Phenomenology of Excitation in 2-D Cellular Automata and Swarm Systems

Chaos, Solitons and Fractals

Volumn 9, Issue 7, 1998, Pages 1233-1265

  Adamatzky, Andrew ^a   Holland, Owen ^a  

^a UNIVERSITY OF THE WEST OF ENGLAND   (United Kingdom)

Author keywords

Cellular automata; Excitable media; Pattern formation; Self organisation; Swarm

Indexed keywords

ARTIFICIAL INTELLIGENCE; AUTOMATA THEORY; COMPUTER SIMULATION; MATHEMATICAL MODELS;

CELLULAR AUTOMATA; LATTICE SWARM SYSTEMS;

COMPUTATION THEORY;

EID: 0032120638     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(97)00123-9     Document Type: Article

References (58)

1. Wiener, N., Rosenblueth, A., The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle. Arch. Inst. Cardiol. Mex., 1946, 16, 205-265.
2. Balakhovsky, L. S., Several modes of excitation movement in ideal excitable tissue. Biophysics, 1965, 10, 1175.
3. Reshod'ko, L. V., Bures, J., Computer simulations of reverberating spreading depression in a network of cell automata. Biol. Cyber., 1975, 18, 181-189.
4. Zykov, V. S., Simulation of Wave Processes in Excitable Media. Manchester University Press, Manchester, 1987.
5. Gerhardt, M., Schuster, H., Tyson, J., A cellular automaton model of excitable media. II. Curvature, dispersion, rotating waves and meandering waves. Phys. D., 1990, 46, 392-415.
6. Gerhardt, M., Schuster, H., Tyson, J., A cellular automaton model of excitable media. III. Fitting the Belousov-Zhabotinskii reaction. Phys. D, 1990, 46, 416-426.
7. Gerhardt, M., Schuster, H., Tyson, J., A cellular automaton model of excitable media, IV. Untwisted scroll rings. Phys. D, 1991, 50, 189-206.
8. Ulam, S. M., On some mathematical problems connected with patterns of growth of figure. Proc. Sympos. Appl. Math., 1962, 14, 215-224.
9. von Neumann, J., Theory of Self-Reproducing Automata. University of Illinois Press, 1966.
10. Aladyev, V., Mathematical Theory of Homogeneous Structures and Their Applications. Valgue Press, Tallinn, 1972.
11. Toffoli, T. and Margolus, N., Cellular Automata Machines. MIT Press, 1987.
12. Wuensche, A. and Lesser, M., The Global Dynamics of Cellular Automata. Addison-Wesley, 1992.
13. Adamatzky, A., Identification of Cellular Automata. Taylor and Francis, London, 1994.
14. Deneubourg, J.-L., Theraulaz, G. and Beckers, R., Swarm-made architectures. In Proc. 1st Europ. Conf. on Artificial Life. 1990, pp. 123-133.
15. Deneubourg, J.-L., Goss, S., Pasteels, J. M., Fresneau, D. and Lachaud, J.-P., Self-organization mechanisms in ant societies (II): learning in foraging and division of labor. In From Individual to Collective. Behavior in Social Insects, ed. J. M. Pasteels and J.-L. Deneubourg. Birkhauser, Basel, 1987, pp. 177-196.
16. Tsetlin, M. L., Automata Theory and Simulation of Biological Processes (in Russian). Nauka, Moscow, 1969.
17. Beni, G. and Wang, J., Swarm intelligence in cellular robotics systems. In Proc. NATO Adv. Workshop on Robotics and Biological Systems, 1989.
18. Rennie, M. K., Models for multiply-modal systems. Z. math. Logik Grundlagen Math., 1970, 16, 279-292.
19. Fischer, M. J. and Immerman, N., Foundations of knowledge for distributed systems. In Theoretical Aspects of Reasoning About Knowledge, ed. J. Y. Halpern. Morgan Kaufmann, California, 1986.
20. Halpern, J. Y., Using reasoning about knowledge to analyze distributed systems. Ann. Rev. Comput. Sci., 1987, 2, 37-68.
21. Zakharov, A. A., Organization of Ant Communities (in Russian). Nauka Publishers, Moscow, 1991.
22. Holldobler, B. and Wilson, E. O., Journey to the Ants. The Belknap Press of Harward University Press, Cambridge, 1995.
23. Wilson, E. O., Holldobler, B., Dense heterarchies and mass communication as the basis of organization in ant colonies. TREE, 1988, 3, 65-68.
24. Rauch, E. M., Millonas, M. M. and Chialvo, D. R., Pattern formation and functionality in swarm models. SFI Working Paper 95-08-073, 1995.
25. Theraulaz, G., Bonabeau, E., Coordination in distributed building. Science, 1995, 269, 686-688.
26. Beckers, R., Holland, O. E., Deneubourg, J. L., From local actions to global tasks: stigmergy and collective robotics. ALIFE, 1994, IV, 181-189.
27. Schoonderwoerd, R., Holland, O., Bruten, J. and Rothkrantz, L., Ant-based load balancing in telecommunications networks. Adaptive Behavior, 1996, 5, 169-207.
28. Dorigo, M., Maniezzo, V., Colorni, A., The Ant system: optimization by a colony of cooperating agents. IEEE Trans. Systems Man Cybernet., 1996, B26, 1-13.
29. Adamatzky, A. I., On complexity of serial simulation of cellular automata. Automat. i. Telemekh. (Automat. Remote Control), 1994, 3, 149-160, (in Russian).
30. Harris, T. E., Contact interaction on a lattice. Ann. Probab., 1974, 2, 969 988.
31. Spitzer, F., Uniform motion with elastic collisions of an infinite particle system. J. Math. Mech., 1970, 18, 970-990.
32. Ligget, T. M., Interacting Particle Systems, Springer, New York, 1985.
33. Sudbury, A., A model of spatial conflicts. Biometrika, 1973, 60, 581-588.
34. Ligget, T. M., Long-range exclusion processes. Ann. Probab., 1980, 11, 16-33.
35. Wolfram, S., Universality and complexity in cellular automata. Phys. D, 1984, 10, 1-35.
36. +-medium. Adv. Mater. Optics Electronics, 1995, 5, 145-155.
37. Adamatzky, A. I., On the particle like waves in the discrete model of excitable medium. Neural Network World, 1996, 1, 3-10.
38. Langton, C. G., Computation at the edge of chaos: phase transitions and emergent computation. Phys. D, 1990, 42, 12-27.
39. Wuensche, A., Complexity in one-dimensional cellular automata: gliders, basis of attraction and Z parameter. Santa Fe Institute Working Paper 94-04-025, 1994.
40. Mitchell, M., Computation in cellular automata: a selected review. Santa Fe Institute Working Paper 96-09-074, 1996.
41. Othmer, H. G., The mathematical problem of oscillations. In Oscillations and Traveling Waves in Chemical Systems, ed. R. J. Field and M. Burger. John Wiley and Sons, 1985.
42. Ashkenazi, M., Othmer, H. G., Spatial patterns in coupled biochemical oscillators. J. Math. Biol., 1978, 5, 305.
43. Marek, M., Svobodova, E., Nonlinear phenomenon in oscillatory systems of homogeneous reaction. Experimental observation. Biophys. Chem., 1975, 3, 263.
44. Aliev, B. R., Panfilov, A. V., A simple 2-variable model of cardiac excitation. Chaos, Solitons & Fractals, 1996, 7(3), 293-301.
45. Wilby, M. R., Propagation beats and fibrillation in a cellular automata model of an excitable media. Chaos, Solitons & Fractals, 1995, 5(3/4), 623-34.
46. Courtemanche, M., Wave propagation and curvature effects in a model of an excitable media. Chaos, Solitons & Fractals, 1995, 5(3/4), 623-634.
47. Rauch, E. M., Millonas, M. M., Chialvo, D. R., Pattern-formation and functionality in swarm models. Phys. Lett. A, 1995, 207(3/4), 185-193.
48. Ord, G. N., Fractal space-time and the statistical-mechanics of random walks. Chaos, Solitons & Fractals, 1996, 7(6), 821-843.
49. Holden, A. V., Poole, M. J., Tucker, J. V., An algorithmic model of the mammalian heart: Propagation, vulnerability, re-entry and fibrillation. Internat. J. Bifur. Chaos, 1996, 6(9), 1623-1635.
50. Gunaratne, G. H., A theory of patterns. Chaos, Solitons & Fractals, 1995, 5(8), 1447-1454.
51. El Naschie, M. S., Iterated function systems and the 2-slit experiment of quantum mechanics. Chaos, Solitons & Fractals, 1994, 4(10), 1965-1968.
52. Palmore, J., Chaos, entropy and integrals for discrete dynamical systems on lattices. Chaos, Solitons & Fractals, 1995, 5(8), 1397-1418.
53. Fredkin, E., Digital mechanics. Phys. D, 1990, 45, 254-270.
54. Toffoli, T., Magolus, N., Programmable matter: Concepts and realizations. Phys. D, 1990, 47, 263-272.
55. + medium. Adv. Mater. Optics Electronics, 1997, 7, 263-272.
56. El Naschie, M. S., A note on quantum-mechanics, diffusional interference and informions. Chaos, Solitons & Fractals, 1995, 5(5), 881-884.
57. Conrad, M., Fluctuons. III Gravity. Chaos, Solitons & Fractals, 1996, 7(8), 1261-1303.
58. Stephanovitch, V. A., Self-localized carrier states in disordered ferroelectrics. JETP Lett., 1997, 65(5), 446-451.