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We compare several definitions for number-conserving cellular automata that we prove to be equivalent. A necessary and sufficient condition for cas to be number-conserving is proved. Using this condition, we give a linear-time algorithm to decide number-conservation. The dynamical behavior of number-conserving cas is studied and a classification that focuses on chaoticity is given.
Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter, and features a global symmetry. One then extends th
We investigate number conserving cellular automata with up to five inputs and two states with the goal of comparing their dynamics with diffusion. For this purpose, we introduce the concept of decompression ratio describing expansion of configuration
The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules with comp
We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically sensitive e
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at 0. Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are defined as linea