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Morphonomy of collision-based gates realized in molecular arrays

Andrew Adamatzky*

Intelligent Autonomous Systems Lab University of the West of England,
Bristol, United Kingdom

This is an abstract for a presentation given at the
Eighth Foresight Conference on Molecular Nanotechnology.
There will be a link from here to the full article when it is available on the web.

 

A dynamical computation universality, which is dealt with in the paper, employs an architecture-less collison-based approache. Autonomous signals travel in a uniform space and perform computation by colliding with other travelling signals. Truth-values are represented by either absence or presence of information quanta or by various states of the quanta. Three key stones might be put in a basis of collision-based computing: proof of universality of Game of Life via collision of glider streams [1], construction of billiard ball model in the context of the conservative logic [2] and development of a concept of computation in cellular automata with soliton-like patterns [3]. These ideas are evolved to a theory of dynamical computing in excitable lattices, which is developed in [4].

The paper explores material basis of dynamical universal computing in non-linear media and varieties of collision based gates. The interactions of mobile self-localizations in DNA molecules, monomolecular arrays of Scheibe aggregates and tubulin arrays of microtubules are discussed in the context of existence and morphonomy of collision-based logical gates.

The first part of the paper deals with breather collision-based gates that can be implemented in a DNA molecule. Basing on numerical results of [5] we construct a catalogue of logical gates that are realized in collisions between breathers and impurities in the DNA molecule. The findings are discussed in the context of particle machines [6] and filtrons [7]. In the second part we speculate about collisions of excitons in monomolecular arrays of Scheibe aggregates [8]. We also set up analogies between cellular automata models of excitable media [4] and excitable monomolecular arrays. The third part of the paper discovers a possibility for collision-based computing in microtubules, where quanta of information are represented by either finite groups of antialigned dipoles [9] or solitons [10].

References

  1. Berlekamp E., Conway J. And Guy R. Winning way, vol. 2 (NY: Academic Press, 1982)
  2. Fredkin E. and Toffoli T. Int. J. Theor. Phys. 21 (1982) 219 - 253.
  3. Steiglitz K., Kamal I. and Watson A. IEEE Trans. on Computers 37 (1988) 138 - 145.
  4. Adamatzky A. Int. J. Theor. Phys. 37 (1998) 3069 - 3108.
  5. Forinash K., Peyrard M. and Malomed B. Phys. Review E 49 (1994) 3400 - 3411.
  6. Jakubowski M.H., Steiglitz K. And Squier R. Phys. Review 58 (1998) 6752 - 6758.
  7. Siwak P. Int. J. General Systems 27 (1998) 181 - 229.
  8. Moebius D. and Kuhn H. J. Appl. Phys. 64 (1979) 5138 - 5141.
  9. Brown J.A. and Tuszynski J.A. Phys. Review E 56 (1997) 5834 - 5839.
  10. Trpisova B. and Tuszynski J.A. Phys. Review E 55 (1997) 3288 - 3305.

*Corresponding Address:
Andrew Adamatzky
Intelligent Autonomous Systems Lab
University of the West of England
DuPont Building, Frenchay Campus, Coldharbour Lane
Bristol, BS16 1QY United Kingdom
E-mail: Andrew.Adamatzky@uwe.ac.uk
Web: http://www.ias.uwe.ac.uk/~a-adamat/



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