Embedding a Logically Universal Model and a Self-Reproducing Model into Number-Conserving Cellular Automata

Authors:
Katsunobu Imai;Kenji Fujita;Chuzo Iwamoto;Kenichi Morita
Affiliations:
-;-;-;-
Venue:
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
Year:
2002

Citing 2
Cited 3

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Physica D
Number-conserving cellular automaton rules

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Theoretical Computer Science - Special issue: Theoretical aspects of cellular automata
On universality of radius 1/2 number-conserving cellular automata

UC'10 Proceedings of the 9th international conference on Unconventional computation
Fluctuation-driven computing on number-conserving cellular automata

Information Sciences: an International Journal

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Abstract

A number-conserving cellular automaton (NCCA) is a cellular automaton (CA) such that all states of cells are represented by integers and the total number of its configuration is conserved throughout its computing process. It can be thought as a kind of modelization of the physical conservation law of mass or energy. Although NCCAs with simple rules are studied widely, it is quite difficult to design NCCAs with complex transition rules. We show a condition for two-dimensional von Neumann neighbor NCCAs with special symmetric rules and we construct a logically universal NCCA and a self-reproducing NCCA by employing this condition.