# Towards Large-Scale Simulations of Open-Ended Evolution in Continuous Cellular Automata

arXiv: https://arxiv.org/abs/2304.05639 · HTML: https://mlsanity.com/paper/2304.05639/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2023.

## Built on by (most cited first, 10 of 10)

- [Automating the Search for Artificial Life with Foundation Models](https://mlsanity.com/paper/2412.17799/) (2024)
- [Biomaker CA: a Biome Maker project using Cellular Automata](https://mlsanity.com/paper/2307.09320/) (2023)
- [Discovering Sensorimotor Agency in Cellular Automata using Diversity Search](https://mlsanity.com/paper/2402.10236/) (2024)
- [Exploring Flow-Lenia Universes with a Curiosity-driven AI Scientist: Discovering Diverse Ecosystem Dynamics](https://mlsanity.com/paper/2505.15998/) (2025)
- [Flow-Lenia: Emergent evolutionary dynamics in mass conservative continuous cellular automata](https://mlsanity.com/paper/2506.08569/) (2025)
- [Capturing Emerging Complexity in Lenia](https://mlsanity.com/paper/2305.09378/) (2023)
- [Guiding Evolution of Artificial Life Using Vision-Language Models](https://mlsanity.com/paper/2509.22447/) (2025)
- [The Emergence of Complex Behavior in Large-Scale Ecological Environments](https://mlsanity.com/paper/2510.18221/) (2025)
- [Evolving Many Worlds: Towards Open-Ended Discovery in Petri Dish NCA via Population-Based Training](https://mlsanity.com/paper/2604.11248/) (2026)
- [Self-Replicating Neural Cellular Automata: Quantifying Emergent Phenotypic and Genotypic Diversity in an OpenEnded Substrate](https://mlsanity.com/paper/2609.19902/) (2026)

## Abstract (arXiv)

Inspired by biological and cultural evolution, there have been many attempts to explore and elucidate the necessary conditions for open-endedness in artificial intelligence and artificial life. Using a continuous cellular automata called Lenia as the base system, we built large-scale evolutionary simulations using parallel computing framework JAX, in order to achieve the goal of never-ending evolution of self-organizing patterns. We report a number of system design choices, including (1) implicit implementation of genetic operators, such as reproduction by pattern self-replication, and selection by differential existential success; (2) localization of genetic information; and (3) algorithms for dynamically maintenance of the localized genotypes and translation to phenotypes. Simulation results tend to go through a phase of diversity and creativity, gradually converge to domination by fast expanding patterns, presumably a optimal solution under the current design. Based on our experimentation, we propose several factors that may further facilitate open-ended evolution, such as virtual environment design, mass conservation, and energy constraints.