Title: An algorithm of finding rules for a class of cellular automata

Authors: Lei Kou; Fangfang Zhang; Luobing Chen; Wende Ke; Quande Yuan; Junhe Wan; Zhen Wang

Addresses: Institute of Oceanographic Instrumentation, Qilu University of Technology (Shandong Academy of Sciences), Qingdao, China ' School of Information and Automation Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China ' School of Information and Automation Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China ' Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen, China ' School of Computer Technology and Engineering, Changchun Institute of Technology, Changchun, China ' Institute of Oceanographic Instrumentation, Qilu University of Technology (Shandong Academy of Sciences), Qingdao, China ' Institute of Oceanographic Instrumentation, Qilu University of Technology (Shandong Academy of Sciences), Qingdao, China

Abstract: A cellular automata (CA) is an important modelling paradigm for complex systems. In the design of CA, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled system. A CA with weights (CAW) yields transition rules algorithm is proposed in this paper, which has ample physical meanings and extend the category of CA. Firstly, the weights are increased to connect the updated cell and its neighbours, and the output of each cell depends on the states of cells in the neighbourhood and their respective weights. Secondly, the error correction algorithm is adopted to find correct transition rules by adjusting weights. When the error is zero, the required transition rules with correct weights will be found to describe the fixed configuration. The CAW with the correct rules will relax to the fixed configuration regardless of the initial states. Finally, the mathematical analysis and simulation are carried out with one-dimensional CAW, and the results show that the proposed algorithm has the ability to find correct transition rules as the error converges exponentially.

Keywords: cellular automaton with weights; CAW; transition rules; updated cells; fixed configuration.

DOI: 10.1504/IJBIC.2023.132760

International Journal of Bio-Inspired Computation, 2023 Vol.21 No.4, pp.189 - 199

Received: 16 Feb 2022
Accepted: 30 Aug 2022
Published online: 09 Aug 2023 *

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