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During its Convergenceevolution, an irreversible finite cellular automaton (CA) approaches to a set of configurations that form a cycle called attractor. Attractors can be of different lengths. If the length of an attractor is 1, then it is a point attractor, which is also called as point state attractor, fixed point, single length cycle attractor. When all the attractors of a CA are point attractors, the CA is known as Multiple Attractor Cellular Automaton (MACA). As a special case, if the number of attractors is one and it is a point attractor, then the CA is a Single Attractor Cellular Automaton (SACA). This chapter deals with the cellular automata (CAs) that form only point attractors in their configuration space. Such a CA is converging—that is, if initialized with a configuration, the CA eventually reaches a point attractorConvergencepoint attractor.

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Convergence

  • 章节

  • 发表日期：

    2026年

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  • Sukanta Das,
  • Biplab K. Sikdar

摘要

During its Convergenceevolution, an irreversible finite cellular automaton (CA) approaches to a set of configurations that form a cycle called attractor. Attractors can be of different lengths. If the length of an attractor is 1, then it is a point attractor, which is also called as point state attractor, fixed point, single length cycle attractor. When all the attractors of a CA are point attractors, the CA is known as Multiple Attractor Cellular Automaton (MACA). As a special case, if the number of attractors is one and it is a point attractor, then the CA is a Single Attractor Cellular Automaton (SACA). This chapter deals with the cellular automata (CAs) that form only point attractors in their configuration space. Such a CA is converging—that is, if initialized with a configuration, the CA eventually reaches a point attractorConvergencepoint attractor.