AUTOMATICITY OF COARSE-GRAINING INVARIANT ORBITS OF ONE-DIMENSIONAL LINEAR CELLULAR AUTOMATA-Reference-Cited by-同舟云学术

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

Published:1999-01 Issue:01 Volume:09 Page:67-95
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

BARBÉ ANDRÉ¹,PEITGEN HEINZ-OTTO²,SKORDEV GENCHO²

Affiliation:

1. Katholieke Universiteit Leuven, Department of Electrical Engineering, Kardinaal Mercierlaan 94, B-3001, Leuven, Belgium

2. Center for Complex Systems and Visualization, University of Bremen, Universitätsallee 29, 28359 Bremen, Germany

Abstract

We consider one-dimensional linear cellular automata whose states are the integers modulo a prime power pd and their orbital patterns. We are particulary interested in initial states and their orbital patterns which are invariant under a certain coarse-graining operation. We show that these coarse-graining invariant initial states are p-automatic. The relationship between the solutions of a certain family of coarse-graining invariant problems concerning linear cellular automata over the integers modulo pn is investigated.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127499000043

Reference14 articles.

1. Linear cellular automata, finite automata and Pascal's triangle

2. Automatic maps in exotic numeration systems

3. COARSE-GRAINING INVARIANT PATTERNS OF ONE-DIMENSIONAL TWO-STATE LINEAR CELLULAR AUTOMATA

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

5. Complex Order from Disorder and from Simple Order in Coarse-Graining Invariant Orbits of Certain Two-Dimensional Linear Cellular Automata

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Automatic sets and Delone sets;Journal of Physics A: Mathematical and General;2004-03-17

2. Decimation-invariant sequences and their automaticity;Theoretical Computer Science;2001-05

3. Irreducible Polynomials Generated by Decimations;Finite Fields and Applications;2001

4. FRACTAL DIMENSION, PROBABILITY AND ENTROPY IN MATRIX AND SUMMATION SUBSTITUTION SYSTEMS;Fractals;1999-09

5. Automaticity of Solutions of Mahler Equations;Sequences and their Applications;1999