The Complexity of Cellular Automata

  • Xuewei Li
  • Jinpei Wu
  • Xueyan Li


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.


  1. 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.CrossRefGoogle Scholar
  2. Culik, K., Hurd, L. P., & Yu, S. (1990). Computation theoretic aspects of cellular automata. Physica D: Nonlinear Phenomena, 45(1–3), 357–378.CrossRefGoogle Scholar
  3. Culik, K., & Yu, S. (1988). Undecidability of CA classification schemes. Complex System, 2(2), 177–190.Google Scholar
  4. Delorme, M., & Mazoyer, J. (1998). Cellular automata: A parallel model (1st ed.). Dordrecht, London: Academic Publishers.Google Scholar
  5. Duan, X., Wang, C., & Liu, X. (2012). Theoretical study of cellular automata and the applications of their simulations. Beijing: Science Press.Google Scholar
  6. 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.CrossRefGoogle Scholar
  7. Hanson, J. E., & Crutchfield, J. P. (1992). The attractor-basin portrait of a cellular automaton. Journal of Statistical Physics, 66(5–6), 1415–1463.CrossRefGoogle Scholar
  8. Hopcroft, J. E., & Lllman, J. D. (1979). Introduction to automata theory languages and computation. Reading, MA: Addison-Wesley.Google Scholar
  9. Jackson, E. A. (1991). Perspective of nonlinear dynamics (2nd ed.). London: Cambridge University Press.Google Scholar
  10. Jiang, Z. (2001). A complexity analysis of the elementary cellular automaton of Rule 122. Chinese Science Bulletin, 46(7), 600–603.CrossRefGoogle Scholar
  11. Kari, J. (1992). The nilpotency problem of one-dimensional cellular automata. SIAM Journal on Computing, 21(3), 571–586.CrossRefGoogle Scholar
  12. Livi, R., Nadal, J. P., & Packard, N. (1992). Complex dynamics. New York: Nova Science Publishers.Google Scholar
  13. 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.CrossRefGoogle Scholar
  14. Wolfram, S. (1984a). Computation theory of cellular automata. Communications in Mathematical Physics, 96(1), 1–57.CrossRefGoogle Scholar
  15. Wolfram, S. (1984b). Cellular automata as models of complexity. Nature, 311(4), 419–424.CrossRefGoogle Scholar
  16. Wolfram, S. (1986). Theory and application of cellular automata. Singapore: World Scientific.Google Scholar
  17. Xie, H. M. (2001). The complexity of limit languages of cellular automata: An example. Journal of Systems Sciences and Complexity, 14(1), 17–30.Google Scholar

Copyright information

© Beijing Jiaotong University Press and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Beijing Union UniversityBeijingChina
  2. 2.Wuyi UniversityJiangmenChina
  3. 3.Beijing Jiaotong universityBeijingChina

Personalised recommendations