OCA:Snowflakes

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Snowflakes
Snowflakes rule
Rulestring 02ae3eijkq4iz5ar6i7e/2ci3ai4c8
B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e
Character Chaotic

Snowflakes is an isotropic non-totalistic Life-like cellular automaton first discovered by users BlinkerSpawn and dani. It is named in reference to a very common 21 cell still life (the snowflake) that has a 2 cell seed:

x = 21, y = 9, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e $4bo$2b5o$2bo3bo$b2obob2o6bobo$2bo3bo$2b5o$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
(click above to open LifeViewer)

Snowflakes ranked eighth place in the OCA Discovery of the Year 2017 competition on the ConwayLife.com forums.[1]

Patterns

Oscillators

The rule is notably omniperiodic due to a number of 180-degree spaceship reflectors. Here is a collection of oscillators with periods under 50:

x = 179, y = 222, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e 2$100bo$102bo3bo$66bo8bo25b2o26bo19bo19bo$64b3o6bo25bo13bo17bo35bo$64b o8b2o33bo21b2o35b2o$39bo27bo37bob2o19bo20bo20bo$33b2o3b3o3b2o62bo28b2o 6bo7bo6b2o$10bo23bo4bo4bo22bo31bo13bo23bo23bo$32bo13bo17bo8b2o26b2o34b 2o6bo7bo6b2o$64b3o6bo28bo3bo21bo20bo20bo$66bo8bo24bo29b2o35b2o$131bo 35bo$129bo19bo19bo10$68b2o29bo11bo$68bo2bo29bo7bo26bo26bo$67b2ob2o28b 2o7b2o27bo22bo$11bo23bo7bo28bo25bo13bo24b2o22b2o$9b3o27bo67b2o26bo28bo $9bo26bo2bo23bo3bo4bo2bo32bo39bo2bo$11bo27bo67b2o$10b2o23bo7bo28bo25bo 13bo35bo2bo$67b2ob2o28b2o7b2o24bo28bo$68bo2bo29bo7bo27b2o22b2o$68b2o 29bo11bo26bo22bo$136bo26bo10$37bo3bo59bo7bo52bo$34bo4bo4bo58bo3bo52bo$ 36bo5bo31bo25bo9bo49b2o$35b2o2bo2b2o30b3o28bo57bo$5bo4b2o52bo11bo18bo 19bo41b2o$7bo2bo22bo5bo5bo27bo31bo31bo7bo11bo$6b2o4bo22bo7bo22bo37b3o 32bo17b2o$10b3o21b2o7b2o28bo31bo32b2o5bo17bo$10bo28bo24bo11bo18bo19bo 44b2o$37bo3bo32b3o28bo54bo$74bo25bo9bo51bo$103bo3bo$101bo7bo13$37bo29b o3bo75bo3bo$13bo25bo99bo19bo$11bo26b2o97bo23bo$9bob2o21bo8bo16bo8bo8bo 53bo33bo$40bo58b2o4bo5b2o36bo$35bo30bobobobo27bo10bo23bobo23bobo$7b2ob o29bo57bo6bo7bo35bo$8bo25bo8bo16bo8bo8bo53bo33bo$6bo31b2o97bo23bo$39bo 99bo19bo$37bo29bo3bo75bo3bo11$30b2o12bo$30bo13b3o$29b2o15bo56bo3bo$33b o116bo$7bo3bo27bobobo56bo9bo41bo$9bo23bo40bo76b2o$4bo9bo49bo34bo2bo5bo 2bo33bo$6bo5bo20bo37bobo76bo$5b2o2bo2b2o51bo30bo5bo5bo5bo$74bo75bo$9bo 32bo23b2o31bo2bo5bo2bo33bo10bo$67bo83b2o$42bo22bo34bo9bo41bo$9bo22bobo bo113bo$7bo3bo30bo60bo3bo$29bo15b2o$29b3o13bo$31bo12b2o10$101bo12bo36b o3bo$35bo31b2o34bo8bo34bo11bo$37bo29bo2bo31b2o8b2o35bo7bo$11bo24b2o31b 2o29bo14bo32b2o7b2o$6bo56bo46b2o41bo$12bo23bo74bo$7bobo22bo3b2o3bo22bo bo7bo35b2o36b2o3bo3b2o$36bo63bo14bo33bo7bo$6bo56bo38b2o8b2o33bo5bo5bo$ 36b2o31b2o32bo8bo38bo3bo$37bo29bo2bo30bo12bo$35bo31b2o9$71bo$69bo$64bo 4b2o16bo18bo18bo41bo$66bo22bo33bo41bo$36bo28b2o6bo14b2o33b2o40b2o$38bo 47bo19bo19bo41bo$37b2o28bobobo22b2o6bo7bo6b2o44bo2bo$33bo60bo23bo22bo 7bo17bo$5bo5bo53b2o6bo20b2o6bo7bo6b2o24bo19bo2bo$36bobo2bo24bo19bo19bo 19bo15b2o5bo18bo$3bo8bo51bo4b2o17b2o33b2o40b2o$6bobobo22bo35bo19bo33bo 41bo$37b2o32bo15bo18bo18bo41bo$38bo$36bo9$107bo$63bo10bo34bo$65bo6bo 38b2o33bo15bo$64b2o6b2o38bo35bo11bo$8bo53bo12bo36b3o32b2o11b2o$6bo26bo 6bo29b2o31bo10bo30bo17bo$6b2o3bo59bo86b2o$34bobobo31b2o32bo5bobo46bo$ 9bo2bo49bo12bo82b2o$33bo6bo23b2o6b2o29bo10bo30bo17bo$9bo55bo6bo39b3o 32b2o11b2o$63bo10bo37bo35bo11bo$111b2o33bo15bo$109bo$107bo6$68bo3bo$ 70bo2$68bo3bo2$7bo3b2o47bo19bo37bo11bo21bo21bo$9bo2bo19bo29bo15bo37bo 15bo39bo$8b3ob2o20bo6bo19b2o15b2o36b2o13b2o39b2o$33b2o6bo2bo74bo9bo22b o22bo$12bo28bo23bobobobobobo36b2o26b2o6bo7bo6b2o$45bo48bo7bo9bo27bo23b o$61b2o15b2o16bo15b2o26b2o6bo7bo6b2o$62bo15bo16b2o5bo16bo9bo22bo22bo$ 60bo19bo35b2o13b2o39b2o$116bo15bo39bo$68bo3bo45bo11bo21bo21bo2$70bo$ 68bo3bo7$136bo30bo$105bo3bo28bo26bo$66bo31bo17bo20b2o26b2o$10bo57bo27b o21bo16bo32bo$8b3o25bo30b2o22bo15bo15bo26bo2bo$8bo54bo12bo30bo$42bo51b obo21bobo29bo2bo$31bo32bo3bo4bobo31bo27bo32bo$9bo2bo20bobobobo51bo15bo 15bo13b2o26b2o$8b3o21b2o29bo12bo19bo21bo19bo26bo$67b2o29bo17bo19bo30bo $68bo36bo3bo$7bo3bo54bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
(click above to open LifeViewer)

Spaceships

There are two very important small orthogonal spaceships:

x = 10, y = 3, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e 6bo2bo$obo3b3o$3o4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
(click above to open LifeViewer)

The c/2 is generally labeled as G, and the 2c/4 as R. There exist G guns for all possible periods greater than 11. R guns can exist for periods 9 and above, but no guns have ever been found of periods 9 and 10.

Besides c/2 orthogonal, the only known spaceship speeds are 2c/6 orthogonal, 2c/19 orthogonal and 2c/12 diagonal, with the smallest examples being:

x = 41, y = 10, rule = B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e 9b6o10b3o10bo$5bo2b5obo10bobo9b3o$3o6bobobobo9b3o12bo$8bob3obo9bo3bo$ 4b3o2bo2b3o22bo2bo$bo6bobo10bo9bo$8b3o10bo4bo4bo$5bo15bo9bo$23bo5bo$ 26bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
(click above to open LifeViewer)

The latter two spaceships have since appeared naturally in C1 soups, and have a synthesis from G's. For all known speeds there are puffers, but only the orthogonal speeds have rakes.

A universal constructor is in the works by Goldtiger997 and several other users, which may lead to a very high-period spaceship, much like Life's universal constructor-based spaceships.

References

  1. Rhombic (February 16, 2018). Re: OCA Discovery of the Year 2017 - Results (discussion thread) at the ConwayLife.com forums

External links