Abstract
A number-conserving cellular automaton (NCCA) is a cel lular automaton (CA) such that all states of cells are represented by integers and the total number of its configuration is conserved through- out 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.
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