This is a preview of subscription content, log in via an institution to check access.
Bibliography
Primary Literature
Anderson R et al (1989) Disks, balls, and walls: analysis of a combinatorial game. Am Math Mon 96:981
Bak P, Creutz M (1994) Fractals and self-organized criticality. In: Bunde A, Havlin S (eds) Fractals in science. Springer, Berlin, pp 26–47
Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality. Phys Rev Lett 59:381. (1988) Phys Rev A 38:3645
Bak P, Chen K, Creutz M (1989) Self-organized criticality in the ‘Game of Life’. Nature 342:780
Bennett C, Bourzutschy M (1991) ‘Life’ not critical? Nature 350:468
Berlekamp E, Conway J, Guy R (1982) Winning ways for your mathematical plays, vol 2. Academic, New York. ISBN:0-12-091152-3, chapter 25
Björner A, Lovasz L, Shor P (1991) Chip-firing games on graphs. Eur J Comb 12:283
Bogosian B (1993) Lattice gas hydrodynamics. Nucl Phys B Proc Suppl 30:204
Christensen K (1992) Self-organization in models of sandpiles, earthquakes, and fireflies. PhD thesis, University of Aarhus
Clar S, Drossel B, Schwabl F (1996) Exact results for the one-dimensional self-organized critical forest-fire model. Phys J Condens Matter 8:6803
Creutz M (1991) Abelian sandpiles. Comput Phys 5:198
Creutz M (1992) Abelian sandpiles. Nucl Phys B Proc Suppl 26:252
Creutz M (1997) Cellular automata and self organized criticality. In: Bhanot G, Chen S, Seiden P (eds) Some new directions in science on computers. World Scientific, Singapore, pp 147–169
Dhar D (1990) Self-organized critical state of sandpile automaton models. Phys Rev Lett 64:1613
Dhar D, Majumdar SN (1990) Abelian sandpile model on the Bethe lattice. Phys J A 23:4333
Dhar D, Ramaswamy R (1989) Exactly solved model of self-organized critical phenomena. Phys Rev Lett 63:1659
Eriksson K (1996) Chip- firing games on mutating graphs. SIAM J Discret Math 9:11822
Frette V et al (1996) Avalanche dynamics in a pile of rice. Nature 379:49
Gardner M (1983) Wheels, life, and other mathematical amusements. W.H. Freeman, New York
Goles E, Margenstern M (1996) Sand pile as a universal computer. Int J Mod Phys C 7:113
Levy M, Solomon S, Ram G (1996) Dynamical explanation for the emergence of power law in a stock market model. Int J Mod Phys C 7:65
Majumdar SN, Dhar D (1992) Equivalence between the Abelian sandpile model and the q → 0 limit of the Potts model. Physica A 185:129
Nagel K, Paczuski M (1995) Emergent traffic jams. Phys Rev E 51:2909
Paczuski M, Maslov S, Bak P (1996) Avalanche dynamics in evolution, growth, and depinning models. Phys Rev E 53:414
Press W, Teukolsky S, Vetterling W, Flannery B (1988) Numerical recipes in C. Cambridge University Press, Cambridge
The latest version of the xtoys package is available at http://thy.phy.bnl.gov/www/xtoys/xtoys.html
Toffoli T, Margolus N (1987) Cellular automata machines: a new environment for modeling. MIT Press, Cambridge
Wikipedia (2007a) Conway’s game of life. http://enwikipedia.org/wiki/Conwav’slife. Accessed 6 Apr 2007
Wikipedia (2007b) Garden of Eden pattern. http://en.wikipedia.org/wiki/Garden_of_Eden_pattem. Accessed 6 Apr 2007
Wolfram S (1986) Theory and applications of cellular automata. World Scientific, Singapore
Books and Reviews
Bak P (1996) How nature works: the science of self-organised criticality. Springer, Berlin
Gore A (1992) Earth in the balance: ecology and the human spirit. Plume, Boston
Jensen HJ (1998) Self-organized criticality: emergent complex behavior in physical and biological systems. Cambridge University Press, Cambridge
Wolfram S (1994) Cellular automata and complexity: collected papers. Westview Press, Boulder
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Science+Business Media LLC
About this entry
Cite this entry
Creutz, M. (2018). Self-Organized Criticality and Cellular Automata. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_474-7
Download citation
DOI: https://doi.org/10.1007/978-3-642-27737-5_474-7
Received:
Accepted:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27737-5
Online ISBN: 978-3-642-27737-5
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics
Publish with us
Chapter history
-
Latest
Self-Organized Criticality and Cellular Automata- Published:
- 19 February 2018
DOI: https://doi.org/10.1007/978-3-642-27737-5_474-7
-
Original
Self-Organized Criticality and Cellular Automata- Published:
- 25 September 2015
DOI: https://doi.org/10.1007/978-3-642-27737-5_474-6