Abstract
A Cellular Automaton (CA) is nowadays an object of growing interest as a mathematical model for spatial dynamics simulation. Due to its ability to simulate nonlinear and discontinuous processes, CA is expected [1,2] to become a complement to partial differential equations (PDE). Particularly, CA may be helpful when there is no other mathematical model of a phenomenon which is to be investigated.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
- Cellular Automaton
- Local Operator
- Cellular Neural Network
- Parallel Composition
- Partial Differential Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
T. Toffolli, N. Margolus, Cellular Automata Machines (MIT Press, Cambridge, MA, 1987)
S. Wolfram, A New Kind of Science (Wolfram Media Inc., Champaign, IL, 2002)
O. Bandman, Comparative study of cellular automata diffusion models, ed. by V. Malyshkin, PaCT-1999, LNCS vol. 1662 (Springer, Berlin, 1999), pp. 395–404
G.G. Malinetski, M.E. Stepantsov, Modeling diffusive processes by cellular automata with Margolus neighborhood. Zhurnal Vychislitelnoy Matematiki i Mathematicheskoy Phisiki 36(6), 1017–1021 (1998)
J.K. Park, K. Steiglitz, W.P. Thurston, Soliton-like behavior in automata. Physica D 19, 423–432 (1986)
C. Vannozzi, D. Fiorentino, M. D’Amore et al., Cellular automata model of phase transition in binary mixtures. Ind. Eng. Chem. Res. 45(4), 2892–2896 (2006)
M. Creutz, Celllular automata and self-organized criticality, ed. by G. Bannot, P. Seiden, Some New Directions in Science on Computers (World Scientific, Singapore), pp. 147–169
U. Frish, D. d’Humieres, B. Hasslacher et al., Lattice-gas hydrodynamics in two and three dimensions. Compl. Syst. 1, 649–707 (1987)
D.H. Rothman, S. Zalesky, Lattice-Gas Cellular Automata. Simple Model of Complex Hydrodynamics (Cambridge University Press, Cambridge, UK, 1997)
S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press, New York, NY, 2001)
L. Axner, A.G. Hoekstra, P.M.A. Sloot, Simulating time harmonic flows with the lattice Boltzmann method. Phys. Rev. E 75, 036709 (2007)
V.I. Elokhin, E.I. Latkin, A.V. Matveev, V.V. Gorodetskii, Application of statistical lattice models to the analysis of oscillatory and autowave processes in the reaction of carbon monoxide oxidation over platinum and palladium surfaces. Kinet. Catal. 44(5), 672–700 (2003)
A.P.J. Jansen, An Introduction to Monte-Carlo Simulation of Surface Reactions. ArXiv: cond-mat/0303028 v1 (2003)
I.G. Neizvestny, N.L. Shwartz, Z.Sh. Yanovitskaya, A.V. Zverev, 3D-model of epitaxial growth on porous 111 and 100 Si Surfacex. Comput. Phys. Commun. 147, 272–275 (2002)
M.A. Saum, S. Gavrilets, CA simulation of biological evolution in genetic hyperspace, ed. by S. El Yacoubi, B. Chopard, S. Bandini, ACRI-2006. LNCS vol. 4176 (Springer, Berlin, 2006), pp. 3–13
Y. Wu, N. Chen, M. Rissler, Y. Jiang et al., CA models of myxobacteria sworming ed. by S. El Yacoubi, B. Chopard, S. Bandini, ACRI-2006, LNSC vol. 4176 (Springer, Berlin, 2006), pp. 192–203
M. Ghaemi, A. Shahrokhi, Combination of the cellular potts model and lattice gas cellular automata for simulating the avascular cancer growth, ed. by S. El Yacoubi, B. Chopard, S. Bandini, ACRI-2006, LNSC vol. 4176 (Springer, Berlin, 2006), pp. 297–303
R. Slimi, S. El Yacoubi, Spreadable probabilistic cellular automata models, ed. by S. El Yacoubi, B. Chopard, S. Bandini, ACRI-2006, LNSC vol. 4176 (Springer, Berlin, 2006), pp. 330–336
F. Biondini, F. Bontempi, D.M. Frangopol, P.G. Malerba, Cellular automata approach to durability analysis of concrete structures in aggressive environments. J. Struct. Eng. 130(11), 1724–1737
O. Bandman, Composing fine-grained parallel algorithms for spatial dynamics simulation, ed. by V. Malyshkin, PaCT-2005, LNCS Vol. 3606 (Springer, Berlin, 2005), pp. 99–113
S. Wolfram, Universality and complexity in cellular automata. Physica D 10, 1–35 (1984)
L.O. Chua, CNN: A Paradigm for Complexity (World Scientific, Singapore, 2002)
L.R. Weimar, J.P. Boon, Class of cellular automata for reaction-diffusion systems. Phys Rev E 49, 1749–1752 (1994)
O. Bandman, Simulating spatial dynamics by probabilistic cellular automata, ed. by S. Bandini, B. Chopard, M. Tomassini, ACRI-2002, LNCS vol. 2493 (Springer, Berlin, 2002), pp. 10–20
O. Bandman, Spatial functions approximation by boolean arrays. Bulletin of Novosibirsk Computer Center, series Computer Science 19. ICMMG, Novosibirsk:10–19 (2003)
S. Achasova, O. Bandman, V. Markova, S. Piskunov, Parallel Substitution Algorithm. Theory and Application (World Scientific, Singapore, 1994)
S. Bandini, S. Manzoni, G. Vizzari, SCA: A model to simulate crowding dynamics. IEICE Trans. Inf. Syst. E87-D, 669–676 (2004)
A. Adamatsky, Dynamics of Crowd-Minds. in Series on Nonlinear Science, vol. 54 (World Scientific, Singapore, 2005)
O. Bandman, Coarse-grained parallelisation of cellular-automata simulation algorithms, ed. by V. Malyshkin, PaCT-2007 LNCS vol. 4671 (Springer, Berlin, 2007), pp. 370–384
G. Vichniac, Simulating physics by cellular automata. Physica D 10, 86–112 (1984)
Y. Svirezhev, Nonlinear Waves, Dissipative Structures and Catastrophes in Ecology (Nauka, Moscow, 1987)
R.M. Ziff, E. Gulari, Y. Barshad, Kinetic phase transitions in an irreversible surface-reaction model. Phys. Rev. Lett. 56, 2553 (1986)
F. Schlogl, Chemical reaction models for non-equilibrium phase transitions. Z. Physik 253 147–161 (1972)
C.P. Schrenk, P. Schutz, M. Bode, H.-G. Purwins, Interaction of selforganised quaziparticles in two-dimensional reaction diffusion system: the formation of molecules. Phys. Rev. E 5 (6), 6481–5486 (1918)
A.N. Michel, K. Wang, B. Hu, Qualitative Theory of Dynamics Systems: The Role of Stability Preserving. (CRC Press, New York, NY, 2001).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bandman, O. (2010). Cellular Automata Composition Techniques for Spatial Dynamics Simulation. In: Kroc, J., Sloot, P., Hoekstra, A. (eds) Simulating Complex Systems by Cellular Automata. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12203-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-12203-3_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12202-6
Online ISBN: 978-3-642-12203-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)