Paper Info
Title
A Novel Algorithm For Coarse-Graining Of Cellular Automata
Abstract
The coarse-graining is an approximation procedure widely used for simplification of mathematical and numerical models of multiscale systems. It reduces superfluous - microscopic - degrees of freedom. Israeli and Goldenfeld demonstrated in [1,2] that the coarse-graining can be employed for elementary cellular automata (CA), producing interesting interdependences between them. However, extending their investigation on more complex CA rules appeared to be impossible due to the high computational complexity of the coarse-graining algorithm. We demonstrate here that this complexity can be substantially decreased. It allows for scrutinizing much broader class of cellular automata in terms of their coarse graining. By using our algorithm we found out that the ratio of the numbers of elementary CAs having coarse grained representation to "degenerate" - irreducible - cellular automata, strongly increases with increasing the "grain" size of the approximation procedure. This rises principal questions about the formal limits in modeling of realistic multiscale systems.
Year
DOI
Venue
2014
10.1007/978-3-319-11520-7_27
CELLULAR AUTOMATA: 11TH INTERNATIONAL CONFERENCE ON CELLULAR AUTOMATA FOR RESEARCH AND INDUSTRY
Keywords
Field
DocType
multiscale systems, coarse graining, cellular automata
Cellular automaton,Degenerate energy levels,Elementary cellular automaton,Mobile automaton,Computer science,GrowCut algorithm,Algorithm,Theoretical computer science,Granularity,Stochastic cellular automaton,Computational complexity theory
Conference
Volume
ISSN
Citations 
8751
0302-9743
2
PageRank 
References 
Authors
0.42
1
2
Name
Order
Citations
PageRank
Krzysztof Magiera171.56
Witold Dzwinel213225.14