Abstract
A number-conserving cellular automaton (NCCA) is a cellular automaton such that all states of cells are represented by integers and the total of the numbers (states) of all cells of a global configuration is conserved throughout its computing process. It can be thought to be a kind of modelization of the physical conservation law of mass or energy. In this paper, we show a sufficient condition for a Moore neighborhood CA to be number-conserving. According to this condition, the local function of rotation-symmetric NCCA is expressed by a summation of quaternary functions. On this framework, we construct a 6-state logically universal NCCA.
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Tanimoto, N., Imai, K. (2008). A Construction Method of Moore Neighborhood Number-Conserving Cellular Automata. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_31
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DOI: https://doi.org/10.1007/978-3-540-79992-4_31
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