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...
متن کاملConservation Laws in Cellular Automata
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 ...
متن کاملConservation Laws and Invariant Measures in Surjective Cellular Automata
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 ...
متن کاملA particle displacement representation for conservation laws in two-dimensional cellular automata
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...
متن کاملSpatial Pattern Formation in Asynchronous Cellular Automata with Mass Conservation
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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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2002
ISSN: 0951-7715
DOI: 10.1088/0951-7715/15/6/305