Characteristics of fractal cellular automata constructed from linear rules
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Cellular automata (CAs) have played a significant role in the study of complex systems. Recently, the recursive estimation of neighbors (REN) algorithm was proposed to extend a CA rule with a unit rule radius to rules with larger radii. This framework enables the construction of non-uniform CAs comprising cells that follow different CA rules. A non-uniform CA, referred to as fractal CA (F-CA), which comprises fractally arranged cells, inherits certain characteristics of basic CAs, including pattern replicability and time-reversibility of linear rules. In this paper, F-CAs based on linear rules, particularly the elementary CA #90 and #150, and life-like CA B1357S1357 and B1357S02468 are investigated. Cells in the F-CAs of #90 and B1357S1357 are separated into groups by their rule radius and each group has an independent lifetime. The explicitly constructed inverse rule of F-CA of #150 is more complex than that of F-CA. The complexity of the F-CA of B1357S02468 and its inverse CA is demonstrated by image scrambling. The F-CAs can be applied to encoding and decoding processes for encryption systems.
KeywordsCA Non-uniform Life-like Reversible Inverse Encryption
The author wishes to thank all the anonymous reviewers for valuable comments and suggestions. This research was supported in part by a grant from BAIKA Gakuen, Japan.
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