Nonclassical computation-a dynamical systems perspective

Handbook of Natural Computing

Volumn 4-4, Issue , 2012, Pages 1980-2025

  Stepney, Susan ^a  

^a UNIVERSITY OF YORK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER APPLICATIONS;

COMPUTATIONAL INTERPRETATIONS; COMPUTATIONAL SYSTEM; DISCRETE SYSTEMS; DYNAMICAL SYSTEMS APPROACH; EMBODIED SYSTEMS; MATERIAL SUBSTRATES; NATURAL DYNAMICS; PHYSICAL SYSTEMS;

DYNAMICAL SYSTEMS;

EID: 84903820850     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-92910-9_59     Document Type: Chapter

References (112)

1. Abraham RH (1987) Dynamics and self-organization. In: Yates FE (ed) Self-organizing systems: the emergence of order. Plenum, New York, pp 599-613
2. Abraham RH, Shaw CD (1987) Dynamics: a visual introduction. In: Yates FE (ed) Self-organizing systems:the emergence of order. Plenum, New York, pp 543-597
3. Adamatzky A (ed) (2002) Collision-based computing. Springer, London
4. Adamatzky A, Arena P, Basile A, Carmona-Galan R, Costello B, Fortuna L, Frasca M, Rodriguez-Vazquez A (2004) Reaction-diffusion navigation robot control:from chemical to VLSI analogic processors. IEEE Trans Circuits Syst 51(5):926-938
5. Adamatzky A, Costello BDL, Asai T (2005) Reactiondiffusion computers. Elsevier, Boston, MA
6. Agladze K, Magome N, Aliev R, Yamaguchi T, Yoshikawa K (1997) Finding the optimal path with the aid of chemical wave. Physica D 106:247-254
7. Andersson C, Nordahl MG (1998) Evolving coupled map lattices for computation. In: EuroGP'98, Paris, April 1998. LNCS, vol 1391. Springer, New York, pp 151-162
8. Baguelin M, LeFèvre J, Richard JP (2003) A formalism for models with a metadynamically varying structure. In: Proceedings of the European Control Conference, Cambridge, UK
9. BeerRD (1995) Adynamical systems perspective on agentenvironment interaction. Artif Intell 72:173-215
10. Berlekamp ER, Conway JH, Guy RK (1982) Winning ways for your mathematical plays, vol 2. Academic, New York
11. Bossomaier T, Sibley-Punnett L, Cranny T (2000) Basins of attraction and the density classification problem for cellular automata. In: VirtualWorlds 2000, Paris, July 2000. LNAI, vol 1834. Springer, Heidelberg, pp 245-255
12. Brooks RA (1991) Intelligence without representation. Artif Intell 47:139-159
13. Cariani P (1993) To evolve an ear: epistemological implications of Gordon Pask's electrochemical devices. Syst Res 10(3):19-33
14. Cook M (2004) Universality in elementary cellular automata. Complex Syst 15(1):1-40
15. Cooper D, Stepney S, Woodcock J (2002) Derivation of Z refinement proof rules: forwards and backwards rules incorporating input/output refinement. Tech. Rep. YCS-2002-347, Department of Computer Science, University of York
16. Crutchfield JP (1994) The calculi of emergence. Physica D 75:1154
17. Crutchfield JP, Kaneko K (1987) Phenomenology of spatio-temporal chaos. In: Bin-Lin H (ed) Direction in Chaos, World Scientific, Singapore, pp 272-353
18. Culik K II, Yu S (1988) Undecidability of CA classification schemes. Complex Syst 2(2):177-190
19. Danks G, Stepney S, Caves L (2007) Folding protein-like structures with open L-systems. In: ECAL 2007, Lisbon, Portugal, September 2007. LNAI, vol 4648. Springer, Heidelberg, pp 1100-1109
20. Danks G, Stepney S, Caves L (2008) Protein folding with stochastic L-systems. In: ALife XI, Winchester, UK, MIT Press, Boston, MA, pp 150-157
21. Dasmahapatra S, Werner J, Zauner KP (2006) Noise as a computational resource. Int J Unconventional Comput 2(4):305-319
22. Ditto WL, Murali K, Sinha S (2008) Chaos computing:ideas and implementations. Phil Trans R Soc A 366:653-664
23. Drossel B (2008) Random Boolean Networks. In: Schuster HG (ed) Reviews of nonlinear dynamics and complexity, vol 1, Wiley, Weinheim, arXiv:0706.3351v2 [cond-mat.stat-mech]
24. Durand B, Formenti E, Varouchas G (2003) On undecidability of equicontinuity classification for cellular automata. In: Morvan M, Rémila E (eds) Discrete models for complex systems, DMCS'03, Lyon, France, June 2003. DMTCS, vol AB, pp 117-128
25. Gács P, Kurdyumov GL, Levin LA (1978) One dimensional uniform arrays that wash out finite islands. Probl Peredachi Inf 12:92-98
26. Giavitto JL, Michel O (2002) Data structure as topological spaces. In: Unconventional models of computation, Kobe, Japan, October 2002. LNCS, vol 2509. Springer, Heidelberg, pp 137-150
27. Giavitto JL, Michel O, Cohen J, Spicher A (2005) Computation in space and space in computations. In: UPP 2004, France, September 2004. LNCS, vol 3566. Springer, Berlin, pp 137-152
28. Hammel SM, Yorke JA, Grebogi C (1988) Numerical orbits of chaotic processes represent true orbits. Bull Am Math Soc 19(2):465-469
29. Hao BL, Zheng WM (1998) Applied symbolic dynamics and chaos. World Scientific, Singapore
30. Harding SL, Miller JF (2004) A tone discriminator in liquid crystal. In: CEC 2004, Portland, Oregon. IEEE Press, pp 1800-1807
31. Harding SL, Miller JF (2005) Evolution in materio: A real-time robot controller in liquid crystal. In: Proc. NASA/DoD Conference on Evolvable Hardware, Washington, DC. IEEE Press, pp 229-238
32. Harding SL, Miller JF, Rietman EA (2006) Evolution in materio: exploiting the physics of materials for computation. arXiv:cond-mat/0611462
33. Hayes W, Jackson KR (2005) A survey of shadowing methods for numerical solutions of ordinary differential equations. Appl Numer Math 53:299-321
34. Holden AV, Tucker JV, Zhang H, Poole MJ (1992) Coupled map lattices as computational systems. Chaos 2(3):367-376
35. Hornby GS, Pollack JB (2001) Body-brain coevolution using L-systems as a generative encoding. In: GECCO 2001, Morgan Kaufmann, San Francisco, CA, pp 868-875
36. Ito K, Aoki T, Higuchi T (2004) Design of an excitable digital reaction-diffusion system for shortest path search. In: ITC-CSCC 2004, Japan
37. Kaneko K (1983) Transition from torus to chaos accompanied by frequency lockings with symmetry breaking. Prog Theor Phys 69(5):1427-1442
38. Kaneko K (1984) Period-doubling of kink-antikink patterns, quasiperiodicity in antiferro-like structures and spatial intermittency in coupled logistic lattice. Prog Theor Phys 72(3):480-486
39. Kaneko K (1985) Spatiotemporal intermittency in coupled map lattices. Prog Theor Phys 74(5):1033-1044
40. Kaneko K (1986) Lyapunov analysis and information flow in coupled map lattices. Physica D 23:436-447
41. Kanso A, Smaoui N (2009) Logistic chaotic maps for binary numbers generations. Chaos, Solitons & Fractals 40(5):2557-2568
42. Kauffman SA (1990) Requirements for evolvability in complex systems. Physica D 42:135-152
43. Kauffman SA (1993) The origins of order. Oxford University Press, New York
44. Kelso JAS (1995) Dynamic Patterns. MIT Press, Cambridge, MA
45. Kitano H (2004) Biological robustness. Nat Rev Genet 5:826-837
46. Kocarev L, Jakimoski G (2001) Logistic map as a block encryption algorithm. Phys Lett A 289(4-5):199-206
47. Kuhnert L, Agladze K, Krinsky V (1989) Image processing using light-sensitive chemical waves. Nature 337:244-247
48. Kunishima W, Nishiyama A, Tanaka H, Tokihiro T (2004) Differential equations for creating complex cellular automaton patterns. J Phys Soc Jpn 73:2033-2036
49. Land M, Belew RK (1995) No perfect two-state cellular automata for density classification exists. Phys Rev Lett 74(25):5148-5150
50. Li TY, Yorke JA (1975) Period three implies chaos. Am Math Monthly 82(10):985-992
51. Lorenz EN (1993) The essence of chaos. UCL Press, London
52. Maturana HR, Varela FJ (1980) Autopoiesis and Cognition. D. Reidel, Boston, MA
53. May RM (1976) Simple mathematical models with very complicated dynamics. Nature 261:459-467
54. Melby P, Kaidel J, Weber N, Hübler A (2000) Adaptation to the edge of chaos in a self-adjusting logistic map. Phys Rev Lett 84(26):5991-5993
55. Melby P, Weber N, Hübler A (2002) Robustness of adaptation in controlled self-adjusting chaotic systems. Fluctuation Noise Lett 2(4):L285-L292
56. Melby P, Weber N, Hübler A (2005) Dynamics of selfadjusting systems with noise. Chaos 15:033902
57. Metropolis N, SteinM, Stein P (1973) On finite limit sets for transformations on the unit interval. J Comb Theory 15(1):25-43
58. Mills JW (2008a) The architecture of an extended analog computer core. In: UCAS-4, Austin, TX, USA
59. Mills JW (2008b) The nature of the extended analog computer. Physica D 237(9):1235-1256
60. Mills JW, Parker M, Himebaugh B, Shue C, Kopecky B, Weilemann C (2006) ''Empty Space'' computes: The evolution of an unconventional supercomputer. In: Proceedings of the 3rd ACM computing frontiers conference, New York, pp. 115-126
61. Mitchell M, Crutchfield JP, Das R (1996) Evolving cellular automata with genetic algorithms: a review of recent work. In: Goodman ED, Uskov VL, Punch WF (eds) Evolutionary computation and its applications:EvCA'96, Moscow
62. Motoike IN, Adamatzky A (2004) Three-valued logic gates in reaction-diffusion excitable media. Chaos Solitons Fractals 24:107-114
63. Moulay E, Baguelin M (2005) Meta-dynamical adaptive systems and their application to a fractal algorithm and a biological model. Physica D 207:79-90
64. Murray JD (1993) Mathematical biology, 2nd edn. Springer, New York
65. Měch R, Prusinkiewicz P (1996) Visual models of plants interacting with their environment. In: SIGGRAPH '96, ACM, New Orleans, LA pp 397-410
66. Omohundro S (1984) Modelling cellular automata with partial differential equations. Physica D 10:128-134
67. Ott E, Grebogi C, Yorke JA (1990) Controlling chaos. Phys Rev Lett 64(11):1196-1199
68. Ott E, Sauer T, Yorke JA (eds) (1994) Coping with chaos. Wiley, New York
69. Pareeka NK, Patidara V, Sud KK (2006) Image encryption using chaotic logistic map. Image Vis Comput 24(9):926-934
70. Pask G (1960) The natural history of networks. In: Yovits MC, Cameron S (eds) Self-organizing systems. Pergamon, New York
71. Păun G (2000) Computing with membranes. J Comput Syst Sci 61(1):108-143
72. Phatak SC, Rao SS (1995) Logistic map: a possible random-number generator. Phys Rev E 51(4):3670-3678
73. Powley EJ, Stepney S (2009a) Automorphisms of transition graphs for elementary cellular automata. J Cell Autom 4(2):125-136
74. Powley EJ, Stepney S (2009b) Automorphisms of transition graphs for linear cellular automata. J Cell Autom 4(4):293-310
75. Prusinkiewicz P, Lindenmayer A (1990) The algorithmic beauty of plants. Springer, New York
76. Prusinkiewicz P, James M, Měch R (1994) Synthetic topiary. In: SIGGRAPH '94, ACM, Orlando, FL, pp 351-358
77. Rendell P (2002) Turing universality of the game of life. In: Adamatzky A (ed) Collision-based computing. Springer, London, chap 18
78. Robinson JC (2001) Infinite-dimensional dynamical systems:an introduction to dissipative parabolic PDEs and the theory of global attractors. Cambridge University Press, Cambridge, MA
79. Roselló-Merino M, Bechmann M, Sebald A, Stepney S (2010) Classical computing in nuclear magnetic resonance. Int J Unconventional Comput 6(3-4):163-195
80. Rothemund PWK, Papadakis N, Winfree E (2004) Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biol 2(12):e424
81. Rubel LA (1993) The extended analog computer. Adv Appl Math 14:39-50
82. Sielewiesiuk J, Gorecki J (2001) Logical functions of a cross-junction of excitable chemical media. J Phys Chem A 105(35):8189-8195
83. Sinha S, Ditto WL (1998) Dynamics based computation. Phys Rev Lett 81(10):2156-2159
84. Sinha S, Ditto WL (1999) Computing with distributed chaos. Phys Rev E 60(1):363-377
85. Sinha S, Ditto WL (2006) Exploiting the controlled responses of chaotic elements to design configurable hardware. Phil Trans R Soc A 364:2483-2494
86. Sloane NJA (2008) The on-line encyclopedia of integer sequences. http://www.research.att.com/~njas/sequences/(accessed 10 November 2008)
87. Spicher A, Michel O, Giavitto JL (2004) A topological framework for the specification and the simulation of discrete dynamical systems. In: ACRI 2004, Amsterdam, October 2004. LNCS, vol 3305. Springer, Heidelberg, pp 238-247
88. Steinbock O, Tó th A, Showalter K (1995) Navigating complex labyrinths: optimal paths from chemical waves. Science 267:868-871
89. Stepney S (2007) Embodiment. In: Flower D, Timmis J (eds) In silico immunology, Springer, New York, chap 12, pp 265-288
90. Stepney S (2008) The neglected pillar of material computation. Physica D 237(9):1157-1164
91. Stepney S (2009) Visualising random Boolean network dynamics. In: GECCO 2009, ACM, New York
92. Stepney S, Polack F, Turner H (2006) Engineering emergence. In: ICECCS 2006, IEEE, Stanford, CA pp 89-97
93. Strogatz SH (1994) Nonlinear dynamics and chaos. Westview, Boulder, CO
94. Sutner K (2005) Universality and cellular automata. In: Machines, computations, and universality 2004, Saint Petersburg, September 2004. LNCS, vol 3354. Springer, Heidelberg, pp 50-59
95. Teman R (1997) Infinite-dimensional dynamical systems in mechanics and physics, 2nd edn. Springer, New York
96. Tokihiro T, Takahashi D, Matsukidaira J, Satsuma J (1996) From soliton equations to integrable cellular automata through a limiting procedure. Phys Rev Lett 76(18):3247-3250
97. Tolmachiev D, Adamatzky A (1996) Chemical processor for computation of Voronoi diagram. Adv Mater Opt Electron 6(4):191-196
98. Toth A, Showalter K (1995) Logic gates in excitable media. J Chem Phys 103:2058-2066
99. Ulam SM, von Neumann J (1947) On combination of stochastic and deterministic processes. Bull Am Math Soc 53(11):1120, (abstract 403)
100. Waddington CH (1957) The strategy of the genes. Allen and Unwin, London
101. Weimar JR, Boon JP (1994) Class of cellular automata for reaction-diffusion systems. Phys Rev E 49(2):1749-1752
102. Weyl H (1949) Philosophy of mathematics and natural science. Princeton University Press, Princeton, NJ
103. Winfree E (2003) DNA computing by self-assembly. The Bridge 33(4):31-38
104. Wolfram S (1984a) Computation theory of cellular automata. Commun Math Phys 96:15-57
105. Wolfram S (1984b) Universality and complexity in cellular automata. Physica D 10:1-35
106. Wolfram S (1985) Twenty problems in the theory of cellular automata. Phys Scr T9:170-183
107. Wolfram S (1986a) Cellular automata fluids: basic theory. J Stat Phys 45:471-526
108. Wolfram S (1986b) Random sequence generation by cellular automata. Adv Appl Math 7:123-169
109. Wolz D, de Oliveira PPB (2008) Very effective evolutionary techniques for searching cellular automata rule spaces. J Cell Autom 3(4):289-312
110. Wuensche A (2002) Finding gliders in cellular automata. In: Adamatzky A (ed) Collision-based computing. Springer, London, chap 13
111. Wuensche A, Lesser M (1992) The global dynamics of cellular automata. Addison-Wesley, Reading
112. Yates FE (ed) (1987) Self-organizing systems: the emergence of order. Plenum, New York