Self-Replicating Neural Cellular Automata: Quantifying Emergent Phenotypic and Genotypic Diversity in an Open-Ended Substrate

Abstract

We study an in silico substrate in which every pixel of a two-channel cellular-automata grid carries a tiny neural network (an agent) that senses its Moore neighbourhood. A cell persists only by self-replication: a living neighbour is cloned, and its weights are mutated by a uniform perturbation, so that phenotype (cell state) is driven entirely by genotype (network weights). From a handful of seeded founders, the system grows into a spatially organized ecosystem of coexisting, competing and dominating species. Our main contribution is a battery of coarse-grained diversity metrics that make such growth measurable at two scales: four phenotypic tools based on cellular-type frequency, entropy and cell variance, and two genotypic tools that colour each agent by a hash of its full weight vector versus a sparse random-weight probe. Across a five-fold sweep of 1680 small runs and 24 long (1000-generation, 200 × 200) runs, the substrate is persistent and self-maintaining in 20 of the 24 long configurations and exposes a clear phenotype–genotype diversity trade-off: raising phenotypic diversity collapses genotypic diversity and vice versa. Full-genome hash colouring further reveals lineage structure that a random-weight probe systematically misses.