Self-similarity of linear cellular automata

DOI10.1016/0022-0000(92)90007-6zbMath0743.68105OpenAlexW2038183011MaRDI QIDQ1185247

Satoshi Takahashi

Publication date: 28 June 1992

Published in: Journal of Computer and System Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0000(92)90007-6

zbMATH Keywords

Hausdorff dimensionfractalslinear cellular automataself-similar structure

Mathematics Subject Classification ID

Cellular automata (computational aspects) (68Q80)

Related Items (23)

Singular function emerging from one-dimensional elementary cellular automaton rule 150 ⋮ Limit sets of automatic sequences. ⋮ Scaling properties of generalized Carlitz sequences of polynomials ⋮ A variational formula for dimension spectra of linear cellular automata ⋮ Global analysis of self-similarity features of cellular automata: selected examples ⋮ Cellular automata, matrix substitutions and fractals ⋮ Cellular automata that generate symmetrical patterns give singular functions ⋮ Linear cellular automata, finite automata and Pascal's triangle ⋮ A complete and efficiently computable topological classification of D-dimensional linear cellular automata over Z m ⋮ Structural Properties of Additive Nano/Microcellular Automata ⋮ On the sensitivity of additive cellular automata in Besicovitch topologies ⋮ Why it is sufficient to consider only the case where the seed of linear cellular automata is 1 ⋮ Cellular automata and multifractals: Dimension spectra of linear cellular automata ⋮ Inversion of circulant matrices over $\mathbf{Z}_m$ ⋮ Number of nonzero states in prefractal sets generated by cellular automata ⋮ RESCALED EVOLUTION SETS OF LINEAR CELLULAR AUTOMATA ON A CYLINDER ⋮ The self-affine property of \((U,r)\)-Carlitz sequences of polynomials deciphered in terms of graph directed IFS ⋮ Multifractals Defined by Nonlinear Cellular Automata ⋮ Invertible linear cellular automata over \(\mathbb{Z}_m\): Algorithmic and dynamical aspects ⋮ SELF-SIMILAR STRUCTURE OF RESCALED EVOLUTION SETS OF CELLULAR AUTOMATA I ⋮ On the fractal structure of the rescaled evolution set of Carlitz sequences of polynomials ⋮ Iterated function systems and control languages ⋮ Characteristic parameters and classification of one-dimensional cellular automata

Cites Work

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• Cellular automata can generate fractals
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• Linear cellular automata over \(Z_ m\)
• Dynamical characteristics of linear cellular automata
• Limiting behaviour of linear cellular automata
• The equality of fractional dimensions for certain cellular automata
• Computing fractal dimensions for additive cellular automata
• Recurrent sets
• Congruence properties of ordinary and q-binomial coefficients
• Tessellation structures for reproduction of arbitrary patterns
• Pattern reproduction in tessellation automata of arbitrary dimension
• Iterated function systems and the global construction of fractals
• Dimension and Dynamics for Fractal Recurrent Sets
• On the structure of self-similar sets

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