Cellular Automata with Particle Conservation
نویسندگان
چکیده
منابع مشابه
Conservation Laws in Cellular Automata
A conservation law in a cellular automaton is the statement of the invariance of a local and additive energy-like quantity. This chapter reviews the basic theory of conservation laws in cellular automata. A general mathematical framework for formulating conservation laws in cellular automata is presented and several characterizations of them are summarized. Computational problems regarding cons...
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If X is a discrete abelian group and A a finite set, then a cellular automaton (CA) is a continuous map F : A −→ A that commutes with all X-shifts. If φ : A −→ R, then, for any a ∈ A, we define Σφ(a) = ∑ x∈X φ(ax) (if finite); φ is conserved by F if Σφ is constant under the action of F. We characterize such conservation laws in several ways, deriving both theoretical consequences and practical ...
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The pattern formation of asynchronous cellular automata with mass conservation is explored. A cellular automaton rule causing a specified kind of pattern was manually designed, and the mechanism of pattern formation was found similar to real chemical process. In addition, a methodology to automatically search for pattern-forming cellular automata is proposed, and its performance is validated. T...
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The problem of describing the dynamics of a conserved energy in a cellular automaton in terms of local movements of “particles” (quanta of that energy) has attracted some people’s attention. The one-dimensional case was already solved by Fukś (2000) and Pivato (2002). For the two-dimensional cellular automata, we show that every (contextfree) conservation law can be expressed in terms of such p...
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We discuss a close link between two seemingly different topics studied in the cellular automata literature: additive conservation laws and invariant probability measures. We provide an elementary proof of a simple correspondence between invariant full-support Bernoulli measures and interaction-free conserved quantities in the case of onedimensional surjective cellular automata. We also discuss ...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 1989
ISSN: 0033-068X,1347-4081
DOI: 10.1143/ptp.81.47