# Flow-Lenia: Emergent evolutionary dynamics in mass conservative continuous cellular automata

arXiv: https://arxiv.org/abs/2506.08569 · HTML: https://mlsanity.com/paper/2506.08569/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Lenia - Biology of Artificial Life](https://mlsanity.com/paper/1812.05433/) (2018)
- [evosax: JAX-based Evolution Strategies](https://mlsanity.com/paper/2212.04180/) (2022)
- [Lenia and Expanded Universe](https://mlsanity.com/paper/2005.03742/) (2020)
- [Flow-Lenia: Towards open-ended evolution in cellular automata through mass conservation and parameter localization](https://mlsanity.com/paper/2212.07906/) (2022)
- [Towards Large-Scale Simulations of Open-Ended Evolution in Continuous Cellular Automata](https://mlsanity.com/paper/2304.05639/) (2023)
- [Discovering Sensorimotor Agency in Cellular Automata using Diversity Search](https://mlsanity.com/paper/2402.10236/) (2024)
- [Self-Replication, Spontaneous Mutations, and Exponential Genetic Drift in Neural Cellular Automata](https://mlsanity.com/paper/2305.13043/) (2023)
- [Requirements for Open-Ended Evolution in Natural and Artificial Systems](https://mlsanity.com/paper/1507.07403/) (2015)
- [Emergence of Self-Reproducing Metabolisms as Recursive Algorithms in an Artificial Chemistry](https://mlsanity.com/paper/2103.08245/) (2021)
- [Self-Reproduction and Evolution in Cellular Automata: 25 Years after Evoloops](https://mlsanity.com/paper/2402.03961/) (2024)

## Built on by (most cited first, 2 of 2)

- [Neuroevolution Arena: Nested Ecological Evaluation of Update-and-Inheritance Regimes across Neural Architectures](https://mlsanity.com/paper/2608.10323/) (2026)
- [The Artificial Experimentalist: Discovery and Control of Self-Organizing Phenomena with Autotelic Reinforcement Learning](https://mlsanity.com/paper/2608.26116/) (2026)

## Abstract (arXiv)

Central to the artificial life endeavour is the creation of artificial systems spontaneously generating properties found in the living world such as autopoiesis, self-replication, evolution and open-endedness. While numerous models and paradigms have been proposed, cellular automata (CA) have taken a very important place in the field notably as they enable the study of phenomenons like self-reproduction and autopoiesis. Continuous CA like Lenia have been showed to produce life-like patterns reminiscent, on an aesthetic and ontological point of view, of biological organisms we call creatures. We propose in this paper Flow-Lenia, a mass conservative extension of Lenia. We present experiments demonstrating its effectiveness in generating spatially-localized patters (SLPs) with complex behaviors and show that the update rule parameters can be optimized to generate complex creatures showing behaviors of interest. Furthermore, we show that Flow-Lenia allows us to embed the parameters of the model, defining the properties of the emerging patterns, within its own dynamics thus allowing for multispecies simulations. By using the evolutionary activity framework as well as other metrics, we shed light on the emergent evolutionary dynamics taking place in this system.