Cellular Automata Automatically Constructed from a Bioconvection Pattern

  • Akane Kawaharada
  • Erika Shoji
  • Hiraku Nishimori
  • Akinori Awazu
  • Shunsuke Izumi
  • Makoto Iima
Chapter
Part of the Mathematics for Industry book series (MFI, volume 14)

Abstract

We construct cellular automaton models for the spatio-temporal pattern of Euglena gracilis bioconvection, which is generated when a suspension of Euglena gracilis is illuminated from the bottom with strong light intensity through a statistical construction method of cellular automata. The method of construction is introduced by Kawaharada and Iima (A. Kawaharada and M. Iima, “Constructing Cellular Automaton Models from Observation Data”, In 2013 First International Symposium on Computing and Networking, pp. 559–562 (2013)). Some features of the original patterns are reproduced by one dimensional deterministic CA with the nearest three neighbors and eight possible states for a site.

Keywords

Euglena gracilis Bioconvection Spatio-temporal pattern Cellular automata Observation data Constructing method of cellular automata 

References

  1. Pedley, T.J., Kessler, J.O.: Hydrodynamic phenomema in suspensions of swimming microorganisms. Ann. Rev. Fluid Mech. 24, 313–358 (1992)MathSciNetCrossRefMATHGoogle Scholar
  2. Hill, N.A., Pedley, T.J.: Bioconvection. Fluid Dyn. Res. 37(1–2), 1–20 (2005)Google Scholar
  3. Suematsu, N.-J., Awazu, A., Izumi, S., Noda, S., Nakata, S., Nishimori, H.: Localized bioconvection of Euglena caused by Phototaxis in the lateral direction. J. Phys. Soc. Jpn. 80(6), 064003 (2011)Google Scholar
  4. Shoji, E., Nishimori, H., Awazu, A., Izumi, S., Iima, M.: Localized bioconvection patterns and their initial state dependency in Euglena gracilis suspensions in an annular container. J. Phys. Soc. Jpn. 83, 043001 (2014)CrossRefGoogle Scholar
  5. Watanabe, T., Iima, M., Nishiura, Y.: Spontaneous formation of travelling localized structures and their asymptotic behaviour in binary fluid convection. J. Fluid Mech. 712, 219–243 (2012)Google Scholar
  6. Iima, M., Shoji, E., Suematsu, N., Awazu, A., Izumi, S., Nishimori, H.: A Governing Equation of Localized Bioconvection Patterns in Euglena gracilis Suspensions. (in preparation)Google Scholar
  7. Kitchens, B.P.: Symbolic Dynamics: One-Sided, Two-Sided and Countable State Markov Shifts. Universitext. Springer, Berlin (1998)Google Scholar
  8. Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge (1995)CrossRefMATHGoogle Scholar
  9. Keller, G.: Equilibrium States in Ergodic Theory. London Mathematical Society Student Texts, vol. 42. Cambridge University Press, Cambridge (1998)Google Scholar
  10. Hedlund, G.A.: Endormorphisms and automorphisms of the shift dynamical system. Math. Syst. Theory 3, 320–375 (1969)MathSciNetCrossRefGoogle Scholar
  11. Kurka, P.: Topological dynamics of cellular automata. In: Codes, Systems, and Graphical Models, Minneapolis, MN, 1999. The IMA Volumes in Mathematics and its Applications, vol. 123, pp. 447–485. Springer, New York (2001)Google Scholar
  12. Hurley, M.: Attractors in cellular automata. Ergodic Theory Dynam. Syst. 10(1), 131–140 (1990)MathSciNetCrossRefGoogle Scholar
  13. Milnor, J.: On the entropy geometry of cellular automata. Complex Syst. 2(3), 357–385 (1988)MathSciNetGoogle Scholar
  14. Meyerovitch, T.: Finite entropy for multidimensional cellular automata. Ergodic Theory Dynam. Syst. 28(4), 1243–1260 (2008)MathSciNetCrossRefGoogle Scholar
  15. Kawaharada, A.: Ulam’s cellular automaton and rule 150. Hokkaido Math. J. (to be published)Google Scholar
  16. Hardy, J., Pomeau, Y., de Pazzis, O.: Time evolution of a two dimensional model system. i. invariant states and time correlation functions. J Math. Phys. 14(12), 1746–1759 (1973)CrossRefGoogle Scholar
  17. Hardy, J., de Pazzis, O., Pomeau, Y.: Molecular dynamics of a classical lattice gas: transport properties and time correlation functions. Phys. Rev. A 13, 1949–1961 (1976)CrossRefGoogle Scholar
  18. Frisch, U., Hasslacher, B., Pomeau, Y.: Lattice-gas automata for the Navier-Stokes equation. Phys. Rev. Lett. 56, 1505–1508 (1986)CrossRefGoogle Scholar
  19. McNamara, G., Zanetti, G.: Use of the Boltzmann equation to simulate lattice gas automata. Phys. Rev. Lett. 61(20), 2332–2335 (1988)CrossRefGoogle Scholar
  20. Gerhardt, M., Schuster, H., Tyson, J.J.: A cellular automaton model of excitable media: Ii. curvature, dispersion, rotating waves and meandering waves. Physica D 46(3):392–415 (1990)Google Scholar
  21. Gerhardt, M., Schuster, H., Tyson, J.J.: A cellular automaton model of excitable media: Iii. fitting the belousov-zhabotinskii reaction. Physica D 46(3):416–426 (1990)Google Scholar
  22. Kusch, I., Markus, M.: Mollusc shell pigmentation: cellular automaton simulations and evidence for undecidability. J. Theoret. Biol. 178(3), 333–340 (1996)CrossRefMATHGoogle Scholar
  23. Young, David A.: A local activator-inhibitor model of vertebrate skin patterns. Math. Biosci. 72(1), 51–58 (1984)MathSciNetCrossRefGoogle Scholar
  24. Kawaharada, A., Iima, M.: Constructing cellular automaton models from observation data. In: 2013 First International Symposium on Computing and Networking, pp. 559–562 (2013)Google Scholar
  25. Kawaharada, A., Iima, M.: An application of data-based construction method of cellular automata to physical phenomena. J. Cell. Automata 1–21 (2014) (submitted)Google Scholar

Copyright information

© Springer Japan 2016

Authors and Affiliations

  • Akane Kawaharada
    • 1
    • 2
  • Erika Shoji
    • 1
  • Hiraku Nishimori
    • 1
    • 3
  • Akinori Awazu
    • 1
    • 3
  • Shunsuke Izumi
    • 1
  • Makoto Iima
    • 1
    • 2
  1. 1.Hiroshima UniversityHigashi-HiroshimaJapan
  2. 2.Core Research for Evolutional Science and TechnologyJapan Science and Technology AgencyTokyoJapan
  3. 3.Research Center for the Mathematics on Chromatin Live DynamicsHiroshima-UniversityHigashi-HiroshimaJapan

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