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

arXiv: https://arxiv.org/abs/2609.19902 · HTML: https://mlsanity.com/paper/2609.19902/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [Lenia - Biology of Artificial Life](https://mlsanity.com/paper/1812.05433/) (2018)
- [Lenia and Expanded Universe](https://mlsanity.com/paper/2005.03742/) (2020)
- [Towards Large-Scale Simulations of Open-Ended Evolution in Continuous Cellular Automata](https://mlsanity.com/paper/2304.05639/) (2023)
- [Biomaker CA: a Biome Maker project using Cellular Automata](https://mlsanity.com/paper/2307.09320/) (2023)
- [Self-Replication, Spontaneous Mutations, and Exponential Genetic Drift in Neural Cellular Automata](https://mlsanity.com/paper/2305.13043/) (2023)
- [Self-Organizing Intelligent Matter: A blueprint for an AI generating algorithm](https://mlsanity.com/paper/2101.07627/) (2021)
- [Online adaptation in robots as biological development provides phenotypic plasticity](https://mlsanity.com/paper/2006.02367/) (2020)
- [Capturing Emerging Complexity in Lenia](https://mlsanity.com/paper/2305.09378/) (2023)

## Abstract (arXiv)

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.