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Upper Bound on the Products of Particle Interactions in Cellular Automata | | Wim Hordijk
; Cosma Rohilla Shalizi
; James P. Crutchfield
; | | Date: |
30 Aug 2000 | | Journal: | Physica D 154 (2001): 240--258 | | Subject: | Cellular Automata and Lattice Gases; Adaptation and Self-Organizing Systems; Pattern Formation and Solitons | nlin.CG nlin.AO nlin.PS | | 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. | | Source: | arXiv, nlin.CG/0008038 | | Services: | Forum | Review | PDF | Favorites | |
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