Isn't this single frame state of a classic cellular automata? Note, not "just" because I mean no disrespect. I don't understand how this differs from Conway's life other than nuances of the live or die rule.
CGL doesn't have the scale invariance ("fractality") of ASM. ASM criticality is stable and persistent. "fractal life on edge"?
what that looks like
I don't believe that Game of Life is Abelian.