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Evolution Theory, Periodic Particles, and Solitons in Cellular Automata
Author(s) -
Papatheodorou T. S.,
Fokas A. S.
Publication year - 1989
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1989802165
Subject(s) - cellular automaton , automaton , property (philosophy) , characterization (materials science) , soliton , mathematics , state (computer science) , statistical physics , pure mathematics , physics , theoretical physics , computer science , nonlinear system , quantum mechanics , theoretical computer science , algorithm , philosophy , epistemology , optics
A theory for soliton automata is developed and applied to the analysis and prediction of patterns in their behavior. A complete characterization and method of construction of 1‐periodic particles is given. A general evolution theorem (GET) is obtained which provides significant information for a state in terms of preceding states. Application of this theorem yields several interesting results predicting periodicity and solitonic collisions. The GET explains and is based on a fundamental property of soliton automata, observed and analyzed in this paper, namely that pieces of information are lost on the left and reappear on the right.