo4b4obob43obob4o4b9ob7o b7ob2obob8ob4ob15obob4o4b4obob4ob14ob11ob11ob11ob11ob6ob2ob3obob3ob10o $10ob2ob3obob3ob10o2b10ob2ob3ob2ob4ob2ob4obob3obob3ob2ob10o3b4obob4ob 5ob7ob7ob2ob7ob3obob3ob2ob10o2b12obob2ob6ob11ob11ob11ob11ob9ob15obob4o $2b30o6b55o4b67o6b103o$4bo2bo2bo2bo2bo2bo2bo2bo2b2o10bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobo8bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b o2bo2bo2bo2bo2bo2bo2bo2bo2bobo10bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bobo!
#C 4c/12 x = 213, y = 14, rule = B3/S012345678 163bo$162b4o9b3o$162b6o5bob3o11b2o$160b5ob4ob4ob5o6b4ob2o$22bo56bo25bo 54b4ob4obob3ob4ob2o4b4ob4o$3b2o16b3o54b3o23b4o51b7ob17o2b5ob4o$b5o5b3o 6b6o50b6o20bob3obo5bo45bob6ob3obob3obob5obob9o$b4o6b4o5bob4o3b2ob2ob2o 4b2ob2ob2o4b2ob2ob2o4b2ob2ob2o3b4obo7bo10b6ob10o2b3o37b6ob9ob6obob6ob 2obob2o8b3o$7o2b6o4b9ob8ob2ob8ob2ob8ob2ob8ob9o4b4o7b3ob4ob3obob3obob3o bob3obo5bo15b2o7b4ob4obob3ob4ob5ob4ob6obo7b5o$bob4o2b4obo5b4obob4ob2ob 8ob2ob8ob2ob8ob2ob4obob4o5b4o6b35ob5o3bo8b5o4b7ob17ob6ob4ob5ob4ob4o$ 16o3b9ob8ob2ob8ob2ob8ob2ob8ob9o3b7o3b5obob3obob3obob3obob3obob3obob3ob ob3obob2o3b4o5bob6ob3obob3obob5obob11ob4ob7o$b4obobo2b4o5bob4ob4ob2ob 8ob2ob8ob2ob8ob2ob4ob4obo5bob4o2b2obob6ob41ob7o3b16ob6obob6ob2obob6ob 6obo$b14o5b62o5b67o5b53o$3bo2bo2bo2bo9bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo9bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bobo9bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b o2bo!
#C 4c/13 x = 507, y = 52, rule = B3/S012345678 39bo$37b4o$36b2ob4o117b2o$34b4ob4o115b4ob2o$34b4ob6o113b4ob4o$33b8obob 2o111b5ob4o$34bob2ob6obo109bobob8o$33b5ob4ob5o105bob6ob2obo$34b4ob8ob 3o101b5ob4ob5o$33b8obob7o99b3ob8ob4o$34bob2ob6obob4o98b7obob8o$33b5ob 4ob5obob2o95b4obob6ob2obo$34b4ob8ob5obo95bob5ob4ob5o$33b8obob7ob5o91b 5ob8ob4o$34bob2ob6obob7ob3o86b4ob7obob8o$33b5ob4ob5obob7o84b2ob7obob6o b2obo$34b4ob8ob5obob4o82b7obob5ob4ob5o$33b8obob7ob5obobo81b3obob5ob8ob 4o$34bob2ob6obob7ob5obo79bob5ob7obob8o$33b5ob4ob5obob7ob5o75b5ob7obob 6ob2obo$34b4ob8ob5obob7ob3o71b3ob7obob5ob4ob5o$33b8obob7ob5obob7o69bob 7obob5ob8ob4o$34bob2ob6obob7ob5obob4o67b6obob5ob7obob8o$33b5ob4ob5obob 7ob5obo67b3obob5ob7obob6ob2obo$34b4ob8ob5obob7ob5o65bob5ob7obob5ob4ob 5o$33b8obob7ob5obob7ob4o60b5ob7obob5ob8ob4o$34bob2ob6obob7ob5obob7ob2o 56b3ob7obob5ob7obob8o12b3o$33b5ob4ob5obob7ob5obob7o55b7obob5ob7obob6ob 2obo12b4o5bo$34b4ob8ob5obob7ob5obob3o52b6obob5ob7obob5ob4ob5o11b6ob5o$ 33b8obob7ob5obob7ob5obo52b2obob5ob7obob5ob8ob4o12bob3obob3obob3obo$34b ob2ob6obob7ob5obob7ob5o49bob5ob7obob5ob7obob8o10b5ob16o2b3o$33b5ob4ob 5obob7ob5obob7ob3o45b5ob7obob5ob7obob6ob2obo12b4ob3obob3obob3obob3obo 5bo$34b4ob8ob5obob7ob5obob7obo41b3ob7obob5ob7obob5ob4ob5o10b37o3bo$33b 8obob7ob5obob7ob5obob6o40b7obob5ob7obob5ob8ob4o12bob3obob3obob3obob3ob ob3obob3obob3obo5bo$34bob2ob6obob7ob5obob7ob5obob3o37b5obob5ob7obob5ob 7obob8o10b5ob40ob5o$33b5ob4ob5obob7ob5obob7ob5obo36b2obob5ob7obob5ob7o bob6ob2obo12b4ob3obob3obob3obob3obob3obob3obob3obob3obob3obo$34b4ob8ob 5obob7ob5obob7ob5o33bob5ob7obob5ob7obob5ob4ob5o10b61o2b3o$33b8obob7ob 5obob7ob5obob7ob3o29b5ob7obob5ob7obob5ob8ob4o12bob3obob3obob3obob3obob 3obob3obob3obob3obob3obob3obob3obo5bo92b2o$34bob2ob6obob7ob5obob7ob5ob ob7o27b3ob7obob5ob7obob5ob7obob8o10b5ob70o3bo83b5o$33b5ob4ob5obob7ob5o bob7ob5obob6o24b7obob5ob7obob5ob7obob6ob2obo12b4ob3obob3obob3obob3obob 3obob3obob3obob3obob3obob3obob3obob3obob3obo5bo74b2ob4o13b3o2b3o3b2o 105bo3bo$34b4ob8ob5obob7ob5obob7ob5obob2o23b4obob5ob7obob5ob7obob5ob4o b5o10b85ob5o39b2ob3o25b4ob4o11b4ob2ob4ob4ob3o2b2o3bo90b3ob3o$6bo26b8ob ob7ob5obob7ob5obob7ob5obo20b2obob5ob7obob5ob7obob5ob8ob4o12bob3obob3ob ob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3ob o30b4ob4o24b4ob7o8b4ob5ob4ob4ob4ob4o3b2o4bo78b7obo13b2ob2o$4b4o26bob2o b6obob7ob5obob7ob5obob7ob5o17bob5ob7obob5ob7obob5ob7obob8o10b5ob94o2b 3o23b4ob4o12b3ob3o4b8obob2o7b5ob2ob4ob4ob4ob4ob4ob4ob4ob2o3bo69bob2ob 6o9bob6o$3b2ob4o13b2o8b5ob4ob5obob7ob5obob7ob5obob7ob3o13b5ob7obob5ob 7obob5ob7obob6ob2obo12b4ob3obob3obob3obob3obob3obob3obob3obob3obob3obo b3obob3obob3obob3obob3obob3obob3obob3obo5bo14b8obo12b3ob4o4bob2ob6obo 4b2obob8ob4ob4ob4ob4ob4ob4ob4ob4o2b3o4bo47b3obo5b5ob4ob3o5b6ob2o$b4ob 4o11b4ob2o6b4ob8ob5obob7ob5obob7ob5obob7o11b3ob7obob5ob7obob5ob7obob5o b4ob5o10b115o3bo9bob2ob6o9bob7o3b5ob4ob5obob6ob2ob4ob4ob4ob4ob4ob4ob4o b4ob4ob4ob4ob3o2b2o35b4ob4o4b4ob8o3b3ob4ob4o$b4ob6o9b4ob4o3b8obob7ob5o bob7ob5obob7ob5obob5o9b7obob5ob7obob5ob7obob5ob8ob4o12bob3obob3obob3ob ob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3ob ob3obob3obob3obo4b6ob4ob4o2bob6ob2obo4b4ob8ob5ob4ob5ob4ob4ob4ob4ob4ob 4ob4ob4ob4ob4ob4ob4o2b3o3b2o25b4ob3obob9obob5ob8ob4o$8obob2o7b5ob4o4bo b2ob6obob7ob5obob7ob5obob7ob5obob2o7b4obob5ob7obob5ob7obob5ob7obob8o 10b5ob121ob4ob8ob5ob4ob5o2b8obob5ob8ob2ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4o b4ob4ob4ob4ob4ob3o2b2o3bo10b13obob2ob6obob5obob8o$bob2ob6obo5bobob8o2b 5ob4ob5obob7ob5obob7ob5obob7ob5obo5bobob5ob7obob5ob7obob5ob7obob6ob2ob o12b4ob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3ob ob3obob3obob3obob3obob3obob3obob3obob9obob5ob8ob4o4bob2ob6obob5obob8ob 4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4o3b2o2b2obob3obob2ob 6ob4ob5obob6ob2obo$5ob4ob5obob6ob2obo4b4ob8ob5obob7ob5obob7ob5obob7ob 5obob5ob7obob5ob7obob5ob7obob5ob4ob5o10b127obob2ob6obob5obob8o2b5ob4ob 5obob6ob2ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob6o b7ob4ob8ob5ob4ob5o$b4ob8ob5ob4ob5o3b7obob7ob5obob7ob5obob7ob5obob7ob5o b7obob5ob7obob5ob7obob5ob8ob4o12bob3obob3obob3obob3obob3obob3obob3obob 3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob2ob6o b4ob5obob6ob2obo4b4ob8ob5ob4ob5ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob4ob 4ob4ob4ob4ob4ob4ob3ob4ob3obob9obob5ob8ob4o$b28o7b131o12b156o4b167o$3bo 2bo2bo2bo2bo2bo2bo2bobo11bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo16b2o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo8bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo!
Dean also discovered some slow parasitic vines:
#C 4c/13 parasite x = 57, y = 35, rule = B3/S012345678 3bo3bo$2b3ob3o$b7obo$bob2ob6o$5ob4ob3o$b4ob8o$8obob4o$bob2ob6obob2o$5o b4ob5obo$b4ob8ob5o$8obob7ob3o$bob2ob6obob7o$5ob4ob5obob4o$b4ob8ob5obob o$8obob7ob5obo$bob2ob6obob7ob5o$5ob4ob5obob7ob3o$b4ob8ob5obob7o$8obob 7ob5obob4o$bob2ob6obob7ob5obo$5ob4ob5obob7ob5o$b4ob8ob5obob7ob4o$8obob 7ob5obob7ob2o15b2o$bob2ob6obob7ob5obob7o13b5o$5ob4ob5obob7ob5obob3o14b 4o$b4ob8ob5obob7ob5obo12b7o$8obob7ob5obob7ob5o10b4obo$bob2ob6obob7ob5o bob7ob3o7b8o$5ob4ob5obob7ob5obob7obo6bob4o$b4ob8ob5obob7ob5obob6o4b8o$ 8obob7ob5obob7ob5obob3o4b4obo$bob2ob6obob7ob5obob7ob5obob10o$b4ob4ob5o bob7ob5obob7ob6obob4o$3b53o$5bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo!
#C 4c/11 parasite x = 323, y = 44, rule = B3/S012345678 315bo$310b11o$309b4ob3ob4o$309b13o$309bob3obob3obo$308b15o$309b4ob3ob 4o$308b15o$309bob3obob3obo$297b2o9b15o$296b5o6bob4ob3ob4o$283bo13b4o6b 16o$282b3o10b7o3b3obob3obob3obo$116bo152bo11b6o8b4obob21o$111b11o145b 4o10bob4obo4b10obob2ob4ob3ob4o$110b4ob3ob4o144b4obo7b10ob3obob4ob4ob 16o$110b13o132b3o8b9o6b4obob16ob3obob3obob3obo$110bob3obob3obo130b5o9b ob4ob3o2b10obob2ob4obob21o$109b15o117b3o9b4obo7b10ob3obob4ob4ob10obob 2ob4ob3ob4o$110b4ob3ob4o118b4o7b9obob2ob4obob16ob3obob4ob4ob16o$109b 15o103b2o10b6o6bobob4ob4ob10obob2ob4obob16ob3obob3obob3obo$110bob3obob 3obo104b4o8b4obo5b12ob3obob4ob4ob10obob2ob4obob21o$98b2o9b15o103b4o6b 10obob2ob4obob16ob3obob4ob4ob10obob2ob4ob3ob4o$97b5o6bob4ob3ob4o89b3o 10b7o3b3obob4ob4ob10obob2ob4obob16ob3obob4ob4ob16o$85b2o9bob4o6b16o88b 5o8b4obobo2b13ob3obob4ob4ob10obob2ob4obob16ob3obob3obob3obo$84b5o5b9o 3b3obob3obob3obo75b3o10bob4o6b10obob2ob4obob16ob3obob4ob4ob10obob2ob4o bob21o$21bo50b2o9bob4o3b3ob4obob21o73b4o10b9ob3obob4ob4ob10obob2ob4obo b16ob3obob4ob4ob10obob2ob4ob3ob4o$16b11o44b5o5b10ob12obob2ob4ob3ob4o 62b2o10b7o7b4obob16ob3obob4ob4ob10obob2ob4obob16ob3obob4ob4ob16o$15b4o b3ob4o31b2o9bob4o3b3ob4obob5obob4ob4ob16o59b5o9bob4ob2o3b10obob2ob4obo b16ob3obob4ob4ob10obob2ob4obob16ob3obob3obob3obo$15b13o30b5o5b10ob12ob ob11ob3obob3obob3obo49bo10b4obo7b10ob3obob4ob4ob10obob2ob4obob16ob3obo b4ob4ob10obob2ob4obob21o$15bob3obob3obo18b2o9bob4o3b3ob4obob5obob4ob5o b4obob21o47b3o8b9o4bob4obob16ob3obob4ob4ob10obob2ob4obob16ob3obob4ob4o b10obob2ob4ob3ob4o$14b15o16b5o5b10ob12obob10ob12obob2ob4ob3ob4o35bo10b 6o8bob4ob4ob10obob2ob4obob16ob3obob4ob4ob10obob2ob4obob16ob3obob4ob4ob 16o$15b4ob3ob4o16bob4o3b3ob4obob5obob4ob5ob4obob5obob4ob4ob16o33b4o8b 4obo6b11ob3obob4ob4ob10obob2ob4obob16ob3obob4ob4ob10obob2ob4obob16ob3o bob3obob3obo$3b2o9b15o13b10ob12obob10ob12obob11ob3obob3obob3obo34b4o7b 9obob2ob4obob16ob3obob4ob4ob10obob2ob4obob16ob3obob4ob4ob10obob2ob4obo b21o$2b5o6bobob3obob3obo5b3o4b3ob4obob5obob4ob5ob4obob5obob4ob5ob4obob 21o19b2o10b7o4b2obob4ob4ob10obob2ob4obob16ob3obob4ob4ob10obob2ob4obob 16ob3obob4ob4ob10obob2ob4ob3ob4o$3b4o6b16o3b4o3b13obob10ob12obob10ob 12obob2ob4ob3ob4o19b5o8b4obo4b13ob3obob4ob4ob10obob2ob4obob16ob3obob4o b4ob10obob2ob4obob16ob3obob4ob4ob16o$b7o3b3ob4ob3ob4o4b11obob4ob5ob4ob ob5obob4ob5ob4obob5obob4ob4ob16o5bo13b4o6b10obob2ob4obob16ob3obob4ob4o b10obob2ob4obob16ob3obob4ob4ob10obob2ob4obob16ob3obob3obob3obo$b4obob 21o3bob3obobob10ob12obob10ob12obob11ob3obob3obob3obo5b3o10b7o3b3obob4o b4ob10obob2ob4obob16ob3obob4ob4ob10obob2ob4obob16ob3obob4ob4ob10obob2o b4obob21o$9obob2obob3obob3obo3b12ob4obob5obob4ob5ob4obob5obob4ob5ob4ob ob21o3b6o8b4obob16ob3obob4ob4ob10obob2ob4obob16ob3obob4ob4ob10obob2ob 4obob16ob3obob4ob4ob10obob2ob4ob3ob4o$bob4ob4ob16o3b4obob13obob10ob12o bob10ob12obob2ob4ob3ob4o4bob4obo4b10obob2ob4obob16ob3obob4ob4ob10obob 2ob4obob16ob3obob4ob4ob10obob2ob4obob16ob3obob4ob4ob16o$10ob3ob4ob3ob 4o3b12obob4ob5ob4obob5obob4ob5ob4obob5obob4ob4ob16o2b10ob3obob4ob4ob 10obob2ob4obob16ob3obob4ob4ob10obob2ob4obob16ob3obob4ob4ob10obob2ob4ob ob16ob3obob3obob3obo$b4obob20o4bob3obobob10ob12obob10ob12obob11ob3obob 3obob3obo4b4obob16ob3obob4ob4ob10obob2ob4obob16ob3obob4ob4ob10obob2ob 4obob16ob3obob4ob4ob10obob2ob4obob20o$b25o6b91o4b193o$3bo2bo2bo2bo2bo 2bo2bobo10bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bobo8bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bobo!
Dean has also recently solved the long-open problem of finding quadratic growth patterns: the following pattern starts growing at period 25196 some time around generation 64000. It fills a single quadrant, so four copies of it can be used to fill the whole plane to constant density.
x = 47, y = 47, rule = B3/S012345678 3b2o26b2o$3b4o23b5o$3b4o24b4o$b7o21b7o$b4obo22b4obo$8o20b8o$bob4o22bob 4o$8o20b8o3bo$b4obo22b4obo2b2o$8o20b8o2bo$bob4o22bob4o$8o20b7o2bobobob o$b4obo22b17o$8o20b10ob3ob3o$bob4o22b18o$8o20b19o$b4obo21b8ob3ob3obo$ 8o22b14o$bob4o23b2obobobobobo$8o$b4obo$8o$bob4o$8o$b4obo$8o$bob4o$8o$b 4obo$8o$bob4o$8o$b4obo$8o$bob4o$8o$b4obo$8o$bob4o$7o2bobobobobobobobob obobobobobobobobobo$b45o$10ob3ob3ob3ob3ob3ob3ob3ob3ob3o$b46o$47o$8ob3o b3ob3ob3ob3ob3ob3ob3ob3o$2b42o$2b2obobobobobobobobobobobobobobobobobob obo!
Another very simple seed eventually settles down in two of its four quadrants exhibiting glide symmetry in those quadrants:
x = 3, y = 3, rule = B3/S012345678 2o2$2bo!
Comments:
None
2009-06-07T16:09:46Z
Do you have a picture/animation of it?
2009-06-07T16:09:46Z
Do you have a picture/animation of it?
None
2009-06-07T16:14:26Z
Never mind, I downloaded and ran the program to see it. It's neat although not illuminating (to, say, a random schmuck such as myself) but I can see that it would be a nice mathematical question to figure out the fastest possible speed
2009-06-07T16:14:26Z
Never mind, I downloaded and ran the program to see it. It's neat although not illuminating (to, say, a random schmuck such as myself) but I can see that it would be a nice mathematical question to figure out the fastest possible speed
11011110
2009-06-08T04:58:05Z
(see ETA in post for credit)
2009-06-08T04:58:05Z
(see ETA in post for credit)