Self-Similar Fractals can be Generated by Cellular Automata

1993 ◽  
pp. 463-471 ◽  
Author(s):  
Bruno Martin
Keyword(s):  
Cellular Automata ◽  
Self Similar

SELF-SIMILAR STRUCTURE OF RESCALED EVOLUTION SETS OF CELLULAR AUTOMATA II

2001 ◽  
Vol 11 (04) ◽  
pp. 927-941 ◽  
Author(s):  
F. v. HAESELER ◽  
H.-O. PEITGEN ◽  
G. SKORDEV
Keyword(s):  
Hausdorff Dimension ◽  
Cellular Automata ◽  
Prime Number ◽  
Scaling Procedure ◽  
Scaling Sequence ◽  
Self Similar

The description of the rescaled evolution set of p-Fermat cellular automata developed in the first part of this paper is applied for the calculation of the Hausdorff dimension of this set. The scaling procedure is analyzed and an appropriate scaling sequence for cellular automata with states in the integers modulo m is given. New proof of the main theorem of the first part of the paper is presented for the linear cellular automata with states in the integers modulo a power of prime number.

COARSE-GRAINING INVARIANT ORBITS OF ONE-DIMENSIONAL ℤp-LINEAR CELLULAR AUTOMATA

1996 ◽  
Vol 06 (12a) ◽  
pp. 2237-2297 ◽  
Author(s):  
ANDRÉ M. BARBÉ
Keyword(s):  
Cellular Automata ◽  
Periodic Solutions ◽  
Time Evolution ◽  
Coarse Graining ◽  
One Dimensional ◽  
State Time ◽  
All Solutions ◽  
Invariance Problem ◽  
Self Similar ◽  
Existence Of Periodic Solutions

This paper studies the properties of state-time evolution patterns of one-dimensional linear cellular automata over the field ℤp (p prime) which are invariant under certain coarse-graining operations. A procedure is developed for finding all solutions to this invariance problem. The resulting patterns display a complexity which may range from periodic over self-similar, quasi-periodic, quasi-randomlike towards randomlike. Conditions for the existence of periodic solutions are derived.

Self-Similar Functions Generated by Cellular Automata

Fractals ◽  
1998 ◽  
Vol 06 (04) ◽  
pp. 371-394 ◽  
Author(s):  
Heinz-Otto Peitgen ◽  
Anna Rodenhausen ◽  
Gencho Skordev
Keyword(s):  
Cellular Automata ◽  
Iterated Function Systems ◽  
The Self ◽  
Self Similarity ◽  
Hausdorff Dimensions ◽  
Fractal Sets ◽  
Sequential Machines ◽  
Iterated Function ◽  
Self Similar

The self-similarity properties of the functions (closed relations) associated 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 Hausdorff dimensions of the graphs is one for one-sided cellular automata and two for two-sided automata.

SELF-SIMILAR STRUCTURE OF RESCALED EVOLUTION SETS OF CELLULAR AUTOMATA I

2001 ◽  
Vol 11 (04) ◽  
pp. 913-926 ◽  
Author(s):  
F. v. HAESELER ◽  
H.-O. PEITGEN ◽  
G. SKORDEV
Keyword(s):  
Cellular Automata ◽  
Iterated Function Systems ◽  
The Self ◽  
Self Similarity ◽  
Scaling Procedure ◽  
Iterated Function ◽  
Self Similar

The self-similarity properties of the orbits of a class of cellular automata are deciphered by matrix substitutions, hierarchical iterated function systems and appropriate scaling procedure.

Self-similar collapse with non-radial motions

2006 ◽  
Vol 20 ◽  
pp. 1-4
Author(s):  
A. Nusser
Keyword(s):  
Self Similar

A TCAD tool for the simulation of the CVD process based on cellular automata

2001 ◽  
Vol 11 (PR3) ◽  
pp. Pr3-205-Pr3-212
Author(s):  
G. Ch. Sirakoulis ◽  
I. Karafyllidis ◽  
A. Thanailakis
Keyword(s):  
Cellular Automata
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