Simulations between triangular and hexagonal number-conserving cellular automata

Katsunobu Imai 1, 2, * Bruno Martin 2
Abstract : 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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Communication dans un congrès
International Workshop on Natural Computing, Sep 2008, Yokohama, Japan
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Dernière modification le : lundi 5 novembre 2018 - 15:48:02
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  • HAL Id : hal-00315932, version 1
  • ARXIV : 0809.0355

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Katsunobu Imai, Bruno Martin. Simulations between triangular and hexagonal number-conserving cellular automata. International Workshop on Natural Computing, Sep 2008, Yokohama, Japan. 〈hal-00315932〉

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