Identification of ECA rules forming MACA in periodic boundary condition

Som Banerjee () and Mamata Dalui
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Som Banerjee: Department of Computer Science and Engineering, National Institute of Technology, Durgapur, West Bengal 713209, India
Mamata Dalui: Department of Computer Science and Engineering, National Institute of Technology, Durgapur, West Bengal 713209, India

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 01, 1-17

Abstract: Cellular automaton (CA) is a computing model which is emerging rapidly. It is largely used in different types of scientific applications and simulations due to its ability to solve complex problems using simple rule(s). Cellular automata (CAs) are used in different types of applications like cryptography, VLSI systems, fault detection, etc. Typically, most of these applications utilize one-dimensional, 2-state, 3-neighborhood CAs. This paper explores the concept of Next State RMT Transition Diagram (NSRTD) for characterization of all the Elementary Cellular Automata (ECA) rules in periodic boundary condition leading to the identification of all ECA rules forming more than two fixed points (referred to as Single Length Cycle Multi-Attractor CA (MACA)) for an arbitrary CA length (n). For this, the 88 Wolfram classification rules and their equivalent rules have been utilized to reduce the search complexity by avoiding exhaustive searching on all the 256 ECA rules.

Keywords: Cellular automata; MACA; fixed point attractor; NSRTD; periodic boundary CA (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183124501730

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