Computing fractal dimensions for additive cellular automata
type: Item
instance of: scholarly article
title: Computing fractal dimensions for additive cellular automata
zbMATH Open document ID: 0634.68047
DOI: 10.1016/0167-2789(87)90074-1
author: Stephen J. Willson
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: Efficient methods are given for finding the statistics of symbol blocks occurring in the graphs of additive cellular automata after large numbers of iterations. In particular, the methods yield fractal dimensions, entropies, and a recurrence relation for the number of nonzero symbols. The methods are based on the construction of a nonnegative integer matrix A closely related to the automaton. The largest eigenvalue of A tells the fractal dimension, while the corresponding eigenvector gives the relative frequencies of blocks.
Mathematics Subject Classification ID: 68Q80
zbMATH DE Number: 4033086
zbMATH Keywords: symbol blocks
zbMATH Keywords: graphs of additive cellular automata
zbMATH Keywords: fractal dimension
describes a project that uses: EISPACK
MaRDI profile type: Publication
full work available at URL: 0167-2789(87)90074-1
OpenAlex ID: W2064955512
cites work: Tessellation structures for reproduction of arbitrary patterns
cites work: Q4187223
cites work: Q3944542
cites work: The realization of distances in measurable subsets covering \(R^ n\).
cites work: Q3254327
cites work: Pattern formation and periodic structures in systems modeled by reaction-diffusion equations
cites work: Algebraic properties of cellular automata
cites work: Matrix eigensystem routines - EISPACK guide. 2nd ed
cites work: Q3675527
cites work: The equality of fractional dimensions for certain cellular automata
cites work: Statistical mechanics of cellular automata
cites work: Q3675526
cites work: Twenty Problems in the Theory of Cellular Automata
cites work: Computation theory of cellular automata
cites work: Q5531981
description: scientific article; zbMATH DE number 4033086