Cellular Automata in Hyperbolic Space

[Mandelbrot]

God it really has been two years since I used this account...

So recently I've been playing this game called HyperRogue, a game that takes place on a tiling of the hyperbolic plane. For those who don't know what the hyperbolic plane is, I'd recommend watching this video, and/or playing HyperRogue itself. But to provide an oversimplified explanation, hyperbolic space is a space that curves away from itself, causing lines that would be parallel in normal space to diverge in hyperbolic space.

Anyway, the grid-based nature of HyperRogue got me wondering... what if we emulated cellular automata on the hyperbolic plane?

Turns out I was not the first person to ask this question. Upon looking it up I saw someone took it upon themselves to try and put life on the hyperbolic plane, and although he didn't do much of a thorough investigation into what kind of structures or spaceships or whatever could be made using various rules and tilings, he did still get a basic program working at the end of the day. (Well, basic isn't exactly an accurate term to use given this is super complicated math and stuff but you get what I mean.)

Hopefully with this topic started you guys can look into this further, as I see this as a topic with a lot of stuff to find.

[hotdogPi]

HyperRogue actually has a cellular automata feature.

[Mandelbrot]

HyperRogue actually has a cellular automata feature.

Yes, I was aware it had that! I just made this thread so people could discuss ther findings and such.

[Mandelbrot]

Bumping this thread cause I'd love to learn more about this and this thread seems to be ignored for some reason.

Also I'm a tad lonely.

[breaker's glider gun]

Oh, living cave (and living fjord) are ca too.

[muzik]

Interestingly, "parity"/"everything replicates" rules seem to not really exist on hyperbolic grids. Plugging in the expected values just produces a pattern that explodes infinitely, likely due to the increased amount of diagonal neighbours each cell attains.



Worth noting is the fact that this is unlike the triangular Euclidean neighbourhood - it has these replication rules as you'd expect:

Code: Select all

 x = 1, y = 1, rule = B13579Y/S13579YL
o!

Code: Select all

 x = 1, y = 1, rule = B13579Y/S02468XZL
o!

[breaker's glider gun]

what app/web thing did you use? That is definetly not hyperrouge.

definetly

somehow I can't spell it right - help please!

[Ohhhhhhhhh]

definetly

somehow I can't spell it right - help please!

It’s definitely.

[breaker's glider gun]

thanks!