{"ID":2894009,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.12306","arxiv_id":"2507.12306","title":"MaCE: General Mass Conserving Dynamics for Cellular Automata","abstract":"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.","short_abstract":"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 expl...","url_abs":"https://arxiv.org/abs/2507.12306","url_pdf":"https://arxiv.org/pdf/2507.12306v1","authors":"[\"Vassilis Papadopoulos\",\"Etienne Guichard\"]","published":"2025-07-16T15:04:52Z","proceeding":"nlin.CG","tasks":"[\"nlin.CG\",\"cs.NE\",\"nlin.AO\"]","methods":"[]","has_code":false}