Emergence of Traveling Localizations in Mutualistic-Excitation Media

  • Andrew Adamatzky
Part of the Advanced Information and Knowledge Processing book series (AI&KP)


Cellular Automaton Spiral Wave Physical Review Letter Refractory State Mobile Localization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adamatzky, A. (2001). Computing in Nonlinear Media and Automata Collectives. IOP, Bristol and Philadelphig.CrossRefGoogle Scholar
  2. Adamatzky, A. (2004). Collision-based computing in Belousov-Zhabotinsky medium. Chaos, Solitons & Fractals, 21:1259–1264.CrossRefGoogle Scholar
  3. Adamatzky, A. (2007). Localizations in cellular automata with mutualistic excitation rules. Chaos, Solitons & Fractals in press.Google Scholar
  4. Adamatzky, A., De Lacy Costello, B., and Asai T. (2005). Reaction-Diffusion Computers. Elsevier.Google Scholar
  5. Adamatzky, A., Martínez, G. and Juan, C. Seck Tuoh Mora (2006). Phenomenology of reaction-diffusion binary-state cellular automata. Int. J. Bifurcation and Chaos, in press.Google Scholar
  6. Alonso-Sanz, R., and Martin, M. (2006). Elementary cellular automata with elementary memory rules in cells: The case of linear rules. Journal of Cellular Automata, 1:70–86.MathSciNetzbMATHGoogle Scholar
  7. Aubry, S. (1997). Breathers in nonlinear lattices: Existence, linear stability and quantization. Physica D, 103:201–250.MathSciNetCrossRefGoogle Scholar
  8. Beato, V., and Engel, H. (2003). Pulse propagation in a model for the photosensitive Belousov-Zhabotinsky reaction with external noise. In Schimansky-Geier, L., Abbott, D., Neiman, A., Van den Broeck, C., editors, Noise in Complex Systems and Stochastic Dynamics, volume 5114 of Proceedings of SPIE, pages 353–362, SPIE.Google Scholar
  9. Bode, M., Liehr, A. W., Schenk, C. P., and Purwins, H.-G. (2002). Interaction of dissipative solitons: Particle-Like behaviour of localized structures in a three-component reaction-diffusion system. Physica D, 161: 45–66.MathSciNetCrossRefGoogle Scholar
  10. Brown, J. A. and Tuszynski, J. A. (1999). A review of the ferroelectric model of microtubules. Ferroelectrics, 220:141–156.CrossRefGoogle Scholar
  11. Chopard, B. and Droz, M. (2005). Cellular Automata Modeling of Physical Systems, Cambridge University Press.Google Scholar
  12. Dennin, M., Treiber, M., Kramer, L., Ahlers, G., and Cannell, D. S. (1996). Origin of traveling rolls in electroconvection of nematic liquid crystals. Phys. Rev. Lett., 76:319–322.CrossRefGoogle Scholar
  13. Edmundson, D.E. and Enns, R.H. (1993). Fully 3–dimensional collisions of bistable light bullets. Optics Letters, 18:1609–1611.CrossRefGoogle Scholar
  14. Field, R. J., and Noyes, R. M. (1974). Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction. Journal of Chemical Physics, 60:1877–1884.CrossRefGoogle Scholar
  15. Forinash, K., Peyrard, M., and Malomed, B. (1994). Interaction of discrete breathers with impurity modes. Physical Review E, 49:3400–3411.CrossRefGoogle Scholar
  16. Greenberg, J. M., and Hastings, S. P. (1978). Spatial patterns for discrete models of diffusion in excitable media. SIAM Journal of Applied Mathematics, 34:515–523.MathSciNetCrossRefGoogle Scholar
  17. Ilachinski, A. (2001). Cellular Automata: A Discrete University. World Scientific, Singapore.CrossRefGoogle Scholar
  18. Heudin, J.-K. (1996). A new candidate rule for the game of two-dimensional life. Complex Systems, 10:367–381.MathSciNetzbMATHGoogle Scholar
  19. Gardner, M. (1970). Mathematical Games—The fantastic combinations of John H. Conway’s new solitaire game Life. Scientific American, 223:120–123.CrossRefGoogle Scholar
  20. Griffeath, D., and Moore, C. (2003). New Constructions in Cellular Automata, Oxford University Press.Google Scholar
  21. Martínez, G. J., Adamatzky, A., and McIntosh, H. (2006). Localization dynamic in binary two-dimensional cellular automaton: Diffusion Rule. Journal of Cellular Automata, in press .Google Scholar
  22. Maruno, K. and Biondini, G. (2004). Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete analogues. Journal of Physics A: Mathematical and General, 37:11819–11839.MathSciNetCrossRefGoogle Scholar
  23. Riecke, H., and Granzow, G.D. Localization of waves without bistability: Worms in nematic electroconvection. Scholar
  24. Rotermund, H.H., Jakubith, S., von Oertzen, A. and Ertl, G. (1991). Solitons in a surface reaction. Physical Review Letters, 66:3083–3086.CrossRefGoogle Scholar
  25. Sendiña-Nadal, I., Mihaliuk, E., Wang, J., Pérez-Muñuzuri, V., and Showalter, K. (2001). Wave propagation in subexcitable media with periodically modulated excitability. Physical Review Letters, 86:1646–1649.CrossRefGoogle Scholar
  26. Toyozawa, Y. (1983). Localization and delocalization of an exciton in the phonon field. In Reineker, P., Haken, H., and Wolf, H.C., editors, Organic Molecular Aggregates: Electronic Excitation and Interaction Processes, pages 90–106. Springer-Verlag, Berlin and Heidelberg.CrossRefGoogle Scholar
  27. Vanag, V. K., and Epstein, I. R. (2001). Pattern formation in a tunable medium: The Belousov-Zhabotinsky reaction in an Aerosol OT microemulsion. Physical Review Letters, 87:1–4.CrossRefGoogle Scholar
  28. Wang, J., Kada, S., Jung, P. and Showalter, K. (1999). Noise driven avalanche behaviour in subexitable media. Physical Review Letters, 82:855–858.CrossRefGoogle Scholar
  29. Wuensche, A. (2004). Self-reproduction by glider collisions: The beehive rule. In Pollack, J., Bedau, M. A., Husbands, P., Ikegami, T., Watson, R. A., Artificial Life IX: Proceedings of the Ninth International Conference on the Simulation and Synthesis of Living Systems, Boston, USA, 12–15 September 2004, pages 286–291. MIT Press, Cambridge, MA.Google Scholar
  30. Wuensche, A., and Adamatzky, A. (2006). On spiral glider-guns in hexagonal cellular automata: Activator-inhibitor paradigm. International Journal of Modern Physics, 17:1009–1026.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  • Andrew Adamatzky

There are no affiliations available

Personalised recommendations