Phyllosilicate Automata

  • Andrew AdamatzkyEmail author
Part of the Emergence, Complexity and Computation book series (ECC, volume 12)


The chapter is an overview of our finding on a novel class of regular automata networks, the phyllosilicate automata. Phyllosilicate is a sheet of silicate tetrahedra bound by basal oxygens. A phyllosilicate automaton is a regular network of finite state machines, which mimics structure of the phyllosilicate. A node of a binary state phyllosilicate automaton takes states 0 and 1. A node updates its state in discrete time depending on a sum of states of its three (silicon nodes) or six (oxygen nodes) closest neighbours. By extensive sampling of the node state transition rule space we classify rules by main types of patterns generated by them based on the patterns shape (convex and concave hulls, almost circularly growing patterns, octagonal patterns, dendritic growth); and, the patterns interior (disordered, solid, labyrinthine). We also present rules exhibiting travelling localizations attributed to Conway’s Game of Life: gliders, oscillators, still lifes, and a glider gun.


Cellular Automaton Hyperbolic Plane Large Circle Internal Morphology Halting Problem 
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.


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  1. 1.
    Adamatzky, A.: Identification of Cellular Automata. Taylor and Francis (1994)Google Scholar
  2. 2.
    Adamatzky, A. (ed.): Collision-Based Computing. Elsevier (2002)Google Scholar
  3. 3.
    Adamatzky, A., De Lacy Costello, B., Asai, T.: Reaction Diffusion Computers. Elsevier (2005)Google Scholar
  4. 4.
    Adamatzky, A., Martinez, G.J., Mora, J.C.S.T.: Phenomenology of reaction diffusion binary-state cellular automata. Int. J. Bifurcation and Chaos 16, 2985–3005 (2007)CrossRefGoogle Scholar
  5. 5.
    Adamatzky, A., Chua, L.: Phenomenology of retained refractoriness: On semi-memristive discrete media. Int. J. Bifurcation and Chaos 22, 1230036 (2012)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Adamatzky, A.: Reaction-Diffusion Automata. Springer (2012)Google Scholar
  7. 7.
    Adamatzky, A.: On binary-state phyllosilicate automata. Int. J. Bifurcation and Chaos (2013)Google Scholar
  8. 8.
    Adamatzky, A.: On oscillators in phyllosilicate excitable automata. Int. J. Mod. Phys. C 24, 1350034 (2013) (10 pages)Google Scholar
  9. 9.
    Adamatzky, A.: Game of Life on Phyllosilicates: Gliders, Oscillators and Still Life. Physics Letters A 377, 1597–1605 (2013)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Ballantine, J.A., Purnell, J.H., Thomas, J.M.: Sheet silicates: broad spectrum catalysts for organic synthesis. J. Molecular Catalysis 27, 157–167 (1984)CrossRefGoogle Scholar
  11. 11.
    Bandyopadhyay, A., Pati, R., Sahu, S., Peper, F., Fujita, D.: Massively parallel computing on an organic molecular layer. Nature Physics 6, 369–375 (2010)Google Scholar
  12. 12.
    Adamatzky, A.: Molecular computing: Aromatic arithmetic. Nature Nature Physics 6, 325–326 (2010)CrossRefGoogle Scholar
  13. 13.
    Adamatzky, A., Chua, L.: Memristive excitable cellular automata. Int. J. Bifurcation and Chaos 21, 3083 (2011)CrossRefzbMATHGoogle Scholar
  14. 14.
    Bays, C.: The discovery of glider guns in a Game of Life for the triangular tessellation. J. Cellular Automata 2(4), 345–350 (2007)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Bergaya, F., Theng, B.G.K., Lagaly, G. (eds.): Handbook of Clay Science. Elsevier (2006)Google Scholar
  16. 16.
    Bleam, W.: Atomic theories of phyllosilicates: Quantum chemistry, statistical mechanics, electrostatic theory, and crystal chemistry. Reviews Geophysics 31(1), 51–73 (1993)CrossRefGoogle Scholar
  17. 17.
    Bulatov, V.V., Justo, J.F., Wei Cai, S., Yip, A.S., Argon, T., Lenosky, M., de la Rubia, T.D.: Parameter-free Modeling of Dislocation Motion: The Case of Silicon. Philosophical Magazine A 81, 1257–1281 (2001)CrossRefGoogle Scholar
  18. 18.
    Carrado, K.A., Macha, S.M., Tiede, D.M.: Effects of surface functionalization and organo-tailoring of synthetic layer silicates on the immobilization of cytochrome c. Chem. Mater. 16, 2559–2566 (2004)CrossRefGoogle Scholar
  19. 19.
    Clarridge, A.G., Salomaa, K.: An improved cellular automata based algorithm for the 45-Convex hull problem. Journal of Cellular Automata 5, 107–112 (2010)zbMATHMathSciNetGoogle Scholar
  20. 20.
    Field, R.J., Noyes, R.M.: Oscillations in chemical systems IV. Limit cycle behavior in a model of a real chemical reaction. J. Chem. Phys. 60, 1877–1884 (1974)Google Scholar
  21. 21.
    Goucher, A.P.: Gliders in cellular automata on Penrose tilings. J. Cellular Automata (2012) (in Press)Google Scholar
  22. 22.
    Greenberg, J., Hastings, S.: Spatial patterns for discrete models of diffusion in excitable media. SIAM J. Applied Math. 34, 515–523 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Griffen, D.T.: Silicate Crystal Chemistry. Oxford University Press (1992)Google Scholar
  24. 24.
    Janavicus, A.J., Storasta, J., Purlys, R., Mekys, A., Balakauskas, S., Norgela, Z.: Crystal lattice and carriers hall mobility relaxation processes in Si crystal irradiated by soft X-rays. Acta Physica Polonica 112, 55–67 (2007)Google Scholar
  25. 25.
    Lehmann, T., Wolff, T., Hamel, C., Veit, P., Garke, B., Seidel-Morgenstern, A.: Physico-chemical characterization of Ni/MCM-41 synthesized by a template ion exchange approach. Microporous and Mesoporous Materials 151, 113–125 (2012)CrossRefGoogle Scholar
  26. 26.
    Liebau, F.: Structural Chemistry of Silicates: Structure, Bonding, and Classification. Springer (1985)Google Scholar
  27. 27.
    Law, M.E., Gilmer, G.H., Jaraíz, M.: Simulation of defects and diffusion phenomena in silicon. MRS Bulletin, 46–51 (June 2000)Google Scholar
  28. 28.
    Margenstern, M.: New Tools for Cellular Automata in the Hyperbolic Plane. J. UCS 6(12), 1226–1252 (2000)zbMATHMathSciNetGoogle Scholar
  29. 29.
    Margenstern, M.: A universal cellular automaton on the heptagrid of the hyperbolic plane with four states. Theor. Comput. Sci. 412(1-2), 33–56 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Margenstern, M.: Universal Cellular Automata with Two States in the Hyperbolic Plane. J. Cellular Automata 7(3), 259–284 (2012)zbMATHMathSciNetGoogle Scholar
  31. 31.
    Margenstern, M.: Universality and the Halting Problem for Cellular Automata in Hyperbolic Spaces: The Side of the Halting Problem. In: Durand-Lose, J., Jonoska, N. (eds.) UCNC 2012. LNCS, vol. 7445, pp. 12–33. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  32. 32.
    Margenstern, M.: Small Universal Cellular Automata in Hyperbolic Spaces: A Collection of Jewels. Springer (2013)Google Scholar
  33. 33.
    McDonald, A., Scott, B., Villemure, G.: Hydrothermal preparation of nanotubular particles of a 1:1 nickel phyllosilicate. Microporous and Mesoporous Materials 120, 263–266 (2009)CrossRefGoogle Scholar
  34. 34.
    Monnier, A., Schuth, F., Huo, Q., Kumar, D., Margolese, D., Maxwell, R.S., Stucky, G.D., Krishnamurty, M., Petroff, P., Firouzi, A., Janicke, M., Chmelka, B.F.: Cooperative formation of inorganic-organic interfaces in the synthesis of silicate mesostructures. Science 261, 1299–1303 (1993)CrossRefGoogle Scholar
  35. 35.
    Owens, N., Stepney, S.: Investigations of Game of Life cellular automata rules on Penrose tilings: Lifetime, ash, and oscillator Statistics. J. Cellular Automata 5, 207–225 (2010)zbMATHMathSciNetGoogle Scholar
  36. 36.
    Pauling, L.: The structure of the micas and related minerals. Proc. Natl. Acad. Sci. U.S.A. 16, 123–129 (1930)CrossRefGoogle Scholar
  37. 37.
    Pizzagalli, L., Godet, J., Guenole, J., Brochard, S.: Dislocation cores in silicon: new aspects from numerical simulations. Journal of Physics: Conference Series 281, 012002 (2011)Google Scholar
  38. 38.
    Richardson, I.G.: The calcium silicate hydrates. Cement and Concrete Research 38, 137–158 (2008)CrossRefGoogle Scholar
  39. 39.
    Sokolski, M.M.: Structure and kinetics of defects in silicon. NASA TN D-4154, Washington (1967)Google Scholar
  40. 40.
    Specht, K.M., Jackson, M., Sunkel, B., Boucher, M.A.: Synthesis of a functionalized sheet silicate derived from apophyllite and further modification by hydrosilylation. Applied Clay Science 47, 212–216 (2010)CrossRefGoogle Scholar
  41. 41.
    Suh, W.H., Suslick, K.S., Stucky, G.D., Suh, Y.-H.: Nanotechnology, nanotoxicology, and neuroscience. Progress in Neurobiology 87, 133–170 (2009)CrossRefGoogle Scholar
  42. 42.
    Tanimura, K., Tanaka, T., Itoh, N.: Creation of quasistable lattice defects by electronic excitation in SiO2. Phys. Rev. Lett. 51, 423–426 (1983)CrossRefGoogle Scholar
  43. 43.
    Torbey, S., Akl, S.G.: An exact solution to the two-dimensional arbitrary-threshold density classification problem. Journal of Cellular Automata 4, 225–235 (2009)zbMATHMathSciNetGoogle Scholar
  44. 44.
    Velichko, O.I., Dobrushkin, V.A., Muchynski, A.N., Tsurko, V.A., Zhuk, V.A.: Simulation of coupled diffusion of impurity atoms and point defects under nonequilibrium conditions in local domain. J. Comput Physics 178, 196–209 (2002)CrossRefzbMATHGoogle Scholar
  45. 45.
    Watkins, G.D.: Lattice vacancies and interstitials in silicon. Proc. of the US-ROC Solid State Physics Seminar. Chinese, J. Physics 15, 92–102 (1977)Google Scholar
  46. 46.
    Watkins, G.D.E.: studies of lattice defects in semiconductors. In: Henderson, B., Hughes, A.E. (eds.) Defects and Their Structure in Non-metallic Solids, p. 203. Plenum Press, New York (1976)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Unconventional Computing CentreUniversity of the West of EnglandBristolUK

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