A friend of mine has done something similar, albeit he turned it into quite an engine for creating CA universes:

https://wizard23.github.io/evocell/cellspace.html

"All rule lookups and most of the collission detections are calculated on the GPU."

Every time I swing by Evocell to have a look, I am impressed with the performance he has managed to gain ..

I've been interested in continuous automata for a good while! I usually call it "Reaction Diffusion" (good old Turing!) but a lot of people hearing that might think I might just mean "Gray Scott", but I actually mean the whole realm of solving various types of equations (in feedback of course) on continuous-valued fields. My software of choice for that is gollygang/Ready (where some of my experiments are available to play with in the release) and also Houdini, to use the resulting simulation data in whatever way one creatively desires!

Here's one from my channel:

https://youtu.be/W6sO8ZkgU9s?si=x-_e3j4IFX0qtekL

Edit:Typo

I have been asking myself for a while: Why has Artificial Life not had its AlexNet moment with GPUs yet?

Had hoped to see Neural Cellular Automata [1] mentioned as an extension of continuous, learnable automata.

[1] https://distill.pub/2020/growing-ca/