Cellular automata and multifractals: Dimension spectra of linear cellular automata

DOI10.1016/0167-2789(90)90172-LzbMath0711.58019OpenAlexW2068853655MaRDI QIDQ923451

Satoshi Takahashi

Publication date: 1990

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(90)90172-l

zbMATH Keywords

limit setdimension spectrummultifractallinear cellular automata

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Topological dynamics (37B99) Cellular automata (computational aspects) (68Q80) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (7)

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 ⋮ TIME EVOLUTION OF CIRCULAR CELLULAR AUTOMATA ON SQUARE LATTICES ⋮ MULTIFRACTAL PROPERTIES OF R90 CELLULAR AUTOMATON WITH MEMORY ⋮ On the evolution of the cellular automaton of rule 150 from some simple initial states ⋮ Dimension spectra of self-affine sets

Cites Work

• Cellular automata can generate fractals
• The infinite number of generalized dimensions of fractals and strange attractors
• The equality of fractional dimensions for certain cellular automata
• Computing fractal dimensions for additive cellular automata
• Calculating growth rates and moments for additive cellular automata
• Self-similarity of linear cellular automata
• Tessellation structures for reproduction of arbitrary patterns
• Pattern reproduction in tessellation automata of arbitrary dimension
• Fractal measures and their singularities: The characterization of strange sets
• Products of Random Matrices
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