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2018 | OriginalPaper | Chapter

4. The Complexity of Cellular Automata

Authors : Xuewei Li, Jinpei Wu, Xueyan Li

Published in: Theory of Practical Cellular Automaton

Publisher: Springer Singapore

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Abstract

Numerous complex systems exist in nature. The structure of every single component of these systems may be very simple, but because the existence of certain connections (or so called coupling) among various parts, the eventual display of the overall state is quite complex. Cellular automata are the ideal mathematical model for studying complex systems. Through modeling based on the complex system of cellular automata, we can simulate complex systems’ evolutionary phenomena and mechanisms. But at a deeper level, although the evolution of cellular automata simulates the phenomena of the development and the variation of complex systems, for model building itself, it is not capable of analyzing the ultimate cause for complex systems in generating complexity. The mechanism of the generation of complexity is still unknown and indescribable. Only by further analyzing and describing the mechanism of the generation of cellular automata’s complexity, can we explain and analyze the complexity of various systems in depth.

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Literature
go back to reference Boccara, N., Nasser, J., & Roger, M. (1991). Particle like structures and their interactions in spatial temporal patterns generated by one-dimensional deterministic cellular automata rules. Physical Review A, 44(2), 866–875.CrossRef Boccara, N., Nasser, J., & Roger, M. (1991). Particle like structures and their interactions in spatial temporal patterns generated by one-dimensional deterministic cellular automata rules. Physical Review A, 44(2), 866–875.CrossRef
go back to reference Culik, K., Hurd, L. P., & Yu, S. (1990). Computation theoretic aspects of cellular automata. Physica D: Nonlinear Phenomena, 45(1–3), 357–378.CrossRef Culik, K., Hurd, L. P., & Yu, S. (1990). Computation theoretic aspects of cellular automata. Physica D: Nonlinear Phenomena, 45(1–3), 357–378.CrossRef
go back to reference Culik, K., & Yu, S. (1988). Undecidability of CA classification schemes. Complex System, 2(2), 177–190. Culik, K., & Yu, S. (1988). Undecidability of CA classification schemes. Complex System, 2(2), 177–190.
go back to reference Delorme, M., & Mazoyer, J. (1998). Cellular automata: A parallel model (1st ed.). Dordrecht, London: Academic Publishers. Delorme, M., & Mazoyer, J. (1998). Cellular automata: A parallel model (1st ed.). Dordrecht, London: Academic Publishers.
go back to reference Duan, X., Wang, C., & Liu, X. (2012). Theoretical study of cellular automata and the applications of their simulations. Beijing: Science Press. Duan, X., Wang, C., & Liu, X. (2012). Theoretical study of cellular automata and the applications of their simulations. Beijing: Science Press.
go back to reference Eloranta, K., & Nummelin, E. (1992). The kink of cellular automata Rule 18 performs a random walk. Journal of Statistical Physics, 69(5–6), 1131–1136.CrossRef Eloranta, K., & Nummelin, E. (1992). The kink of cellular automata Rule 18 performs a random walk. Journal of Statistical Physics, 69(5–6), 1131–1136.CrossRef
go back to reference Hanson, J. E., & Crutchfield, J. P. (1992). The attractor-basin portrait of a cellular automaton. Journal of Statistical Physics, 66(5–6), 1415–1463.CrossRef Hanson, J. E., & Crutchfield, J. P. (1992). The attractor-basin portrait of a cellular automaton. Journal of Statistical Physics, 66(5–6), 1415–1463.CrossRef
go back to reference Hopcroft, J. E., & Lllman, J. D. (1979). Introduction to automata theory languages and computation. Reading, MA: Addison-Wesley. Hopcroft, J. E., & Lllman, J. D. (1979). Introduction to automata theory languages and computation. Reading, MA: Addison-Wesley.
go back to reference Jackson, E. A. (1991). Perspective of nonlinear dynamics (2nd ed.). London: Cambridge University Press. Jackson, E. A. (1991). Perspective of nonlinear dynamics (2nd ed.). London: Cambridge University Press.
go back to reference Jiang, Z. (2001). A complexity analysis of the elementary cellular automaton of Rule 122. Chinese Science Bulletin, 46(7), 600–603.CrossRef Jiang, Z. (2001). A complexity analysis of the elementary cellular automaton of Rule 122. Chinese Science Bulletin, 46(7), 600–603.CrossRef
go back to reference Kari, J. (1992). The nilpotency problem of one-dimensional cellular automata. SIAM Journal on Computing, 21(3), 571–586.CrossRef Kari, J. (1992). The nilpotency problem of one-dimensional cellular automata. SIAM Journal on Computing, 21(3), 571–586.CrossRef
go back to reference Livi, R., Nadal, J. P., & Packard, N. (1992). Complex dynamics. New York: Nova Science Publishers. Livi, R., Nadal, J. P., & Packard, N. (1992). Complex dynamics. New York: Nova Science Publishers.
go back to reference Marr, C., & Hutt, M. T (2005). Topology regulates pattern formation capacity of binary cellular automata on graphs. Physica A: Statistical Mechanics and Its Applications, 354(15), 641–662.CrossRef Marr, C., & Hutt, M. T (2005). Topology regulates pattern formation capacity of binary cellular automata on graphs. Physica A: Statistical Mechanics and Its Applications, 354(15), 641–662.CrossRef
go back to reference Wolfram, S. (1984a). Computation theory of cellular automata. Communications in Mathematical Physics, 96(1), 1–57.CrossRef Wolfram, S. (1984a). Computation theory of cellular automata. Communications in Mathematical Physics, 96(1), 1–57.CrossRef
go back to reference Wolfram, S. (1984b). Cellular automata as models of complexity. Nature, 311(4), 419–424.CrossRef Wolfram, S. (1984b). Cellular automata as models of complexity. Nature, 311(4), 419–424.CrossRef
go back to reference Wolfram, S. (1986). Theory and application of cellular automata. Singapore: World Scientific. Wolfram, S. (1986). Theory and application of cellular automata. Singapore: World Scientific.
go back to reference Xie, H. M. (2001). The complexity of limit languages of cellular automata: An example. Journal of Systems Sciences and Complexity, 14(1), 17–30. Xie, H. M. (2001). The complexity of limit languages of cellular automata: An example. Journal of Systems Sciences and Complexity, 14(1), 17–30.
Metadata
Title
The Complexity of Cellular Automata
Authors
Xuewei Li
Jinpei Wu
Xueyan Li
Copyright Year
2018
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-10-7497-4_4