Author:
Adamatzky Andrew,Martinez Genaro J.
Abstract
PurposeStudies 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/approachLet 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.FindingsThe 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/implicationsThe 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/valueThe hierarchy built presents the first ever approach to formally characterize generative potential of cellular automata.
Subject
Computer Science (miscellaneous),Social Sciences (miscellaneous),Theoretical Computer Science,Control and Systems Engineering,Engineering (miscellaneous)
Reference27 articles.
1. Adamatzky, A. (1994), Identification of Cellular Automata, Taylor & Francis, London.
2. Adamatzky, A. (Ed.) (2003), Collision Based Computing, Springer, New York, NY.
3. Adamatzky, A. and Grube, M. (2009), “Minimal cellular automaton model of inter‐species interactions: phenomenology, complexity and interpretations”, in Hoekstra, A., Kroc, J. and Sloot, P. (Eds), Modeling of Complex Systems Using Cellular Automata, Springer, New York, NY.
4. Batty, M. (2007), Cities and Complexity: Understanding Cities with Cellular Automata, Agent‐based Models, and Fractals, MIT Press, Cambridge, MA.
5. Brooks, D.R. and McLennan, D.A. (2002), The Nature of Diversity: An Evolutionary Voyage of Discovery, University of Chicago Press, Chicago, IL.
Cited by
14 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献