EXPRESSIVENESS OF ELEMENTARY CELLULAR AUTOMATA

We investigate expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically inspired parameters for biodiversity are applied to the configurations of cellular automata. This paper contains a survey of the Elementary Cellular Automata in terms of their expressiveness and an evaluation whether expressiveness is a meaningful term in the context of simulated biology.

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Automatic Texture Based Classification of the Dynamics of One-Dimensional Binary Cellular Automata

International Journal of Natural Computing Research ◽

10.4018/ijncr.2019100104 ◽

2019 ◽

Vol 8 (4) ◽

pp. 41-61

Author(s):

Marcelo Arbori Nogueira ◽

Pedro Paulo Balbi de Oliveira

Keyword(s):

Cellular Automata ◽

Dynamic Behavior ◽

Temporal Evolution ◽

Computational Cost ◽

Great Variability ◽

Texture Descriptor ◽

One Dimensional ◽

Binary Images ◽

Elementary Cellular Automata

Cellular automata present great variability in their temporal evolutions due to the number of rules and initial configurations. The possibility of automatically classifying its dynamic behavior would be of great value when studying properties of its dynamics. By counting on elementary cellular automata, and considering its temporal evolution as binary images, the authors created a texture descriptor of the images - based on the neighborhood configurations of the cells in temporal evolutions - so that it could be associated to each dynamic behavior class, following the scheme of Wolfram's classic classification. It was then possible to predict the class of rules of a temporal evolution of an elementary rule in a more effective way than others in the literature in terms of precision and computational cost. By applying the classifier to the larger neighborhood space containing 4 cells, accuracy decreased to just over 70%. However, the classifier is still able to provide some information about the dynamics of an unknown larger space with reduced computational cost.

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Formal Logic of Cellular Automata

Complex Systems ◽

10.25088/complexsystems.30.2.187 ◽

2021 ◽

Vol 30 (2) ◽

pp. 187-203

Author(s):

Sukanta Das ◽

◽

Mihir K. Chakraborty ◽

Keyword(s):

Cellular Automata ◽

Cellular Automaton ◽

Formal Logic ◽

One Dimensional ◽

Elementary Cellular Automata ◽

Binary Strings

This paper develops a formal logic, named L CA , targeting modeling of one-dimensional binary cellular automata. We first develop the syntax of L CA , then give semantics to L CA in the domain of all binary strings. Then the elementary cellular automata and four-neighborhood binary cellular automata are shown as models of the logic. These instances point out that there are other models of L CA . Finally it is proved that any one-dimensional binary cellular automaton is a model of the proposed logic.

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Classifying elementary cellular automata using compressibility, diversity and sensitivity measures

International Journal of Modern Physics C ◽

10.1142/s0129183113500988 ◽

2014 ◽

Vol 25 (03) ◽

pp. 1350098 ◽

Cited By ~ 8

Author(s):

Shigeru Ninagawa ◽

Andrew Adamatzky

Keyword(s):

Cellular Automata ◽

Cellular Automaton ◽

Initial Conditions ◽

Morphological Diversity ◽

Compression Algorithm ◽

One Dimensional ◽

Elementary Cellular Automata ◽

Eca Rules ◽

Substantial Correlation ◽

Elementary Cellular Automaton

An elementary cellular automaton (ECA) is a one-dimensional, synchronous, binary automaton, where each cell update depends on its own state and states of its two closest neighbors. We attempt to uncover correlations between the following measures of ECA behavior: compressibility, sensitivity and diversity. The compressibility of ECA configurations is calculated using the Lempel–Ziv (LZ) compression algorithm LZ78. The sensitivity of ECA rules to initial conditions and perturbations is evaluated using Derrida coefficients. The generative morphological diversity shows how many different neighborhood states are produced from a single nonquiescent cell. We found no significant correlation between sensitivity and compressibility. There is a substantial correlation between generative diversity and compressibility. Using sensitivity, compressibility and diversity, we uncover and characterize novel groupings of rules.

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2D ELEMENTARY CELLULAR AUTOMATA WITH FOUR NEIGHBORS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127413500600 ◽

2013 ◽

Vol 23 (04) ◽

pp. 1350060 ◽

Cited By ~ 1

Author(s):

JOSÉ ANTÓNIO FREITAS ◽

RICARDO SEVERINO

Keyword(s):

Cellular Automata ◽

Significant Role ◽

Reflection Symmetry ◽

Final States ◽

Final State ◽

One Dimensional ◽

Elementary Cellular Automata ◽

Symmetry Transformations

This paper is focused on the study of square boolean synchronous four-neighbor peripheral cellular automata. It is first shown that, due to conjugation and plane reflection symmetry transformations, the number of dynamically nonequivalent such automata is equal to 4856. The cellular automata for which the homogeneous final states play a significant role are then identified. Finally, it is shown that, contrary to what happens in the case of one-dimensional boolean three-neighbor cellular automata, for some peripheral automata, there is coexistence between a homogeneous final state and other dynamics.

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