MaCE: General Mass Conserving Dynamics for Cellular Automata
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909691698741248 |
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| author | Papadopoulos, Vassilis Guichard, Etienne |
| author_facet | Papadopoulos, Vassilis Guichard, Etienne |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12306 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | MaCE: General Mass Conserving Dynamics for Cellular Automata Papadopoulos, Vassilis Guichard, Etienne Cellular Automata and Lattice Gases Neural and Evolutionary Computing Adaptation and Self-Organizing Systems 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. |
| title | MaCE: General Mass Conserving Dynamics for Cellular Automata |
| topic | Cellular Automata and Lattice Gases Neural and Evolutionary Computing Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2507.12306 |