Skip to main content
SpringerLink
Log in

Programming Reaction-Diffusion Processors

  • Conference paper
Unconventional Programming Paradigms (UPP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3566))

Included in the following conference series:

Abstract

In reaction-diffusion (RD) processors, both the data and the results of the computation are encoded as concentration profiles of the reagents. The computation is performed via the spreading and interaction of wave fronts. Most prototypes of RD computers are specialized to solve certain problems, they can not be, in general, re-programmed. In the paper, we try to show possible means of overcoming this drawback. We envisage an architecture and interface of programmable RD media capable of solving a wide range of problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adamatzky, A.: Reaction-diffusion and excitable processors: a sense of the unconventional. Parallel and Distributed Computing 3, 113–132 (2000)

    Google Scholar 

  2. Adamatzky, A.: Computing in Nonlinear Media and Automata Collectives. Institute of Physics Publishing (2001)

    Google Scholar 

  3. Adamatzky, A., De Lacy Costello, B., Ratcliffe, N.M.: Experimental reaction-diffusion pre-processor for shape recognition. Physics Letters A 297, 344–352 (2002)

    Article  MATH  Google Scholar 

  4. Adamatzky, A., De Lacy Costello, B.P.J.: Experimental logical gates in a reaction-diffusion medium: The XOR gate and beyond. Phys. Rev. E 66, 046112 (2002)

    Article  Google Scholar 

  5. Adamatzky, A., De Lacy Costello, B.P.J.: On some limitations of reaction-diffusion computers in relation to Voronoi diagram and its inversion. Physics Letters A 309, 397–406 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Adamatzky, A., De Lacy Costello, B.P.J.: Reaction-diffusion path planning in a hybrid chemical and cellular-automaton processor. Chaos, Solitons & Fractals 16, 727–736 (2003)

    Article  Google Scholar 

  7. Adamatzky, A., De Lacy Costello, B., Melhuish, C., Ratcliffe, N.: Experimental reaction-diffusion chemical processors for robot path planning. J. Intelligent & Robotic Systems 37, 233–249 (2003)

    Article  MATH  Google Scholar 

  8. Adamatzky, A.: Computing with waves in chemical media: massively parallel reaction-diffusion processors. IEICE Trans (2004) (in press)

    Google Scholar 

  9. Adamatzky, A.: Collision-based computing in BelousovZhabotinsky medium. Chaos, Solitons & Fractals 21, 1259–1264 (2004)

    Article  MATH  Google Scholar 

  10. Adamatzky, A., Arena, P., Basile, A., Carmona-Galan, R., De Lacy Costello, B., Fortuna, L., Frasca, M., Rodriguez-Vazquez, A.: Reaction-diffusion navigation robot control: from chemical to VLSI analogic processors. IEEE Trans. Circuits and Systems I 51, 926–938 (2004)

    Article  Google Scholar 

  11. Adamatzky, A., Motoike, I.: Three-valued logic gates in excitable media (2004) (in preparation)

    Google Scholar 

  12. Agladze, K., Magome, N., Aliev, R., Yamaguchi, T., Yoshikawa, K.: Finding the optimal path with the aid of chemical wave. Physica D 106, 247–254 (1997)

    Article  Google Scholar 

  13. Asai, T., Kato, H., Amemiya, Y.: Analog CMOS implementation of diffusive Lotka-Volterra neural networks. In: INNS-IEEE Int. Joint Conf. on Neural Networks, P-90, Washington DC, USA, July 15–19 (2001)

    Google Scholar 

  14. Asai, T., Nishimiya, Y., Amemiya, Y.: A CMOS reaction-diffusion circuit based on cellular-automaton processing emulating the Belousov-Zhabotinsky reaction. IEICE Trans. on Fundamentals of Electronics, Communications and Computer E85-A, 2093–2096 (2002)

    Google Scholar 

  15. Asai, T., Amemiya, Y.: Biomorphic analog circuits based on reaction-diffusion systems. In: Proc. 33rd Int. Symp. on Multiple-Valued Logic, Tokyo, Japan, May 16-19, 2003, pp. 197–204 (2003)

    Google Scholar 

  16. Asai, T., Adamatzky, A., Amemiya, Y.: Towards reaction-diffusion semiconductor computing devices based on minority-carrier transport. Chaos, Solitons & Fractals 20, 863–876 (2004)

    Article  MATH  Google Scholar 

  17. Beato, V., Engel, H.: Pulse propagation in a model for the photosensitive Belousov-Zhabotinsky reaction with external noise. In: Noise in Complex Systems and Stochastic Dynamics. In: Schimansky-Geier, L., Abbott, D., Neiman, A., Van den Broeck, C. (eds.) Proc. SPIE, vol. 5114, pp. 353–362 (2003)

    Google Scholar 

  18. Bouzat, S., Wio, H.S.: Pattern dynamics in inhomogeneous active media. Physica A 293, 405–420 (2001)

    Article  MATH  Google Scholar 

  19. Brandtstädter, H., Braune, M., Schebesch, I., Engel, H.: Experimental study of the dynamics of spiral pairs in light-sensitive BelousovZhabotinskii media using an open-gel reactor. Chem. Phys. Lett. 323, 145–154 (2000)

    Article  Google Scholar 

  20. Chua, L.O.: CNN: A Paradigm for Complexity. World Scientific Publishing, Singapore (1998)

    Book  MATH  Google Scholar 

  21. Chua, L.O., Roska, T.: Cellular Neural Networks and Visual Computing: Foundations and Applications. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  22. De Kepper, P., Dulos, E., Boissonade, J., De Wit, A., Dewel, G., Borckmans, P.: Reaction-diffusion patterns in confined chemical systems. J. Stat. Phys. 101, 495–508 (2000)

    Article  MATH  Google Scholar 

  23. Feeney, R., Schmidt, S.L., Ortoleva, P.: Experiments of electric field-BZ chemical wave interactions: annihilation and the crescent wave. Physica D 2, 536–544 (1981)

    Article  MathSciNet  Google Scholar 

  24. Gorecki, J., Yoshikawa, K., Igarashi, Y.: On chemical reactors that can count. J. Phys. Chem. A 107, 1664–1669 (2003)

    Article  Google Scholar 

  25. Grill, S., Zykov, V.S., Müller, S.C.: Spiral wave dynamics under pulsatory modulation of excitability. J. Phys. Chem. 100, 19082–19088 (1996)

    Article  Google Scholar 

  26. Kastánek, P., Kosek, J., Snita, D., Schreiber, I., Marek, M.: Reduction waves in the BZ reaction: Circles, spirals and effects of electric field. Physica D 84, 79–94 (1995)

    Article  Google Scholar 

  27. Kuhnert, L.: Photochemische Manipulation von chemischen Wellen. Naturwissenschaften 76, 96–97 (1986)

    Article  Google Scholar 

  28. Kuhnert, L., Agladze, K.L., Krinsky, V.I.: Image processing using light–sensitive chemical waves. Nature 337, 244–247 (1989)

    Article  Google Scholar 

  29. Masia, M., Marchettini, N., Zambranoa, V., Rustici, M.: Effect of temperature in a closed unstirred Belousov-Zhabotinsky system. Chem. Phys. Lett. 341, 285–291 (2001)

    Article  Google Scholar 

  30. Motoike, I.N., Yoshikawa, K.: Information operations with multiple pulses on an excitable field. Chaos, Solitons & Fractals 17, 455–461 (2003)

    Article  Google Scholar 

  31. Muenster, A.F., Watzl, M., Schneider, F.W.: Two-dimensional Turing-like patterns in the PA-MBO-system and effects of an electric field. Physica Scripta T67, 58–62 (1996)

    Article  Google Scholar 

  32. Muñuzuri, A.P., Davydov, V.A., Pérez-Muñuzuri, V., Gómez-Gesteira, M., Pérez-Villar, V.: General properties of the electric-field-induced vortex drift in excitable media. Chaos, Solitons, & Fractals 7, 585–595 (1996)

    Article  Google Scholar 

  33. Ortoleva, P.: Chemical wave-electrical field interaction phenomena. Physica D 26, 67–84 (1987)

    Article  MATH  Google Scholar 

  34. Rambidi, N.G., Yakovenchuck, D.: Finding path in a labyrinth based on reaction–diffusion media. Adv. Materials for Optics and Electron. 7, 67–72 (1999)

    Google Scholar 

  35. Rambidi, N.: Chemical-based computing and problems of high computational complexity: The reaction-diffusion paradigm. In: Seinko, T., Adamatzky, A., Rambidi, N., Conrad, M. (eds.) Molecular Computing. MIT Press, Cambridge (2003)

    Google Scholar 

  36. Sakurai, T., Miike, H., Yokoyama, E., Muller, S.C.: Initiation front and annihilation center of convection waves developing in spiral structures of Belousov-Zhabotinsky reaction. J. Phys. Soc. Japan 66, 518–521 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  37. Schebesch, I., Engel, H.: Wave propagation in heterogeneous excitable media. Phys. Rev. E 57, 3905–3910 (1998)

    Article  Google Scholar 

  38. Seipel, M., Schneider, F.W., Mnster, A.F.: Control and coupling of spiral waves in excitable media. Faraday Discussions 120, 395–405 (2001)

    Article  Google Scholar 

  39. Sielewiesiuka, J., Górecki, J.: On the response of simple reactors to regular trains of pulses. Phys. Chem. Chem. Phys. 4, 1326–1333 (2002)

    Article  Google Scholar 

  40. Sevćikova, H., Marek, M.: Chemical waves in electric field. Physica D 9, 140–156 (1983)

    Article  Google Scholar 

  41. Sevćikova, H., Marek, M.: Chemical front waves in an electric field. Physica D 13, 379–386 (1984)

    Article  Google Scholar 

  42. Steinbock, O., Schutze, J., Muller, S.C.: Electric-field-induced drift and deformation of spiral waves in an excitable medium. Phys. Rev. Lett. 68, 248–251 (1992)

    Article  Google Scholar 

  43. Steinbock, O., Tóth, A., Showalter, K.: Navigating complex labyrinths: optimal paths from chemical waves. Science 267, 868–871 (1995)

    Article  Google Scholar 

  44. Tabata, O., Hirasawa, H., Aoki, S., Yoshida, R., Kokufuta, E.: Ciliary motion actuator using selfoscillating gel. Sensors and Actuators A 95, 234–238 (2002)

    Article  Google Scholar 

  45. Tóth, A., Showalter, K.: Logic gates in excitable media. J. Chem. Phys. 103, 2058–2066 (1995)

    Article  Google Scholar 

  46. Wang, J.: Light-induced pattern formation in the excitable Belousov-Zhabotinsky medium. Chem. Phys. Lett. 339, 357–361 (2001)

    Article  Google Scholar 

  47. Yoneyama, M.: Optical modification of wave dynamics in a surface layer of the Mn-catalyzed Belousov-Zhabotinsky reaction. Chem. Phys. Lett. 254, 191–196 (1996)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Computing, Engineering and Mathematics, University of the West of England, UK

    Andrew Adamatzky

Authors
  1. Andrew Adamatzky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Université de Rennes I and INRIA/IRISA, Campus de Beaulieu, 35042, Rennes Cedex, France

    Jean-Pierre Banâtre

  2. INRIA Rhône-Alpes - POP ART project, 655 avenue de l’Europe, 38330, Montbonnot, France

    Pascal Fradet

  3. LaMI UMR 8042 CNRS – Université d’Evry, Genopole, 523 place des Terrasses de l’Agora, 91000, Evry, France

    Jean-Louis Giavitto  & Olivier Michel  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Adamatzky, A. (2005). Programming Reaction-Diffusion Processors. In: Banâtre, JP., Fradet, P., Giavitto, JL., Michel, O. (eds) Unconventional Programming Paradigms. UPP 2004. Lecture Notes in Computer Science, vol 3566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527800_3

Download citation

  • DOI: https://doi.org/10.1007/11527800_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27884-9

  • Online ISBN: 978-3-540-31482-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation