Guy Birkin on Nostr: Among the various patterns produced by applying 2-colour block cellular automaton ...
Among the various patterns produced by applying 2-colour block cellular automaton rule 39 to all 1024 possible initial conditions for a CA size of 10 cells, it seems that there are relatively few unique patterns, not counting translational and rotational symmetries. I count 9 unique patterns so far. working on a way to confirm this estimate mathematically and calculate the number of unique patterns for any given size...
Published at
2026-07-30 18:37:09 UTCEvent JSON
{
"id": "4cee2184821993b8d4ee56787698518ad06bd14e55c61563a9f00daeb5607748",
"pubkey": "1881231f442566876d748aeb46ce6303211563a170382ee73043b358b84197ea",
"created_at": 1785436629,
"kind": 1,
"tags": [
[
"imeta",
"url https://post.lurk.org/system/media_attachments/files/117/010/344/505/564/239/original/fecb7c6c2fc55eca.png",
"m image/png",
"dim 1952x1952",
"blurhash U2G95C4nRj%M4nayWBj[%MRjofWB?bayj[j["
],
[
"proxy",
"https://post.lurk.org/users/GuyBirkin/statuses/117010374930354961",
"activitypub"
],
[
"client",
"Mostr",
"31990:6be38f8c63df7dbf84db7ec4a6e6fbbd8d19dca3b980efad18585c46f04b26f9:mostr",
"wss://relay.ditto.pub"
]
],
"content": "Among the various patterns produced by applying 2-colour block cellular automaton rule 39 to all 1024 possible initial conditions for a CA size of 10 cells, it seems that there are relatively few unique patterns, not counting translational and rotational symmetries. I count 9 unique patterns so far. working on a way to confirm this estimate mathematically and calculate the number of unique patterns for any given size...\n\nhttps://post.lurk.org/system/media_attachments/files/117/010/344/505/564/239/original/fecb7c6c2fc55eca.png",
"sig": "e556541ec1cc414a8ded5639e2bc782239799043bd02cda9ab13d92926c90cb1a5b822d718f67a8295d9490f64655a4fd6ebe34baf5490e53cd6bc53d986c024"
}
