Contradiction Between Parallelization Efficiency and Stochasticity in Cellular Automata Models of Reaction-Diffusion Phenomena

In low dimensions, reaction-diffusion phenomena may not be correctly described by the usual differential equations: fluctuations play an important role on the time behavior of these systems. We present a cellular automata model which simulate such processes, taking into account all the fluctuations and giving the correct dynamics. The implementation of this model on a Connection Machine CM-2 is discussed, as well as the results of the numerical simulations.

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Statistical Complexity of Boolean Cellular Automata with Short-Term Reaction-Diffusion Memory on a Square Lattice

Complex Systems ◽

10.25088/complexsystems.28.3.357 ◽

2019 ◽

Vol 28 (3) ◽

pp. 357-391

Author(s):

Zakarya Zarezadeh ◽

Giovanni Costantini ◽

Keyword(s):

Cellular Automata ◽

Reaction Diffusion ◽

Square Lattice ◽

Short Term ◽

Statistical Complexity

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Parallel simulation of reaction–diffusion phenomena in percolation processes

Future Generation Computer Systems ◽

10.1016/s0167-739x(00)00051-0 ◽

2001 ◽

Vol 17 (6) ◽

pp. 679-688 ◽

Cited By ~ 15

Author(s):

Stefania Bandini ◽

Giancarlo Mauri ◽

Giulio Pavesi ◽

Carla Simone

Keyword(s):

Reaction Diffusion ◽

Parallel Simulation ◽

Diffusion Phenomena ◽

Percolation Processes

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EVOLVING LOCALIZATIONS IN REACTION-DIFFUSION CELLULAR AUTOMATA

International Journal of Modern Physics C ◽

10.1142/s0129183108012376 ◽

2008 ◽

Vol 19 (04) ◽

pp. 557-567 ◽

Cited By ~ 1

Author(s):

ANDREW ADAMATZKY ◽

LARRY BULL ◽

PIERRE COLLET ◽

EMMANUEL SAPIN

Keyword(s):

Cellular Automata ◽

Chemical Species ◽

Reaction Diffusion ◽

Discrete Systems ◽

Chemical Systems ◽

Transition Functions ◽

Phenomenological Studies ◽

Spatially Extended ◽

Limited Diffusion

We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e., how many neighbours are in each one state. We employ evolutionary algorithms to breed local transition functions that support mobile localizations (gliders), and characterize sets of the functions selected in terms of quasi-chemical systems. Analysis of the set of functions evolved allows to speculate that mobile localizations are likely to emerge in the quasi-chemical systems with limited diffusion of one reagent, a small number of molecules are required for amplification of travelling localizations, and reactions leading to stationary localizations involve relatively equal amount of quasi-chemical species. Techniques developed can be applied in cascading signals in nature-inspired spatially extended computing devices, and phenomenological studies and classification of non-linear discrete systems.

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Creativity and ALife

Artificial Life ◽

10.1162/artl_a_00176 ◽

2015 ◽

Vol 21 (3) ◽

pp. 354-365 ◽

Cited By ~ 6

Author(s):

Margaret A. Boden

Keyword(s):

Genetic Algorithms ◽

Cellular Automata ◽

Reaction Diffusion ◽

Evolutionary Programming ◽

Diffusion Models ◽

Do So

Three forms of creativity are exemplified in biology and studied in ALife. Combinational creativity exists as the first step in genetic algorithms. Exploratory creativity is seen in models using cellular automata or evolutionary programs. Transformational creativity can result from evolutionary programming. Even radically novel forms can do so, given input from outside the program itself. Transformational creativity appears also in reaction-diffusion models of morphogenesis. That there are limits to biological creativity is suggested by ALife work bearing on instances of biological impossibility.

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