On generative morphological diversity of elementary cellular automata

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 limita...

[1]  R. Mace,et al.  The evolution of cultural diversity : a phylogenetic approach , 2005 .

[2]  M Herr Christiane,et al.  Using Cellular Automata to Generate High-Density Building Form , 2005 .

[3]  Andrew Adamatzky,et al.  Collision-Based Computing , 2002, Springer London.

[4]  Robert J Henry,et al.  Plant Diversity and Evolution: Genotypic and Phenotypic Variation in Higher Plants , 2004 .

[5]  Andrew Wuensche,et al.  Complexity in One-D Cellular Automata: Gliders, Basins of Attraction and the Z Parameter , 1994 .

[6]  Nizam Omar,et al.  Definition and Application of a Five-Parameter Characterization of One-Dimensional Cellular Automata Rule Space , 2001, Artificial Life.

[7]  Michael Batty,et al.  Cities and complexity - understanding cities with cellular automata, agent-based models, and fractals , 2007 .

[8]  Stephen Wolfram,et al.  Cellular Automata And Complexity , 1994 .

[9]  Bruce B. Collette,et al.  The Diversity of Fishes , 1997 .

[10]  Tomasz Arciszewski,et al.  Morphogenesis and structural design: cellular automata representations of steel structures in tall buildings , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[11]  Genaro Juárez Martínez,et al.  On the Representation of Gliders in Rule 54 by De Bruijn and Cycle Diagrams , 2008, ACRI.

[12]  G. Helfman,et al.  The Diversity of Fishes: Biology, Evolution, and Ecology , 2009 .

[13]  Juan Carlos Seck Tuoh Mora,et al.  Complex Dynamics Emerging in Rule 30 with Majority Memory , 2009, Complex Syst..

[14]  Andrew Adamatzky,et al.  Language networks: Their structure, function, and evolution , 2010 .

[15]  Antonio Nicita,et al.  The evolution of economic diversity , 2001 .

[16]  Victor A. Skormin,et al.  Immunocomputing - principles and applications , 2003 .

[17]  Andrew Wuensche,et al.  The global dynamics of cellular automata : an atlas of basin of attraction fields of one-dimensional cellular automata , 1992 .

[18]  Alan S. Perelson,et al.  Population Diversity in an Immune System Model: Implications for Genetic Search , 1992, FOGA.

[19]  Christopher G. Langton,et al.  Computation at the edge of chaos: Phase transitions and emergent computation , 1990 .

[20]  Sten A. O. Thore,et al.  The diversity, complexity, and evolution of high tech capitalism , 1995 .

[21]  Genaro J.. Martinez.  On complexity of chaotic elementary cellular automaton with memory: Rule 126 , 2009 .

[22]  Andrew Adamatzky,et al.  Minimal Cellular Automaton Model of Inter-species Interactions: Phenomenology, Complexity and Interpretations , 2010, Simulating Complex Systems by Cellular Automata.

[23]  Wentian Li,et al.  The Structure of the Elementary Cellular Automata Rule Space , 1990, Complex Syst..

[24]  Daniel R. Brooks,et al.  The Nature of Diversity: An Evolutionary Voyage of Discovery , 2002 .

[25]  Juan Carlos Seck Tuoh Mora,et al.  Reproducing the Cyclic Tag System Developed by Matthew Cook with Rule 110 Using the Phases fi_1 , 2011, J. Cell. Autom..

[26]  Stephen A. Billings,et al.  The Identification of Cellular Automata , 2006, J. Cell. Autom..

[27]  Wentian Li,et al.  Phenomenology of nonlocal cellular automata , 1992 .