Abstract
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.
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References
Adamatzky, A.: Identification of Cellular Automata. Taylor and Francis (1994)
Adamatzky, A. (ed.): Collision-Based Computing. Elsevier (2002)
Adamatzky, A., De Lacy Costello, B., Asai, T.: Reaction Diffusion Computers. Elsevier (2005)
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)
Adamatzky, A., Chua, L.: Phenomenology of retained refractoriness: On semi-memristive discrete media. Int. J. Bifurcation and Chaos 22, 1230036 (2012)
Adamatzky, A.: Reaction-Diffusion Automata. Springer (2012)
Adamatzky, A.: On binary-state phyllosilicate automata. Int. J. Bifurcation and Chaos (2013)
Adamatzky, A.: On oscillators in phyllosilicate excitable automata. Int. J. Mod. Phys. C 24, 1350034 (2013) (10 pages)
Adamatzky, A.: Game of Life on Phyllosilicates: Gliders, Oscillators and Still Life. Physics Letters A 377, 1597–1605 (2013)
Ballantine, J.A., Purnell, J.H., Thomas, J.M.: Sheet silicates: broad spectrum catalysts for organic synthesis. J. Molecular Catalysis 27, 157–167 (1984)
Bandyopadhyay, A., Pati, R., Sahu, S., Peper, F., Fujita, D.: Massively parallel computing on an organic molecular layer. Nature Physics 6, 369–375 (2010)
Adamatzky, A.: Molecular computing: Aromatic arithmetic. Nature Nature Physics 6, 325–326 (2010)
Adamatzky, A., Chua, L.: Memristive excitable cellular automata. Int. J. Bifurcation and Chaos 21, 3083 (2011)
Bays, C.: The discovery of glider guns in a Game of Life for the triangular tessellation. J. Cellular Automata 2(4), 345–350 (2007)
Bergaya, F., Theng, B.G.K., Lagaly, G. (eds.): Handbook of Clay Science. Elsevier (2006)
Bleam, W.: Atomic theories of phyllosilicates: Quantum chemistry, statistical mechanics, electrostatic theory, and crystal chemistry. Reviews Geophysics 31(1), 51–73 (1993)
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)
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)
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)
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)
Goucher, A.P.: Gliders in cellular automata on Penrose tilings. J. Cellular Automata (2012) (in Press)
Greenberg, J., Hastings, S.: Spatial patterns for discrete models of diffusion in excitable media. SIAM J. Applied Math. 34, 515–523 (1978)
Griffen, D.T.: Silicate Crystal Chemistry. Oxford University Press (1992)
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)
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)
Liebau, F.: Structural Chemistry of Silicates: Structure, Bonding, and Classification. Springer (1985)
Law, M.E., Gilmer, G.H., JaraÃz, M.: Simulation of defects and diffusion phenomena in silicon. MRS Bulletin, 46–51 (June 2000)
Margenstern, M.: New Tools for Cellular Automata in the Hyperbolic Plane. J. UCS 6(12), 1226–1252 (2000)
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)
Margenstern, M.: Universal Cellular Automata with Two States in the Hyperbolic Plane. J. Cellular Automata 7(3), 259–284 (2012)
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)
Margenstern, M.: Small Universal Cellular Automata in Hyperbolic Spaces: A Collection of Jewels. Springer (2013)
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)
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)
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)
Pauling, L.: The structure of the micas and related minerals. Proc. Natl. Acad. Sci. U.S.A. 16, 123–129 (1930)
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)
Richardson, I.G.: The calcium silicate hydrates. Cement and Concrete Research 38, 137–158 (2008)
Sokolski, M.M.: Structure and kinetics of defects in silicon. NASA TN D-4154, Washington (1967)
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)
Suh, W.H., Suslick, K.S., Stucky, G.D., Suh, Y.-H.: Nanotechnology, nanotoxicology, and neuroscience. Progress in Neurobiology 87, 133–170 (2009)
Tanimura, K., Tanaka, T., Itoh, N.: Creation of quasistable lattice defects by electronic excitation in SiO2. Phys. Rev. Lett. 51, 423–426 (1983)
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)
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)
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)
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)
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Adamatzky, A. (2015). Phyllosilicate Automata. In: Adamatzky, A. (eds) Automata, Universality, Computation. Emergence, Complexity and Computation, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-09039-9_16
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DOI: https://doi.org/10.1007/978-3-319-09039-9_16
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