Self-Replicating Neural Cellular Automata: Quantifying Emergent Phenotypic and Genotypic Diversity in an OpenEnded 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 neighborhood. A cell persists only by self-replication: a living neighbor 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 x 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. Code, data and animations are released as supplementary material.
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BibTeX
@misc{jain2026selfreplicating,
title = {{Self-Replicating Neural Cellular Automata: Quantifying Emergent Phenotypic and Genotypic Diversity in an OpenEnded Substrate}},
author = {Sanyam Jain and Felix Simon Reimers and Stefano Nichele},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19902},
eprint = {2609.19902},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19902},
}
RIS
TY - UNPB
TI - Self-Replicating Neural Cellular Automata: Quantifying Emergent Phenotypic and Genotypic Diversity in an OpenEnded Substrate
AU - Sanyam Jain
AU - Felix Simon Reimers
AU - Stefano Nichele
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19902
UR - https://arxiv.org/abs/2609.19902
AB - 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 neighborhood. A cell persists only by self-replication: a living neighbor 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 x 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. Code, data and animations are released as supplementary material.
ER -