Cellular automata, matrix substitutions and fractals

DOI10.1007/BF01530797zbMath0866.68069OpenAlexW1975659500MaRDI QIDQ1353932

Heinz-Otto Peitgen, Gencho Skordev, Fritz von Haeseler

Publication date: 12 May 1997

Published in: Annals of Mathematics and Artificial Intelligence (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01530797

zbMATH Keywords

cellular automata

Mathematics Subject Classification ID

Cellular automata (computational aspects) (68Q80) Fractals (28A80)

Related Items (18)

Singular function emerging from one-dimensional elementary cellular automaton rule 150 ⋮ Limit sets of automatic sequences. ⋮ Generalized Gandy-Păun-Rozenberg Machines for Tile Systems and Cellular Automata ⋮ Global analysis of self-similarity features of cellular automata: selected examples ⋮ Cellular non-deterministic automata and partial differential equations ⋮ Cellular automata that generate symmetrical patterns give singular functions ⋮ Linear cellular automata, finite automata and Pascal's triangle ⋮ Automaticity of double sequences generated by one-dimensional linear cellular automata ⋮ Why it is sufficient to consider only the case where the seed of linear cellular automata is 1 ⋮ Self-Similar Functions Generated by Cellular Automata ⋮ RESCALED EVOLUTION SETS OF LINEAR CELLULAR AUTOMATA ON A CYLINDER ⋮ Multifractals Defined by Nonlinear Cellular Automata ⋮ AUTOMATICITY OF COARSE-GRAINING INVARIANT ORBITS OF ONE-DIMENSIONAL LINEAR CELLULAR AUTOMATA ⋮ 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 ⋮ FRACTAL DIMENSION, PROBABILITY AND ENTROPY IN MATRIX AND SUMMATION SUBSTITUTION SYSTEMS ⋮ Iterated function systems and control languages ⋮ Graphical limit sets for general cellular automata

Cites Work

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• Cellular automata can generate fractals
• Cellular automata and multifractals: Dimension spectra of linear cellular automata
• The equality of fractional dimensions for certain cellular automata
• Computing fractal dimensions for additive cellular automata
• Recurrent sets
• Self-similarity of linear cellular automata
• Statistical mechanics of cellular automata
• Dimension and Dynamics for Fractal Recurrent Sets
• RESCALED EVOLUTION SETS OF LINEAR CELLULAR AUTOMATA ON A CYLINDER
• Endomorphisms and automorphisms of the shift dynamical system

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