Upper bound on the products of particle interactions in cellular automata

Physica D: Nonlinear Phenomena

Volumn 154, Issue 3-4, 2001, Pages 240-258

  Hordijk, Wim ^a   Shalizi, Cosma Rohilla ^a,b   Crutchfield, James P ^a  

^a SANTA FE INSTITUTE   (United States)

^b University of Wisconsin Madison   (United States)

Author keywords

Cellular automata; Domain transducer; Domains; Gliders; Particle interactions; Particles

Indexed keywords

EID: 0035877216     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(01)00252-4     Document Type: Article

References (60)

1. A.W. Burks (Ed.), Essays on Cellular Automata, University of Illinois Press, Urbana, IL, 1970.
2. E.R. Berlekamp, J.H. Conway, R.K. Guy, Winning Ways for Your Mathematical Plays, Academic Press, New York, 1982.
3. Peyrard M., Kruskal M.D. Kink dynamics in the highly discrete sine-Gordon system. Physica D. 14:1984;88-102.
4. Grassberger P. New mechanism for deterministic diffusion. Phys. Rev. A. 28:1983;3666-3667.
5. Boccara N., Nasser J., Roger M. Particle-like structures and their interactions in spatio-temporal patterns generated by one-dimensional deterministic cellular automaton rules. Phys. Rev. A. 44:1991;866-875.
6. Boccara N., Roger M. Block transformations of one-dimensional deterministic cellular automata. J. Phys. A. 24:1991;1849-1865.
7. Boccara N. Transformations of one-dimensional cellular automaton rules by translation-invariant local surjective mappings. Physica D. 68:1993;416-426.
8. Y. Aizawa, I. Nishikawa, K. Kaneko, Soliton turbulence in cellular automata, in: H. Gutowitz (Ed.), Cellular Automata: Theory and Experiment, MIT Press, Cambridge, MA, 1991, pp. 307-327, also published as Physica D 45 (1990) 1-3.
9. Y. Aizawa, I. Nishikawa, K. Kaneko, Soliton turbulence in cellular automata, in: H. Gutowitz (Ed.), Cellular Automata: Theory and Experiment, MIT Press, Cambridge, MA, 1991, pp. 307-327, also published as Physica D 45 (1990) 1-3.
10. Park J.K., Steiglitz K., Thurston W.P. Soliton-like behavior in automata. Physica D. 19:1986;423-432.
11. S. Wolfram (Ed.), Theory and Applications of Cellular Automata, World Scientific, Singapore, 1986.
12. S. Wolfram, Cellular Automata and Complexity: Collected Papers, Addison-Wesley, Reading, MA, 1994. http://www.stephenwolfram.com/publications/books/ca-reprint/.
13. Lindgren K., Nordahl M.G. Universal computation in a simple one-dimensional cellular automaton. Complex Syst. 4:1990;299-318.
14. Crutchfield J.P., Mitchell M. The evolution of emergent computation. Proc. National Acad. Sci. 92:1995;10742-10746.
15. Yunes J.B. Seven-state solutions to the firing squad synchronization problem. Theoret. Comput. Sci. 127:1994;313-332.
16. Eloranta K. Partially permutive cellular automata. Nonlinearity. 6:1993;1009-1023.
17. Eloranta K. The dynamics of defect ensembles in one-dimensional cellular automata. J. Statist. Phys. 76:1994;1377-1398.
18. Eloranta K., Nummelin E. The kink of cellular automaton rule 18 performs a random walk. J. Statist. Phys. 69:1992;1131-1136.
19. P. Manneville, N. Boccara, G.Y. Vichniac, R. Bidaux (Eds.), Cellular Automata and Modeling of Complex Systems, Proceedings of the Winter School, Les Houches, France, February 21-28, 1989, Springer Proceedings in Physics, Vol. 46, Springer, Berlin, 1990.
20. D. Andre, F.H. Bennett III, J.R. Koza, Evolution of intricate long-distance communication signals in cellular automata using genetic programming, in: C.G. Langton, K. Shimohara (Eds.), Artificial Life, Vol. V, MIT Press, Cambridge, MA, 1997, pp. 513-520.
21. Hanson J.E., Crutchfield J.P. The attractor-basin portrait of a cellular automaton. J. Statist. Phys. 66:1992;1415-1462.
22. J.E. Hanson, Computational mechanics of cellular automata, Ph.D. Thesis, University of California, Berkeley, CA, 1993.
23. Hanson J.E., Crutchfield J.P. Computational mechanics of cellular automata: an example. Physica D. 103:1997;169-189.
24. D. Eppstein, Gliders in life-like cellular automata, Interactive online database of two-dimensional cellular automata rules with gliders. http://fano.ics.uci.edu/ca/.
25. P. Manneville, Dissipative Structures and Weak Turbulence, Academic Press, Boston, MA, 1990.
26. Cross M.C., Hohenberg P. Pattern formation out of equilibrium. Rev. Mod. Phys. 65:1993;851-1112.
27. A.T. Winfree, The Geometry of Biological Time, Springer, Berlin, 1980.
28. A.T. Winfree, When Time Breaks Down: The Three-dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias, Princeton University Press, Princeton, NJ, 1987.
29. E. Infeld, G. Rowlands, Nonlinear Waves, Solitons, and Chaos, Cambridge University Press, Cambridge, 1990.
30. W. Poundstone, The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge, William Morrow, New York, 1984.
31. D. Griffeath, Additive and Cancellative Interacting Particle Systems, Lecture Notes in Mathematics, Vol. 724, Springer, Berlin, 1979.
32. T.M. Liggett, Interacting Particle Systems, Springer, Berlin, 1985.
33. D.H. Rothman, S. Zaleski, Lattice-gas Cellular Automata: Simple Models of Complex Hydrodynamics, Collection Aléa Saclay, Vol. 5, Cambridge University Press, Cambridge, 1997.
34. Steiglitz K., Kamal I., Watson A. Embedding computation in one-dimensional automata by phase coding solitons. IEEE Trans. Comput. 37:1988;138-144.
35. Griffeath D., Moore C. Life without death is P-complete. Complex Syst. 10:1996;437-447.
36. Moore C. Majority-vote cellular automata, Ising dynamics, and P-completeness. J. Statist. Phys. 88:1997;795-805.
37. C. Moore, M.G. Nordahl, Lattice gas prediction is P-complete, Electronic Pre-preprint, 1997. arxiv.org, comp-gas/9704001.
38. R. Das, M. Mitchell, J.P. Crutchfield, A genetic algorithm discovers particle computation in cellular automata, in: Y. Davidor, H.-P. Schwefel, R. Manner (Eds.), Proceedings of the Conference on Parallel Problem Solving in Nature - PPSN, Vol. III, Lecture Notes in Computer Science, Springer, Berlin, 1994, pp. 344-353.
39. W. Hordijk, M. Mitchell, J.P. Crutchfield, Mechanisms of emergent computation in cellular automata, in: A.E. Eiben, T. Bäck, M. Schoenaur, H.-P. Schwefel (Eds.), Parallel Problem Solving in Nature - PPSN, Vol. V, Lecture Notes in Computer Science, Springer, Berlin, 1998, pp. 613-622.
40. N. Margolus, Crystalline computation, in: A.J.G. Hey (Ed.), Feynman and Computation, Addison-Wesley, Reading, MA, 1998, E-print. arxiv.org, comp-gas/9811002.
41. R. Das, The evolution of emergent computation in cellular automata, Ph.D. Thesis, Colorado State University, 1996.
42. W. Hordijk, Dynamics, emergent computation, and evolution in cellular automata, Ph.D. Thesis, University of New Mexico, Albuquerque, NM, 1999. http://www.santafe.edu/projects/evca/Papers/WH-Diss.html.
43. S. Wolfram, Universality and complexity in cellular automata, Physica D 10 (1984) 1-35, reprinted in [11].
44. J.P. Crutchfield, Is anything ever new? Considering emergence, in: G. Cowan, D. Pines, D. Melzner (Eds.), Complexity: Metaphors, Models, and Reality, Santa Fe Institute Studies in the Sciences of Complexity, Vol. 19, Addison-Wesley, Reading, MA, 1994, pp. 479-497.
45. J.H. Holland, Emergence: From Chaos to Order, Addison-Wesley, Reading, MA, 1998.
46. Wuensche A. Classifying cellular automata automatically: finding gliders, filtering, and relating space-time patterns, attractor basins, and the. Z parameter Complexity. 4:1999;47-66.
47. D. Eppstein, Searching for spaceships, E-print, 2000. arxiv.org, cs.AI/0004003.
48. S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys. 55 (1983) 601-644, reprinted in [11].
49. S. Wolfram, Computation theory of cellular automata, Commun. Math. Phys. 96 (1984) 15-57, reprinted in [11].
50. J.E. Hopcroft, J.D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, MA, 1979, Formal Languages and their Relation to Automata, 2nd Edition, 1969.
51. Crutchfield J.P., Young K. Inferring statistical complexity. Phys. Rev. Lett. 63:1989;105-108.
52. Crutchfield J.P., Hanson J.E. Turbulent pattern bases for cellular automata. Physica D. 69:1993;279-301.
53. D.M. Burton, Elementary Number Theory, Allyn & Bacon, Boston, 1976.
54. J.P. Crutchfield, W. Hordijk, M. Mitchell, Computational performance of evolved cellular automata: Parts I and II, in preparation.
55. H.V. McIntosh, Rule 110 as it relates to the presence of gliders, Electronic manuscript, 2000. http://delta.cs.cinvestav.mx/ ~ mcintosh/comun/RULE110W/RULE110.html.
56. J.P. Crutchfield, C.R. Shalizi, Intrinsic computation versus engineered computation: the computational mechanics of rule 110, in preparation.
57. Crutchfield J.P., Hanson J.E. Attractor vicinity decay for a cellular automaton. Chaos. 3:1993;215-224.
58. Ablowitz M.J., Kruskal M.D., Ladik J.F. Solitary wave collisons. SIAM J. Appl. Math. 36:1979;428-437.
59. Goldberg C.H. Parity filter automata. Complex Syst. 2:1988;91-141.
60. Jakubowski M.H., Steiglitz K., Squier R. Information transfer between solitary waves in the saturable Schrödinger equation. Phys. Rev. E. 56:1997;7267-7272.