Does Life Resist Asynchrony?

Undoubtedly, Conway’s Game of Life — or simply Life — is one of the most amazing inventions in the field of cellular automata. Forty years after its discovery, the model still fascinates researchers as if it were an inexhaustible source of puzzles. One of the most intriguing questions is to determine what makes this rule so particular among the quasi-infinite set of rules one can search. In this chapter we analyse how the Game of Life is affected by the presence of two structural pertubations: a change in the synchrony of the updates and a modification of the links between the cells.

[1]  F. Peper,et al.  Kaleidoscope of life: A 24-neighbourhood outer-totalistic cellular automaton , 2008 .

[2]  Nazim Fatès,et al.  Cellular Automata , 2004, Lecture Notes in Computer Science.

[3]  Nazim Fatès,et al.  An Experimental Study of Robustness to Asynchronism for Elementary Cellular Automata , 2004, Complex Syst..

[4]  Nazim Fatès,et al.  Critical phenomena in cellular automata: perturbing the update, the transitions, the topology , 2010 .

[5]  Nazim Fatès,et al.  Fully Asynchronous Behavior of Double-Quiescent Elementary Cellular Automata , 2005, MFCS.

[6]  Roberto A Monetti First-order irreversible phase transitions in a nonequilibrium system: mean-field analysis and simulation results. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Nazim Fatès,et al.  Fully asynchronous behavior of double-quiescent elementary cellular automata , 2006, Theor. Comput. Sci..

[8]  H. O. Mártin,et al.  A survey of cellular automata like the “game of life” , 1997 .

[9]  P. Grassberger SYNCHRONIZATION OF COUPLED SYSTEMS WITH SPATIOTEMPORAL CHAOS , 1999 .

[10]  Sheng-You Huang,et al.  Network-induced nonequilibrium phase transition in the "game of Life". , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  H. Blok,et al.  Synchronous versus asynchronous updating in the ''game of Life'' , 1999 .

[12]  Damien Regnault,et al.  On the analysis of "simple" 2D stochastic cellular automata , 2008, Discret. Math. Theor. Comput. Sci..

[13]  Birger Bergersen,et al.  Effect of boundary conditions on scaling in the ''game of Life'' , 1997 .

[14]  Nazim Fatès,et al.  Robustness of the Critical Behaviour in a Discrete Stochastic Reaction-Diffusion Medium , 2009, IWNC.

[15]  L. Schulman,et al.  Statistical mechanics of a dynamical system based on Conway's game of Life , 1978 .

[16]  S. Ruffo,et al.  Some facts of life , 1991 .

[17]  Thomas E. Fricke Stochastic cellular automata , 1997 .

[18]  Rodney A. Brooks,et al.  Asynchrony induces stability in cellular automata based models , 1994 .

[19]  H. Hinrichsen Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[20]  Albano,et al.  Critical edge between frozen extinction and chaotic life. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  F. Peper,et al.  The Game of Life at finite temperature , 2004 .