Show HN: Game of Life on non-square topologies with 2^32 update rules (github.com)

You can't post something like that without screenshots. It's against Internet law.

Can you extend it to non-uniform causal graphs with continuous state (as opposed to discrete)?

Playing on Klein bottles? That sounds like The Flower Game? https://www.destinypedia.com/Flower_game

(from https://www.destinypedia.com/Garden)

Missed the opportunity to call it Gogol :)

I may be misreading it, but doesn't the GoL as commonly understood also depend on diagonal neighbors (i.e. 8 direct neighbors)? In that case the rule space would explode beyond the 32 bit integer one. (to a 256 bit one)

Look up the b/s format for specifying rules. It is a lot more flexible.

Here's my version : https://github.com/chewxy/ll/blob/main/main.go#L176

I also live coded this in a series of 3 videos:

1. https://youtu.be/5JArQO8YeRo 2. https://youtu.be/ZLUVAWb_31M 3. https://youtu.be/BIypQF7M9c8

My approach differs from yours in that mine is entirely matrix driven.

I don't understand the update rules as described in the readme.

In an 3x3 neighborhood there are 2^9, not 2^5 states. So we should get 2^512 possible update rules, not 2^32.

I think something similar is described in https://conwaylife.com/wiki/Rule_integer.

I'm not sure that all of those rules are valid. We must have translational invariance. One way to do that is to only update the state of the central cell in each considered neighborhood. In that case 2^9 rules are enough. Are there other ways to define consistent rules for a CA?

You might also be interested in https://github.com/bignimbus/game-of-life-n

I don't understand how the border topologies change the game of life compared to when it's set on a regular plane

You say it can be played on a variety of manifolds, but if the topology of a manifold "locally resembles Euclidean space near each point", considering that the game of life rules are always super local, then how does that change anything compared to a plane

Videos!

I really don't understand the diagrams, and how they relate to the shape that each diagram is labeled as.

Penrose tilings

During a recent programming adventure, I discovered that finite elementary cellular automata with periodic boundary conditions can be simulated using matrix-vector multiplication with a circulant matrix and a strange kind of algebra, which I call a kernel algebra. [1] I wonder if this same idea could be generalized to higher dimensional automata on other topological surfaces.

[1]: https://github.com/breandan/galoisenne/blob/8f0f1e9e4e02062c...

Golly is another way to explore 2d cellular automata and it also has a good UI. It is written in Python.

Shameless (related) plug: Check out broader cellular-automata sim with custom update rules you can define in json (and run the game on the page itself).

https://aperocky.com/cellular-automata/

This allows for more "block state" too in addition to just the black and white for GOL. Also allows some time based rules (i.e. change based off block age that it stayed unchanged).

I've gravitated to essentially a file description (and the corresponding parser) to set up the rules - this makes making and adding rules easier.

See also SmoothLife, an amazing continuous version of Game of life. Integers are replaced by floats providing the same patterns with circular shapes. Here: https://conwaylife.com/wiki/OCA:SmoothLife