This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability, the descendant patterns exponentially drift away from ancestral patterns, even when the automaton is deterministic. While this is far from being the first instance of evolutionary dynamics in a cellular automaton, it is the first to do so by exploiting the power and convenience of Neural Cellular Automata, arguably increasing the space of variations and the opportunity for Open Ended Evolution.
These mutations despite the NCA rules being deterministic could be due to rounding errors that often occur with floating point number representation.
It is also possible that stochasticity is introduced elsewhere in the model unbeknownst to the experimenter, or due to the equipment (stochasticity in GPU runs). Note that these causes would still satisfy the definition of closed model by (cite: OEEprize). Finally, there is the possibility that each division is inherently different from the previous one, i.e. that the model that is genuinely deterministic but chaotic. This last hypothesis is reinforced by the fact that running the synchronous model from the same starting point always seems to lead to similar final results, even if those results are far from the initial state.
Mordvintsev, A., Randazzo, E., Niklasson, E., & Levin, M. (2020). Growing Neural Cellular Automata. Distill, 5(2). 10.23915/distill.00023