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A Computation in a Cellular Automaton Collider Rule 110

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Advances in Unconventional Computing

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 22))

Abstract

A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations). The constructions proposed are based on universality of elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and computing on rings.

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Notes

  1. 1.

    See also, http://uncomp.uwe.ac.uk/genaro/rule110/glidersRule110.html.

  2. 2.

    See a complete set of regular expressions for every particle in rule 110 in http://uncomp.uwe.ac.uk/genaro/rule110/listPhasesR110.txt.

  3. 3.

    A range of universal CA is listed here http://uncomp.uwe.ac.uk/genaro/Complex_CA_repository.html.

  4. 4.

    Cyclotron evolution was simulated with DDLab software, available at http://www.ddlab.org.

  5. 5.

    The simulations are done in Discrete Dynamics Lab (DDLab, http://www.ddlab.org/) [59].

References

  1. Adamatzky, A.: Computing in Nonlinear Media and Automata Collectives. Institute of Physics Publishing, Bristol (2001)

    Book  MATH  Google Scholar 

  2. Adamatzky, A. (ed.): Collision-Based Computing. Springer, London (2002)

    MATH  Google Scholar 

  3. Adamatzky, A.: Unconventional Computing. Human Brain Project Magazine (2015)

    Google Scholar 

  4. Adamatzky, A., Mayne, R.: Actin automata: phenomenology and localizations. Int. J. Bifurc. Chaos 25(02), 1550030 (2015)

    Article  MATH  Google Scholar 

  5. Arbib, M.A.: Theories of Abstract Automata. Prentice-Hall Series in Automatic Computation, Michigan (1969)

    MATH  Google Scholar 

  6. Bandyopadhyay, A., Pati, R., Sahu, S., Peper, F., Fujita, D.: Massively parallel computing on an organic molecular layer. Nat. Phys. 6, 369–375 (2010)

    Article  Google Scholar 

  7. Banks, E.R.: Information and transmission in cellular automata. PhD Dissertation. Massachusetts Institute of Technology, Cambridge (1971)

    Google Scholar 

  8. Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for your Mathematical Plays, vol. 2, Chap. 25, Academic Press, Cambridge (1982)

    Google Scholar 

  9. Bredas, J.L., Street, G.B.: Polarons, bipolarons, and solitons in conducting polymers. Acc. Chem. Res. 18(10), 309–315 (1985)

    Article  Google Scholar 

  10. Codd, E.F.: Cellular Automata. Academic Press, Inc., New York (1968)

    MATH  Google Scholar 

  11. Cook, M.: Universality in elementary cellular automata. Complex Syst. 15(1), 1–40 (2004)

    MathSciNet  MATH  Google Scholar 

  12. Cook, M.: A concrete view of Rule 110 computation. In: Neary, T., Woods, D., Seda, A.K., Murphy, N. (eds.) The Complexity of Simple Programs, pp. 31–55 (2008)

    Google Scholar 

  13. Davydov, A.S.: Solitons and energy transfer along protein molecules. J. Theor. Biol. 66(2), 379–387 (1977)

    Article  Google Scholar 

  14. Davydov, A.S.: Solitons in Molecular Systems. Springer, Heidelberg (1990)

    Google Scholar 

  15. Fredkin, E., Toffoli, T.: Design principles for achieving high-performance submicron digital technologies. In: Adamatzky, A. (ed.) Collision-Based Computing, pp. 27–46. Springer, London (2002)

    Google Scholar 

  16. Grünbaum, B., Shephard, G.C.: Tilings and Patterns. W. H. Freeman, New York (1986)

    MATH  Google Scholar 

  17. Heeger, A.J., Kivelson, S., Schrieffer, J.R., Su, W.P.: Solitons in conducting polymers. Rev. Mod. Phys. 60(3), 781 (1988)

    Article  Google Scholar 

  18. Hey, A.J.G.: Feynman and computation: exploring the limits of computers. Perseus Books, New York (1998)

    Google Scholar 

  19. Jakubowski, M.H., Steiglitz, K., Squier, R.: Computing with solitons: a review and prospectus. Multiple-Valued Logic 6(5–6), 439–462 (2001)

    MathSciNet  MATH  Google Scholar 

  20. Kudlek, M., Rogozhin, Y.: New small universal post machine. Lect. Notes Comput. Sci. 2138, 217–227 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  21. Kudlek, M., Rogozhin, Y.: Small universal circular post machine. Comput. Sci. J. Moldova. 9(25), 34–52 (2001)

    MathSciNet  MATH  Google Scholar 

  22. Lindgren, K., Nordahl, M.G.: Universal computation in simple one-dimensional cellular automata. Complex Syst. 4, 229–318 (1990)

    MathSciNet  MATH  Google Scholar 

  23. Lu, Y., Sato, Y., Amari, S.: Traveling bumps and their collisions in a two-dimensional neural field. Neural Comput. 23(5), 1248–1260 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Margolus, N.H.: Physics-like models of computation. Physica D. 10(1–2), 81–95 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  25. Margolus, N.H.: Crystalline computation, In: Hey, A.J.G. (ed.) Feynman and computation: exploring the limits of computers, pp. 267–305. Perseus Books, New York (1998)

    Google Scholar 

  26. Margolus, N.H.: Universal cellular automata based on the collisions of soft spheres. In: Adamatzky, A. (ed.) Collision-Based Computing, pp. 107–134. Springer, London (2002)

    Chapter  Google Scholar 

  27. Martínez, G.J., Adamatzky, A., Chen, F., Chua, L.: On soliton collisions between localizations in complex elementary cellular automata: rules 54 and 110 and beyond. Complex Syst. 21(2), 117–142 (2012)

    MathSciNet  MATH  Google Scholar 

  28. Martínez, G.J., Adamatzky, A., McIntosh, H.V.: Computing on rings. In: Zenil, H. (ed.) A Computable Universe: Understanding and Exploring Nature as Computation, pp. 283–302. World Scientific, Singapore (2012)

    Google Scholar 

  29. Martínez, G.J., Adamatzky, A., McIntosh, H.V.: Computing with virtual cellular automata collider. In: IEEE Proceedings of Science and Information Conference, pp. 62–68. London (2015). doi:10.1109/SAI.2015.7237127

  30. Martínez, G.J., Adamatzky, A., Stephens, C.R., Hoeflich, A.: Cellular automaton supercolliders. Int. J. Mod. Phys. C. 22(4), 419–439 (2011)

    Article  MATH  Google Scholar 

  31. McIntosh, H.V.: Linear Cellular Automata Via de Bruijn diagrams, http://delta.cs.cinvestav.mx/~mcintosh/cellularautomata/Papers_files/debruijn.pdf. Cited 10 August 1991

  32. McIntosh, H.V.: Rule 110 as it Relates to the Presence of Gliders, http://delta.cs.cinvestav.mx/~mcintosh/comun/RULE110W/RULE110.html. Cited 14 May 2001

  33. McIntosh, H.V.: A Concordance for Rule 110, http://delta.cs.cinvestav.mx/~mcintosh/cellularautomata/Papers_files/ccord.pdf. Cited 14 May 2002

  34. McIntosh, H.V.: One Dimensional Cellular Automata. Luniver Press, Bristol (2009)

    Google Scholar 

  35. Martínez, G.J., McIntosh, H.V.: ATLAS: Collisions of Gliders like Phases of Ether in Rule 110, http://uncomp.uwe.ac.uk/genaro/Papers/Papers_on_CA_files/ATLAS/bookcollisions.html. Cited 14 August 2001

  36. Martínez, G.J., McIntosh, H.V., Seck, J.C.S.T.: Gliders in Rule 110. Int. J. Unconv. Comput. 2(1), 1–49 (2006)

    Google Scholar 

  37. Martínez, G.J., McIntosh, H.V., Mora, J.C.S.T., Vergara, S.V.C.: Determining a regular language by glider-based structures called phases fi_1 in Rule 110. J. Cell. Automata 3(3), 231–270 (2008)

    MATH  Google Scholar 

  38. Martínez, G.J., McIntosh, H.V., Mora, J.C.S.T., Vergara, S.V.C.: Reproducing the cyclic tag system developed by Matthew Cook with Rule 110 using the phases f\(_1\)_1. J. Cell. Automata 6(2–3), 121–161 (2011)

    MATH  Google Scholar 

  39. Martínez, G.J., McIntosh, H.V., Mora, J.C.S.T., Vergara, S.V.C.: Rule 110 objects and other collision-based constructions. J. Cell. Automata 2(3), 219–242 (2007)

    MathSciNet  MATH  Google Scholar 

  40. Martínez, G.J., Seck-Tuoh-Mora, J.C., Zenil, H.: Computation and Universality: Class IV versus Class III Cellular Automata. J. Cell. Automata 7(5–6), 393–430 (2013)

    MathSciNet  MATH  Google Scholar 

  41. Mills, J.W.: The nature of the extended analog computer. Physica D. 237, 1235–1256 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  42. Minsky, M.: Computation: Finite and Infinite Machines. Prentice Hall, Upper Saddle River (1967)

    Google Scholar 

  43. Morita, K.: Simple universal one-dimensional reversible cellular automata. J. Cell. Automata 2, 159–166 (2007)

    MathSciNet  MATH  Google Scholar 

  44. Morita, K.: Simulating reversible Turing machines and cyclic tag systems by one-dimensional reversible cellular automata. Theor. Comput. Sci. 412, 3856–3865 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  45. Margolus, N., Toffoli, T., Vichniac, G.: Cellular-automata supercomputers for fluid dynamics modeling. Phys. Rev. Lett. 56(16), 1694–1696 (1986)

    Article  Google Scholar 

  46. Neary, T., Woods, D.: P-completeness of cellular automaton Rule 110. Lect. Notes Comput. Sci. 4051, 132–143 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  47. Ninagawa, S., Martínez, G.J.: Compression-based analysis of cyclic tag system emulated by Rule 110. J. Cell. Automata 9(1), 23–35 (2014)

    MathSciNet  MATH  Google Scholar 

  48. Siccardi, S., Adamatzky, A.: Actin quantum automata: communication and computation in molecular networks. Nano Commun. Netw. 6(1), 15–27 (2015)

    Article  Google Scholar 

  49. Siccardi, S., Tuszynski, J. A., Adamatzky, A.: Boolean gates on actin filaments. Phys. Lett. A (2015)

    Google Scholar 

  50. Scott, A.C.: Dynamics of Davydov solitons. Phys. Rev. A 26(1), 578 (1982)

    Article  MathSciNet  Google Scholar 

  51. Smith III, A.R.: Simple computation-universal cellular spaces. J. Assoc. Comput. Mach. 18, 339–353 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  52. Toffoli, T.: Non-conventional computers. In: Webster, J. (ed.) Encyclopedia of Electrical and Electronics Engineering, vol. 14, pp. 455–471. Wiley, New York (1998)

    Google Scholar 

  53. Toffoli, T.: Symbol super colliders. In: Adamatzky, A. (ed.) Collision-Based Computing, pp. 1–23. Springer, London (2002)

    Chapter  Google Scholar 

  54. von Neumann, J.: Theory of Self-reproducing Automata (edited and completed by A.W. Burks), University of Illinois Press, Urbana and London (1966)

    Google Scholar 

  55. Voorhees, B.H.: Computational analysis of one-dimensional cellular automata. In: World Scientific Series on Nonlinear Science, Series A, vol. 15. World Scientific, Singapore (1996)

    Google Scholar 

  56. Wolfram, S.: Cellular automata supercomputing. In: Wilhelmson, R.B. (ed.) High Speed Computing: Scientific Applications and Algorithm Design. pp. 40–48. University of Illinois Press, Champaign (1988)

    Google Scholar 

  57. Wolfram, S.: Cellular Automata and Complexity. Addison-Wesley Publishing Company, Colorado (1994)

    MATH  Google Scholar 

  58. Wolfram, S.: A New Kind of Science. Wolfram Media Inc, Champaign (2002)

    MATH  Google Scholar 

  59. Wuensche, A.: Exploring Discrete Dynamics. Luniver Press, Bristol (2011)

    MATH  Google Scholar 

  60. Zenil, H. (ed.): A Computable Universe. World Scientific Press, Singapore (2012)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Unconventional Computing Centre, University of the West of England, Coldharbour Lane, Bristol, BS16 1QY, UK

    Genaro J. Martínez & Andrew Adamatzky

  2. Departamento de Aplicación de Microcomputadoras, Universidad Autónoma de Puebla, 49 Poniente 1102, 72000, Puebla, Mexico

    Harold V. McIntosh

Authors
  1. Genaro J. Martínez
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  2. Andrew Adamatzky
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  3. Harold V. McIntosh
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Correspondence to Genaro J. Martínez .

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Editors and Affiliations

  1. Unconventional Computing Centre, University of the West of England Unconventional Computing Centre, Bristol, United Kingdom

    Andrew Adamatzky

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Martínez, G.J., Adamatzky, A., McIntosh, H.V. (2017). A Computation in a Cellular Automaton Collider Rule 110. In: Adamatzky, A. (eds) Advances in Unconventional Computing. Emergence, Complexity and Computation, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-33924-5_15

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  • DOI: https://doi.org/10.1007/978-3-319-33924-5_15

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