MaCE: General Mass Conserving Dynamics for Cellular Automata

2025-07-16

AI Summary

This work addresses the pervasive mass non-conservation problem in cellular automata (CA). We propose MaCE—a general, lightweight mass conservation embedding mechanism—built upon a numerically stable discrete dynamical framework compatible with both continuous and discrete systems. MaCE seamlessly integrates into diverse CA models, including Lenia, neural CAs, and classical discrete CAs. Its key contribution is the first architecture-agnostic realization of universal mass conservation in CA, effectively suppressing pattern explosion or collapse and enabling long-term stable evolution. Experiments demonstrate that MaCE efficiently generates abundant soliton-like states under resource constraints and spontaneously exhibits evolutionary-like dynamic behaviors. By ensuring controllable, scalable, and physically plausible dynamics, MaCE establishes a novel paradigm for modeling complex systems with guaranteed conservation laws.

Technology Category

• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Machine Learning: Evolutionary Learning
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Implement mass conservation in Cellular Automata
• Prevent pattern explosion or extinction in CAs
• Enable diverse behaviors in resource-constrained environments

Innovation

• Mass-conserving evolution rule for CAs
• Numerically stable with simple continuous limit
• Versatile application to Neural and discrete CAs