Simulations between triangular and hexagonal number-conserving cellular automata

Details Simulations between triangular and hexagonal number-conserving cellular automata Simulations between triangular and hexagonal number-conserving cellular automata

2008-09-02

arxiv.org/abs/0809.0355v1

Computer Science

Discrete Mathematics

11 pages; International Workshop on Natural Computing, Yokohama : Japon (2008)

Scientific paper

A number-conserving cellular automaton is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modelization of the physical conservation laws of mass or energy. In this paper, we first propose a necessary condition for triangular and hexagonal cellular automata to be number-conserving. The local transition function is expressed by the sum of arity two functions which can be regarded as 'flows' of numbers. The sufficiency is obtained through general results on number-conserving cellular automata. Then, using the previous flow functions, we can construct effective number-conserving simulations between hexagonal cellular automata and triangular cellular automata.

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