# MaCE: General Mass Conserving Dynamics for Cellular Automata

arXiv: https://arxiv.org/abs/2507.12306 · HTML: https://mlsanity.com/paper/2507.12306/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2025.

## Built on by (most cited first, 1 of 1)

- [Visualizing the Structure of Lenia Parameter Space](https://mlsanity.com/paper/2601.01932/) (2026)

## Abstract (arXiv)

We present Mass-Conserving Evolution (MaCE), a general method for implementing mass conservation in Cellular Automata (CA). MaCE is a simple evolution rule that can be easily 'attached' to existing CAs to make them mass-conserving, which tends to produce interesting behaviours more often, as patterns can no longer explode or die out. We first show that MaCE is numerically stable and admits a simple continuous limit. We then test MaCE on Lenia, and through several experiments, we demonstrate that it produces a wide variety of interesting behaviours, starting from the variety and abundance of solitons up to hints of intrinsic evolution in resource-constrained environments. Finally, we showcase the versatility of MaCE by applying it to Neural-CAs and discrete CAs, and discuss promising research directions opened up by this scheme.