International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, volume 23, issue 09, pages 1350159
ASYMPTOTIC BEHAVIOR AND RATIOS OF COMPLEXITY IN CELLULAR AUTOMATA
2
Universidad Politécnica de San Luis Potosí, San Luis Potosí, México, C.P. 78363, México
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Publication type: Journal Article
Publication date: 2013-10-11
Q1
Q2
SJR: 0.570
CiteScore: 4.1
Impact factor: 1.9
ISSN: 02181274, 17936551
Applied Mathematics
Engineering (miscellaneous)
Modeling and Simulation
Abstract
We study the asymptotic behavior of symbolic computing systems, notably one-dimensional cellular automata (CA), in order to ascertain whether and at what rate the number of complex versus simple rules dominate the rule space for increasing neighborhood range and number of symbols (or colors), and how different behavior is distributed in the spaces of different cellular automata formalisms. Using two different measures, Shannon's block entropy and Kolmogorov complexity, the latter approximated by two different methods (lossless compressibility and block decomposition), we arrive at the same trend of larger complex behavioral fractions. We also advance a notion of asymptotic and limit behavior for individual rules, both over initial conditions and runtimes, and we provide a formalization of Wolfram's classification as a limit function in terms of Kolmogorov complexity.
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Zenil H., VILLARREAL-ZAPATA E. ASYMPTOTIC BEHAVIOR AND RATIOS OF COMPLEXITY IN CELLULAR AUTOMATA // International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 2013. Vol. 23. No. 09. p. 1350159.
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Zenil H., VILLARREAL-ZAPATA E. ASYMPTOTIC BEHAVIOR AND RATIOS OF COMPLEXITY IN CELLULAR AUTOMATA // International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 2013. Vol. 23. No. 09. p. 1350159.
Cite this
RIS
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TY - JOUR
DO - 10.1142/S0218127413501599
UR - https://doi.org/10.1142/S0218127413501599
TI - ASYMPTOTIC BEHAVIOR AND RATIOS OF COMPLEXITY IN CELLULAR AUTOMATA
T2 - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
AU - Zenil, Hector
AU - VILLARREAL-ZAPATA, ELENA
PY - 2013
DA - 2013/10/11
PB - World Scientific
SP - 1350159
IS - 09
VL - 23
SN - 0218-1274
SN - 1793-6551
ER -
Cite this
BibTex (up to 50 authors)
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@article{2013_Zenil,
author = {Hector Zenil and ELENA VILLARREAL-ZAPATA},
title = {ASYMPTOTIC BEHAVIOR AND RATIOS OF COMPLEXITY IN CELLULAR AUTOMATA},
journal = {International Journal of Bifurcation and Chaos in Applied Sciences and Engineering},
year = {2013},
volume = {23},
publisher = {World Scientific},
month = {oct},
url = {https://doi.org/10.1142/S0218127413501599},
number = {09},
pages = {1350159},
doi = {10.1142/S0218127413501599}
}
Cite this
MLA
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Zenil, Hector, and ELENA VILLARREAL-ZAPATA. “ASYMPTOTIC BEHAVIOR AND RATIOS OF COMPLEXITY IN CELLULAR AUTOMATA.” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 23, no. 09, Oct. 2013, p. 1350159. https://doi.org/10.1142/S0218127413501599.