NSRT diagram for identification of SACA and TACA rules in null-boundary

Mamata Dalui, Bidesh Chakraborty (), Nilanjana Das () and Biplab K. Sikdar ()
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Mamata Dalui: Department of Computer Science and Engineering, National Institute of Technology Durgapur, West Bengal 713209, India
Bidesh Chakraborty: ��Department of Computer Science and Engineering, Haldia Institute of Technology, Haldia, West Bengal 721657, India
Nilanjana Das: ��Department of Computer Science and Technology, Indian Institute of Engineering Science and Technology, Shibpur, West Bengal 711103, India
Biplab K. Sikdar: ��Department of Computer Science and Technology, Indian Institute of Engineering Science and Technology, Shibpur, West Bengal 711103, India

International Journal of Modern Physics C (IJMPC), 2022, vol. 33, issue 06, 1-25

Abstract: This work reports characterization of one-dimensional null-boundary cellular automata (CA) rules in 3-neighborhood. The outcome of this characterization is the identification of CA rules that are the probable candidates for producing single length cycle attractor (fixed point). It targets synthesis of CA with only one fixed point (referred to as the single length cycle single attractor CA (SACA)) and the CA with only two fixed points (referred to as single length cycle two attractors CA (TACA)) for arbitrary length. A tool referred to as Next State RMT Transition Diagram (NSRTD) is developed to identify the fixed points as well as the cycles, involving multiple states (multi-length cycles) of a CA. The NSRTD provides the theoretical basis to search for the rules that form SACA and TACA, for all lengths, in null-boundary.

Keywords: Cellular automata; fixed point; SACA; TACA; next state RMT transition diagram (NSRTD) (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0129183122500711

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