Simulations between triangular and hexagonal number-conserving cellular automata
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.
Keywords
Cite
@article{arxiv.0809.0355,
title = {Simulations between triangular and hexagonal number-conserving cellular automata},
author = {Katsunobu Imai and Bruno Martin},
journal= {arXiv preprint arXiv:0809.0355},
year = {2008}
}
Comments
11 pages; International Workshop on Natural Computing, Yokohama : Japon (2008)