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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Pedley, T.J., Kessler, J.O.: Hydrodynamic phenomema in suspensions of swimming microorganisms. Ann. Rev. Fluid Mech. 24, 313–358 (1992)
Hill, N.A., Pedley, T.J.: Bioconvection. Fluid Dyn. Res. 37(1–2), 1–20 (2005)
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)
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)
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)
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)
Kitchens, B.P.: Symbolic Dynamics: One-Sided, Two-Sided and Countable State Markov Shifts. Universitext. Springer, Berlin (1998)
Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge (1995)
Keller, G.: Equilibrium States in Ergodic Theory. London Mathematical Society Student Texts, vol. 42. Cambridge University Press, Cambridge (1998)
Hedlund, G.A.: Endormorphisms and automorphisms of the shift dynamical system. Math. Syst. Theory 3, 320–375 (1969)
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)
Hurley, M.: Attractors in cellular automata. Ergodic Theory Dynam. Syst. 10(1), 131–140 (1990)
Milnor, J.: On the entropy geometry of cellular automata. Complex Syst. 2(3), 357–385 (1988)
Meyerovitch, T.: Finite entropy for multidimensional cellular automata. Ergodic Theory Dynam. Syst. 28(4), 1243–1260 (2008)
Kawaharada, A.: Ulam’s cellular automaton and rule 150. Hokkaido Math. J. (to be published)
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)
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)
Frisch, U., Hasslacher, B., Pomeau, Y.: Lattice-gas automata for the Navier-Stokes equation. Phys. Rev. Lett. 56, 1505–1508 (1986)
McNamara, G., Zanetti, G.: Use of the Boltzmann equation to simulate lattice gas automata. Phys. Rev. Lett. 61(20), 2332–2335 (1988)
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)
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)
Kusch, I., Markus, M.: Mollusc shell pigmentation: cellular automaton simulations and evidence for undecidability. J. Theoret. Biol. 178(3), 333–340 (1996)
Young, David A.: A local activator-inhibitor model of vertebrate skin patterns. Math. Biosci. 72(1), 51–58 (1984)
Kawaharada, A., Iima, M.: Constructing cellular automaton models from observation data. In: 2013 First International Symposium on Computing and Networking, pp. 559–562 (2013)
Kawaharada, A., Iima, M.: An application of data-based construction method of cellular automata to physical phenomena. J. Cell. Automata 1–21 (2014) (submitted)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Japan
About this chapter
Cite this chapter
Kawaharada, A., Shoji, E., Nishimori, H., Awazu, A., Izumi, S., Iima, M. (2016). Cellular Automata Automatically Constructed from a Bioconvection Pattern. In: Suzuki, Y., Hagiya, M. (eds) Recent Advances in Natural Computing. Mathematics for Industry, vol 14. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55429-5_2
Download citation
DOI: https://doi.org/10.1007/978-4-431-55429-5_2
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55428-8
Online ISBN: 978-4-431-55429-5
eBook Packages: EngineeringEngineering (R0)