Upper Bound on the Products of Particle Interactions in Cellular Automata
Abstract
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.
Keywords
Cite
@article{arxiv.nlin/0008038,
title = {Upper Bound on the Products of Particle Interactions in Cellular Automata},
author = {Wim Hordijk and Cosma Rohilla Shalizi and James P. Crutchfield},
journal= {arXiv preprint arXiv:nlin/0008038},
year = {2009}
}
Comments
17 pages, 12 figures, 3 tables, http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and accompanying text modified, to comply with legal demands arising from on-going intellectual property litigation among third parties. V3: Accepted for publication in Physica D. References added and other small changes made per referee suggestions