Cellular Automata Models of Disorder And Organization

Cellular automata are mathematical objects introduced in 1948 by J. von Neumann and S. Ulam to “abstract the logical structure of life” [1], Since then, they have established themselves as unique tools to analyze the emergence of global organization, complexity, and pattern formation from the iteration of local operations between simple elements. They have also been extensively used as models of universal computation, and are being increasingly applied to a variety of concepts from physics and chemistry[2]. They are in fact versatile enough to offer analogies with almost all the themes discussed at this meeting (in particular: self-organization, dissipative systems, spatial vs. thermal fluctuations, neural networks, optimization, ergodicity-breaking, and ultrametricity)

[1]  J. Wheeler,et al.  The Physics of Time Asymmetry , 1974 .

[2]  Tommaso Toffoli,et al.  Cellular automata mechanics. , 1977 .

[3]  R. Tolman,et al.  The Principles of Statistical Mechanics. By R. C. Tolman. Pp. xix, 661. 40s. 1938. International series of monographs on physics. (Oxford) , 1939, The Mathematical Gazette.

[4]  Martin Gardner,et al.  Wheels, life, and other mathematical amusements , 1983 .

[5]  S. Wolfram,et al.  Two-dimensional cellular automata , 1985 .

[6]  E. F. Codd,et al.  Cellular automata , 1968 .

[7]  R. E. Mills,et al.  Critical phenomena in alloys, magnets, and superconductors , 1971 .

[8]  Y. Pomeau.  Invariant in cellular automata , 1984 .

[9]  F. Fogelman-Soulié,et al.  Random Boolean Networks , 1981 .

[10]  G. Grest,et al.  Structure and evolution of quenched Ising clusters , 1984 .

[11]  Eytan Domany,et al.  Equivalence of Cellular Automata to Ising Models and Directed Percolation , 1984 .

[12]  Gérard Y. Vichniac.  Instability in Discrete Algorithms and Exact Reversibility , 1984 .

[13]  F. Dyson,et al.  Disturbing The Universe , 1979 .

[14]  P. Hohenberg,et al.  Theory of Dynamic Critical Phenomena , 1977 .

[15]  Ian G. Enting,et al.  Crystal growth models and Ising models: Disorder points , 1977 .

[16]  R. Feynman.  The Character of Physical Law , 1965 .

[17]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[18]  Y. Pomeau,et al.  Molecular dynamics of a classical lattice gas: Transport properties and time correlation functions , 1976 .

[19]  M. Mézard,et al.  Nature of the Spin-Glass Phase , 1984 .

[20]  Jacques Demongeot,et al.  Dynamical Systems and Cellular Automata , 1985 .

[21]  I. Oppenheim,et al.  Nonlinear transport processes: Hydrodynamics , 1979 .

[22]  David Griffeath,et al.  Multicomponent Random Systems , 1980 .

[23]  W. Kinzel.  Phase transitions of cellular automata , 1985 .

[24]  E. G. Chacc.  Comportement dynamique de réseaux d'automates , 1985 .

[25]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[26]  Tommaso Toffoli,et al.  Cellular automata : proceedings of an interdisciplinary workshop, Los Alamos, New Mexico 87545, USA, March 7-11, 1983 , 1984 .

[27]  Bennett,et al.  Role of irreversibility in stabilizing complex and nonergodic behavior in locally interacting discrete systems. , 1985, Physical Review Letters.

[28]  Arthur W. Burks,et al.  Essays on cellular automata , 1970 .