Upper Bound on the Products of Particle Interactions in Cellular Automata

Details Upper Bound on the Products of Particle Interactions in Cellular Automata Upper Bound on the Products of Particle Interactions in Cellular Automata

2000-08-29

arxiv.org/abs/nlin/0008038v3

Physica D 154 (2001): 240--258

Nonlinear Sciences

Cellular Automata and Lattice Gases

17 pages, 12 figures, 3 tables, http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and accompanying text

Scientific paper

10.1016/S0167-2789(01)00252-4

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can generate. The upper bound is controlled by the structural complexity of the interacting particles---a quantity which is defined here and which measures the amount of spatio-temporal information that a particle stores. Along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata; thereby elucidating why that approach is of general utility. The upper bound is tested against several relatively complex domain-particle cellular automata and found to be tight.

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