Long-range effects in an elementary cellular automaton

1986 ◽  
Vol 45 (1-2) ◽  
pp. 27-39 ◽  
Author(s):  
Peter Grassberger
Keyword(s):  
Cellular Automaton ◽  
Long Range ◽  
Elementary Cellular Automaton

COMPLEX DYNAMICS OF THE ELEMENTARY CELLULAR AUTOMATON RULE 54

2012 ◽  
Vol 23 (07) ◽  
pp. 1250052
Author(s):  
JUNBIAO GUAN
Keyword(s):  
Boundary Conditions ◽  
Cellular Automaton ◽  
Periodic Boundary ◽  
Complex Dynamics ◽  
Bernoulli Shift ◽  
Periodic Boundary Conditions ◽  
Self Similarity ◽  
Symbolic Sequences ◽  
Topologically Mixing ◽  
Elementary Cellular Automaton

This work deals with a discussion of complex dynamics of the elementary cellular automaton rule 54. An equation which shows some degree of self-similarity is obtained. It is shown that rule 54 exhibits Bernoulli shift and is topologically mixing on its closed invariant subsystem. Finally, many complex Bernoulli shifts are explored for the finite symbolic sequences with periodic boundary conditions.

Elementary cellular automaton Rule 110 explained as a block substitution system

Computing ◽  
2010 ◽  
Vol 88 (3-4) ◽  
pp. 193-205
Author(s):  
Juan C. Seck-Tuoh-Mora ◽  
Genaro J. Martínez ◽  
Norberto Hernández-Romero ◽  
Joselito Medina-Marín
Keyword(s):  
Cellular Automaton ◽  
Substitution System ◽  
Elementary Cellular Automaton

scholarly journals Species Formation in Simple Ecosystems

1998 ◽  
Vol 09 (04) ◽  
pp. 555-571 ◽  
Author(s):  
F. Bagnoli ◽  
M. Bezzi
Keyword(s):  
Cellular Automaton ◽  
Long Range ◽  
Mutation Rate ◽  
Total Population ◽  
Fitness Function ◽  
Analytical Approximation ◽  
The Other ◽  
Collective Behaviors ◽  
Species Formation ◽  
Mutational Meltdown

In this paper we consider a microscopic model of a simple ecosystem. The basic ingredients of this model are individuals, and both the phenotypic and genotypic levels are taken in account. The model is based on a long range cellular automaton (CA); introducing simple interactions between the individuals, we get some of the complex collective behaviors observed in a real ecosystem. Since our fitness function is smooth, the model does not exhibit the error threshold transition; on the other hand the size of total population is not kept constant, and the mutational meltdown transition is present. We study the effects of competition between genetically similar individuals and how it can lead to species formation. This speciation transition does not depend on the mutation rate. We present also an analytical approximation of the model.

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