Entropic cellular automata

a system where each cell tries to clamp its local entropy in a range. got the idea while working on my AdS/CFT emergent gravity simulation (WIP, unpublished as of the time i am writing this, probably never finishing it :3)

algorithm

i am losing my sanity trying to get mathjax to work here, so please go to the codeberg repo for the details of the algorithm.

observed behaviour

0. in most cases, an grid of only 0s turns to a grid of only 1s, then turns to a grid of all 0s, and such.
1. tight centered boundaries (e.g. $H_\text{min} = 0.45$, $H_\text{max} = 0.55$) result in noise-like behaviour
2. loosy centered boundaries (e.g. $H_\text{min} = 0.3$, $H_\text{max} = 0.6$) result in clumps of 0s and 1s with 1s scattered around the grid
3. loosier centered boundaries (e.g. $H_\text{min} = 0.3$, $H_\text{max} = 0.7$) result in the "boundries" of the initial "shapes" being replicated in a ripple-like manner

demo

demonstration of the 2nd case: