The equality of fractional dimensions for certain cellular automata
type: Item
instance of: scholarly article
title: The equality of fractional dimensions for certain cellular automata
zbMATH Open document ID: 0634.68046
DOI: 10.1016/0167-2789(87)90073-X
author: Stephen J. Willson
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: A study is made of the development of certain cellular automata with apparently chaotic behavior. Results are obtained for cellular automata arising from additive rules modulo 2. For the corresponding limit sets it is shown that the growth rate dimension, the Kolmogorov dimensions, and the Hausdorff dimensions all coincide. This dimension is moreover independent of the choice of finite initial seed and the sampling times used. These cellular automata thus provide tractable test cases for the production of fractals by local processes.
Mathematics Subject Classification ID: 68Q80
zbMATH DE Number: 4033085
zbMATH Keywords: cellular automata
zbMATH Keywords: chaotic behavior
zbMATH Keywords: growth rate dimension
zbMATH Keywords: Kolmogorov dimensions
zbMATH Keywords: Hausdorff dimensions
zbMATH Keywords: fractals
MaRDI profile type: Publication
cites work: Tessellation structures for reproduction of arbitrary patterns
cites work: Complex analytic dynamics on the Riemann sphere
cites work: Recurrent sets
cites work: The realization of distances in measurable subsets covering \(R^ n\).
cites work: Q5186444
cites work: Q3675525
cites work: Pattern formation and periodic structures in systems modeled by reaction-diffusion equations
cites work: Q3731958
cites work: Q3675524
cites work: Q4740120
cites work: Pattern reproduction in tessellation automata of arbitrary dimension
cites work: Two definitions of fractional dimension
cites work: Q3931654
cites work: On the ergodic theory of cellular automata
cites work: Cellular automata can generate fractals
cites work: Q3675527
cites work: Statistical mechanics of cellular automata
cites work: Q3675526
cites work: Geometry of Binomial Coefficients
cites work: Computing fractal dimensions for additive cellular automata
full work available at URL: 0167-2789(87)90073-x
OpenAlex ID: W2036716999
description: scientific article; zbMATH DE number 4033085