The Dynamics of General Fuzzy Cellular Automata

  • Angelo B. Mingarelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3515)


We continue the investigation into the dynamics and evolution of fuzzy rules, obtained by the fuzzification of the disjunctive normal form, and initiated for rule 90 in [2], for rule 110 in [10] and for rule 30 in [3]. We present general methods for detecting the evolution and dynamics of any one of the 255 fuzzy rules and apply this theory to fuzzy rules 30, 110, 18, 45, and 184, each of which has a Boolean counterpart with interesting features. Finally, it is deduced that (except for at most nine cases) no fuzzy cellular automaton admits chaotic behavior in the sense that no sensitive dependence on the initial string can occur.


Fuzzy Rule Cellular Automaton Local Rule Vertical Column Chaotic Sequence 
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.


  1. 1.
    Wuensche, A.: Personal communication. In: Complex Systems 1998 Conference, University of New South Wales, Australia (Fall 1998)Google Scholar
  2. 2.
    Flocchini, P., Geurts, F., Mingarelli, A., Santoro, N.: Convergence and aperiodicity in fuzzy cellular automata: revisiting rule 90. Physica D 142, 20–28 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Mingarelli, A.B., Beres, E.: The dynamics of fuzzy cellular automata: Rule 30. WSEAS Trans. Circuits and Systems 3(10), 2211–2216 (2004)Google Scholar
  4. 4.
    Cattaneo, G., Flocchini, P., Mauri, G., Quaranta Vogliotti, C., Santoro, N.: Cellular automata in fuzzy backgrounds. Physica D 105, 105–120 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Reiter, C.A.: Fuzzy automata and life. Complexity 7(3), 19–29 (2002)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Maji, P., Nandi, R., Chaudhuri, P.P.: Design of fuzzy cellular automata (FCA) based pattern classifier. In: Fifth International Conference on Advances in Pattern Recognition, ICAPR 2003, Calcutta, India, December 10-13 (2003) (to appear)Google Scholar
  7. 7.
    Cattaneo, G., Flocchini, P., Mauri, G., Santoro, N.: Fuzzy cellular automata and their chaotic behavior. In: Proc. International Symposium on Nonlinear Theory and its Applications, Hawaii. IEICE, vol. 4, pp. 1285–1289 (1993)Google Scholar
  8. 8.
    Wolfram, S.: A New Kind of Science, Wolfram Media, Champaign (2002)Google Scholar
  9. 9.
    John, F.: Partial Differential Equations, 3rd edn., vol. ix, p. 198. Springer, New York (1980)zbMATHGoogle Scholar
  10. 10.
    Mingarelli, A.B.: Fuzzy rule 110 dynamics and the golden number. WSEAS Trans. Computers 2(4), 1102–1107 (2003)Google Scholar
  11. 11.
    Phillips, R.: Steve Wolfram Science Group, Wolfram Corp., personal communications (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Angelo B. Mingarelli
    • 1
  1. 1.School of Mathematics and StatisticsCarleton UniversityOttawaCanada

Personalised recommendations