Evolution Theory, Periodic Particles, and Solitons in Cellular Automata
Theodore S. Papatheodorou, ATHANASSIOS S. FOKAS · Studies in Applied Mathematics · 1989
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.