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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Israeli, N., Goldenfeld, N.: Coarse-graining of cellular automata, emergence, and the predictability of complex systems. Phys. Rev. E. 73(2), 026203 (2006)
Israeli, N., Goldenfeld, N.: Computational irreducibility and the predictability of complex physical systems. Physical Review Letters 92(7), 074105 (2004)
Dzwinel, W.: Complex automata as a novel conceptual framework for modeling biomedical phenomena. In: Byrski, A., Oplatková, Z., Carvalho, M., Dorohnicki, M.K. (eds.) Advances in Intelligent Modelling and Simulation. SCI, vol. 416, pp. 269–298. Springer, Heidelberg (2012)
Dzwinel, W., Yuen, D.A., Boryczko, K.: Bridging diverse physical scales with the discrete-particle paradigm in modeling colloidal dynamics with mesoscopic features. Chemical Engineering Sci. 61, 2169–2185 (2006)
Espanõl, P.: Fluid particle model. Phys. Rev. E 57, 2930–2948 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Magiera, K., Dzwinel, W. (2014). A Novel Algorithm for Coarse-Graining of Cellular Automata. In: Wąs, J., Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2014. Lecture Notes in Computer Science, vol 8751. Springer, Cham. https://doi.org/10.1007/978-3-319-11520-7_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-11520-7_27
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11519-1
Online ISBN: 978-3-319-11520-7
eBook Packages: Computer ScienceComputer Science (R0)