No Access

ON SPIRAL GLIDER-GUNS IN HEXAGONAL CELLULAR AUTOMATA: ACTIVATOR-INHIBITOR PARADIGM

ANDREW WUENSCHE

Discrete Dynamics Lab, Flat 6, 3 Grape Street, London WC2 H8DX, UK

Search for more papers by this author

and

ANDREW ADAMATZKY

Faculty of Computing, Engineering and Mathematical Sciences, University of the West of England, Bristol BS16 1QY, UK

Search for more papers by this author

https://doi.org/10.1142/S012918310600945XCited by:23 (Source: Crossref)

Abstract

We present a cellular-automaton model of a reaction-diffusion excitable system with concentration dependent inhibition of the activator, and study the dynamics of mobile localizations (gliders) and their generators. We analyze a three-state totalistic cellular automaton on a two-dimensional lattice with hexagonal tiling, where each cell connects with 6 others. We show that a set of specific rules support spiral glider-guns (rotating activator-inhibitor spirals emitting mobile localizations) and stationary localizations which destroy or modify gliders, along with a rich diversity of emergent structures with computational properties. We describe how structures are created and annihilated by glider collisions, and begin to explore the necessary processes that generate this kind of complex dynamics.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

A. Adamatzky , B. De Lacy Costello and T. Asai , Reaction-Diffusion Computers ( Elsevier , 2005 ) . Google Scholar
A. Adamatzky (ed.) , Collision-Based Computing ( Springer-Verlag , 2003 ) . Google Scholar
A. Adamatzky, A. Wuensche and B. De Lacy Costello, Chaos, Solitons & Fractals 27, 287 (2006), DOI: 10.1016/j.chaos.2005.03.048. Web of Science, ADS, Google Scholar
M. Bär and L. Brusch, New J. Phys. 6, 5 (2004), DOI: 10.1088/1367-2630/6/1/005. Web of Science, Google Scholar
M. Bodeet al., Physica D 161, 45 (2000), DOI: 10.1016/S0167-2789(01)00360-8. Web of Science, ADS, Google Scholar
M. Gerhardt, H. Schuster and J. J. Tyson, Physica D 46, 392 (1990), DOI: 10.1016/0167-2789(90)90101-T. Web of Science, ADS, Google Scholar
H. Hartman and P. Tamayo, Physica D 45, 293 (1990), DOI: 10.1016/0167-2789(90)90190-Z. Web of Science, ADS, Google Scholar
E. Bilotta, A. Lafusa and P. Pantano, Artificial Life VIII (MIT Press, 2003) p. 38. Google Scholar
J. H. Conway , Winning Ways for Your Mathematical Plays 2 , eds. E. Berlekamp , J. H. Conway and R. Guy ( Academic Press , 1982 ) . Google Scholar
B. Chopard and M. Droz , Cellular Automata Modeling of Physical Systems ( Cambridge University Press , 2005 ) . Google Scholar
G. Gáspár and K. Showalter, J. Am. Chem. Soc. 109, 4869 (1987), DOI: 10.1021/ja00250a019. Web of Science, Google Scholar
A. Ilachinski , Cellular Automata: A Discrete Universe ( World Scientific , 2001 ) . Link, Google Scholar
Q. Ouyang, H. L. Swinney and G. Li, Phys. Rev. Lett. 84, 1047 (2000), DOI: 10.1103/PhysRevLett.84.1047. Web of Science, Google Scholar
I. Sediña-Nadalet al., Phys. Rev. Lett. 86, 1646 (2001), DOI: 10.1103/PhysRevLett.86.1646. Web of Science, ADS, Google Scholar
T. Toffoli and M. Margolus , Cellular Automata Machines ( The MIT Press , 1987 ) . Google Scholar
J. R. Weimar , Simulation with Cellular Automata ( Logos-Verlag , 1998 ) . Google Scholar
A. Wuensche, Complexity 4, 47 (1999), DOI: 10.1002/(SICI)1099-0526(199901/02)4:3<47::AID-CPLX9>3.0.CO;2-V. Google Scholar
A. Wuensche, Discrete Dynamics Lab (DDLab), www.ddlab.org (2005), also follow the links to "spiral-rule" and "self-reproduction" . Google Scholar
A. Wuensche, Int. J. Unconventional Comput. 1, (2005). Google Scholar
S. Yaguma, K. Odagiri and K. Takatsuka, Physica D 197, 34 (2004), DOI: 10.1016/j.physd.2004.06.010. Web of Science, ADS, Google Scholar
X. Yang, Appl. Mathem. Modelling 30, 200 (2006), DOI: 10.1016/j.apm.2005.03.013. Web of Science, Google Scholar
X. Yang, Parallel Comput. 30, 741 (2004), DOI: 10.1016/j.parco.2003.12.013. Web of Science, Google Scholar
D. Young, Math. Biosci. 72, 51 (1984), DOI: 10.1016/0025-5564(84)90060-9. Web of Science, Google Scholar