Self-similar functions generated by cellular automata

Authors
Peitgen, HO Rodenhausen, A Skordev, G
Citation
Ho. Peitgen et al., Self-similar functions generated by cellular automata, FRACTALS, 6(4), 1998, pp. 371-394
Citations number
38
Categorie Soggetti
Multidisciplinary
Journal title
FRACTALS-AN INTERDISCIPLINARY JOURNAL ON THE COMPLEX GEOMETRY OF NATURE
ISSN journal
0218348X → ACNP
Volume
6
Issue
4
Year of publication
1998
Pages
371 - 394
Database
ISI
SICI code
0218-348X(199812)6:4<371:SFGBCA>2.0.ZU;2-E
Abstract
The self-similarity properties of the functions (closed relations) associat ed with one- and two-sided cellular automata are studied. It turns out that these functions are generated by sequential machines, and their graphs are fractal sets generated by hierarchical iterated function systems. The Haus dorff dimensions of the graphs is one for one-sided cellular automata and t wo for two-sided cellular automata.