On generative morphological diversity of elementary cellular automata

Adamatzky, Andrew; Martinez, Genaro J.

Abstract

Purpose: Studies in complexity of cellular automata do usually deal with measures taken on integral dynamics or statistical measures of space-time configurations. No one has tried to analyze a generative power of cellular-automaton machines. The purpose of this paper is to fill the gap and develop a basis for future studies in generative complexity of large-scale spatially extended systems. Design/methodology/approach: Let all but one cell be in alike state in initial configuration of a one-dimensional cellular automaton. A generative morphological diversity of the cellular automaton is a number of different three-by-three cell blocks occurred in the automaton's space-time configuration. Findings: The paper builds a hierarchy of generative diversity of one-dimensional cellular automata with binary cell-states and ternary neighborhoods, discusses necessary conditions for a cell-state transition rule to be on top of the hierarchy, and studies stability of the hierarchy to initial conditions. Research limitations/implications: The method developed will be used - in conjunction with other complexity measures - to built a complete complexity maps of one- and two-dimensional cellular automata, and to select and breed local transition functions with highest degree of generative morphological complexity. Originality/value: The hierarchy built presents the first ever approach to formally characterize generative potential of cellular automata. © Emerald Group Publishing Limited.

Citation

Adamatzky, A., & Martinez, G. J. (2010). On generative morphological diversity of elementary cellular automata. Kybernetes, 39(1), 72-82. https://doi.org/10.1108/03684921011021282

• Journal Article Type: Article
• Publication Date: Jan 1, 2010
• Deposit Date: Jun 2, 2010
• Publicly Available Date: Apr 12, 2016
• Journal: Kybernetes
• Print ISSN: 0368-492X
• Publisher: Emerald
• Peer Reviewed: Peer Reviewed
• Volume: 39
• Issue: 1
• Pages: 72-82
• DOI: https://doi.org/10.1108/03684921011021282
• Keywords: automata theory, cybernetics, systems theory
• Public URL: https://uwe-repository.worktribe.com/output/982610
• Publisher URL: http://www.emeraldinsight.com/10.1108/03684921011021282