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Several cellular automata (CA) models have been developed to simulate self-organization of multiple levels of structures. However, they do not obey microscopic reversibility and conservation laws. In this paper, we describe the construction of a reversible lattice molecular automata (RLMA) model, which simulates molecular interaction and self-organization of higher-order structures. The models strict reversibility entails physically relevant conservation laws, and thus opens a way to precise application and validation of the methods from statistical physics in studying the necessary conditions for such multiple levels of self-organization.
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
We study sources of isomorphisms of additive cellular automata on finite groups (called index-group). It is shown that many isomorphisms (called regular) of automata are reducible to the isomorphisms of underlying algebraic structures (such as the in
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