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Reaction–Diffusion Computing

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Abstract

A reaction–diffusion computer is a spatially extended chemical system, which processes information by transforming an input concentration profile to an output concentration profile in a deterministic and controlled manner. In reaction–diffusion computers, the data are represented by concentration profiles of reagents, information is transferred by propagating diffusive and phase waves, computation is implemented via the interaction of these traveling patterns (diffusive and excitation waves), and the results of the computation are recorded as a final concentration profile. Chemical reaction–diffusion computing is among the leaders in providing experimental prototypes in the fields of unconventional and nature-inspired computing. This chapter provides a case-study introduction to the field of reaction–diffusion computing, and shows how selected problems and tasks of computational geometry, robotics, and logics can be solved by encoding data within transient states of a chemical medium and by programming the dynamics and interactions of chemical waves.

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References

  • Adamatzky A (1994) Reaction-diffusion algorithm for constructing discrete generalized Voronoi diagram. Neural Netw World 6:635–643

    Google Scholar 

  • Adamatzky A (1996) Voronoi-like partition of lattice in cellular automata. Math Comput Modelling 23:51–66

    Article  MathSciNet  MATH  Google Scholar 

  • Adamatzky A (2001) Computing in nonlinear media and automata collectives. IoP Publishing, Bristol

    Book  MATH  Google Scholar 

  • Adamatzky A (ed) (2002) Collision-based computing. Springer, London

    MATH  Google Scholar 

  • Adamatzky A (2004) Collision-based computing in Belousov–Zhabotinsky medium. Chaos Solitons Fractals 21:1259–1264

    Article  MATH  Google Scholar 

  • Adamatzky A, De Lacy Costello BPJ (2002a) Collision-free path planning in the Belousov–Zhabotinsky medium assisted by a cellular automaton. Naturwissenschaften 89:474–478

    Article  Google Scholar 

  • Adamatzky A, De Lacy Costello BPJ (2002b) Experimental logical gates in a reaction-diffusion medium: the XOR gate and beyond. Phys Rev E 66:046112

    Article  Google Scholar 

  • Adamatzky A, De Lacy Costello BPJ (2002c) Experimental reaction-diffusion pre-processor for shape recognition. Phys Lett A 297:344–352

    Article  MATH  Google Scholar 

  • Adamatzky A, De Lacy Costello BPJ (2007) Binary collisions between wave-fragments in a sub-excitable Belousov-Zhabotinsky medium. Chaos Solitons Fractals 34:307–315

    Article  MathSciNet  MATH  Google Scholar 

  • Adamatzky A, Teuscher C (Eds) (2006) From utopian to genuine unconventional computers. Luniver Press, Beckington, UK

    Google Scholar 

  • Adamatzky A, Tolmachiev D (1997) Chemical processor for computation of skeleton of planar shape. Adv Mater Opt Electron 7:135–139

    Article  Google Scholar 

  • Adamatzky A, De Lacy Costello B, Melhuish C, Ratcliffe N (2003) Experimental reaction-diffusion chemical processors for robot path planning. J Intell Robot Syst 37:233–249

    Article  MATH  Google Scholar 

  • Adamatzky A, De Lacy Costello B, Melhuish C, Ratcliffe N (2004) Experimental implementation of mobile robot taxis with onboard Belousov–Zhabotinsky chemical medium. Mater Sci Eng C 24:541–548

    Article  Google Scholar 

  • Adamatzky A, De Lacy Costello B, Skachek S, Melhuish C (2005a) Manipulating objects with chemical waves: open loop case of experimental Belousiv-Zhabotinsky medium. Phys Lett A

    Google Scholar 

  • Adamatzky A, De Lacy Costello B, Asai T (2005b) Reaction diffusion computers. Elsevier, New York

    Google Scholar 

  • Adamatzky A, Bull L, De Lacy Costello B, Stepney S, Teuscher C (eds) (2007) Unconventional computing 2007. Luniver, Beckington, UK

    Google Scholar 

  • Agladze K, Obata S, Yoshikawa K (1995) Phase-shift as a basis of image processing in oscillating chemical medium. Physica D 84:238–245

    Article  Google Scholar 

  • Agladze K, Aliev RR, Yamaguhi T, Yoshikawa K (1996) Chemical diode. J Phys Chem 100:13895–13897

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Akl SG, Calude CS, Dinneen MJ, Rozenberg G (2007) In: Unconventional computation: 6th international conference, Kingston, Canada, August 2007. Lecture notes in computer science, vol 4618

    Google Scholar 

  • Berlekamp ER, Conway JH, Guy RL (1982) Winning ways for your mathematical plays, vol 2. Academic Press, New York

    MATH  Google Scholar 

  • Blum H (1967) A transformation for extracting new descriptors of shape. In: Wathen-Dunn W (ed) Models for the perception of speech and visual form. MIT Press, Cambridge, MA, pp 362–380

    Google Scholar 

  • Blum H (1973) Biological shape and visual science. J Theor Biol 38:205–287

    Article  Google Scholar 

  • Calabi L, Hartnett WE (1968) Shape recognition, prairie fires, convex deficiencies and skeletons. Am Math Mon 75:335–342

    Article  MathSciNet  MATH  Google Scholar 

  • Courant R, Robbins H (1941) What is mathematics? Oxford University Press, New York

    Google Scholar 

  • De Lacy Costello BPJ (2003) Constructive chemical processors – experimental evidence that shows that this class of programmable pattern forming reactions exist at the edge of a highly non-linear region. Int J Bifurcat Chaos 13:1561–1564

    Article  MATH  Google Scholar 

  • De Lacy Costello BPJ, Adamatzky A (2003) On multitasking in parallel chemical processors: experimental findings. Int J Bifurcat Chaos 13:521–533

    Article  MATH  Google Scholar 

  • De Lacy Costello BPJ, Hantz P, Ratcliffe NM (2004b) Voronoi diagrams generated by regressing edges of precipitation fronts. J Chem Phys 120 (5):2413–2416

    Article  Google Scholar 

  • De Lacy Costello BPJ, Adamatzky A, Ratcliffe NM, Zanin A, Purwins HG, Liehr A (2004a) The formation of Voronoi diagrams in chemical and physical systems: experimental findings and theoretical models. Int J Bifurcat Chaos 14(7):2187–2210

    Article  MathSciNet  MATH  Google Scholar 

  • De Lacy Costello B, Toth R, Stone C, Adamatzky A, Bull L (2008) Implementation of glider guns in the light-sensitive Belousov–Zhabotinsky medium. Phys Rev E 79:026114

    Google Scholar 

  • Dupont C, Agladze K, Krinsky V (1998) Excitable medium with left–right symmetry breaking. Physica A 249:47–52

    Article  Google Scholar 

  • Field RJ, Winfree AT (1979) Travelling waves of chemical activity in the Zaikin–Zhabotinsky–Winfree reagent. J Chem Educ 56:754

    Article  Google Scholar 

  • Fredkin F, Toffoli T (1982) Conservative logic. Int J Theor Phys 21:219–253

    Article  MathSciNet  MATH  Google Scholar 

  • Fuerstman MJ, Deschatelets P, Kane R, Schwartz A, Kenis PJA, Deutch JM, Whitesides GM (2003) Langmuir 19:4714

    Article  Google Scholar 

  • Hwang YK, Ahuja N (1992) A potential field approach to path planning. IEEE Trans Robot Autom 8:23–32

    Article  Google Scholar 

  • Gorecka J, Gorecki J (2003) T-shaped coincidence detector as a band filter of chemical signal frequency. Phys Rev E 67:067203

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Gorecki J, Gorecka JN, Yoshikawa K, Igarashi Y, Nagahara H (2005) Phys Rev E 72:046201

    Article  Google Scholar 

  • Ichino T, Igarashi Y, Motoike IN, Yoshikawa K (2003) Different operations on a single circuit: field computation on an excitable chemical system. J Chem Phys 118:8185–8190

    Article  Google Scholar 

  • Klein R (1990) Concrete and abstract Voronoi diagrams. Springer, Berlin

    Google Scholar 

  • Kuhnert L (1986b) Photochemische manipulation von chemischen Wellen. Naturwissenschaften 76:96–97

    Article  Google Scholar 

  • Kuhnert L (1986a) A new photochemical memory device in a light sensitive active medium. Nature 319:393

    Article  Google Scholar 

  • Kuhnert L, Agladze KL, Krinsky VI (1989) Image processing using light-sensitive chemical waves. Nature 337:244–247

    Article  Google Scholar 

  • Kusumi T, Yamaguchi T, Aliev R, Amemiya T, Ohmori T, Hashimoto H, Yoshikawa K (1997) Numerical study on time delay for chemical wave transmission via an inactive gap. Chem Phys Lett 271:355–360

    Article  Google Scholar 

  • Lemmon MD (1991) 2-degree-of-freedom robot path planning using cooperative neural fields. Neural Comput 3:350–362

    Article  Google Scholar 

  • Margolus N (1984) Physics-like models of computation. Physica D 10:81–95

    Article  MathSciNet  Google Scholar 

  • Mills J (2008) The nature of the extended analog computer. In: Teuscher C, Nemenman IM, Alexander FJ (eds) Physica D Special issue: Novel Comput Paradigms Quo Vadis. Physica D 237:1235–1256

    Google Scholar 

  • Motoike IN, Adamatzky A (2004) Three-valued logic gates in reaction-diffusion excitable media. Chaos Solitons Fractals 24:107–114

    MathSciNet  Google Scholar 

  • Motoike IN, Yoshikawa K (1999) Information operations with an excitable field. Phys Rev E 59:5354–5360

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Motoike IN, Yoshikawa K, Iguchi Y, Nakata S (2001) Real-time memory on an excitable field. Phys Rev E 63:036220

    Article  Google Scholar 

  • Nakagaki T, Yamada H, Toth A (2001) Biophys Chem 92:47

    Article  Google Scholar 

  • Rambidi NG (1997) Biomolecular computer: roots and promises. Biosyst 44:1–15

    Article  Google Scholar 

  • Rambidi NG (1998) Neural network devices based on reaction-diffusion media: an approach to artificial retina. Supramol Sci 5:765–767

    Article  Google Scholar 

  • Rambidi NG (2003) 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, MA

    Google Scholar 

  • Rambidi NG, Yakovenchuk D (2001) Chemical reaction-diffusion implementation of finding the shortest paths in a labyrinth. Phys Rev E 63:026607

    Article  Google Scholar 

  • Rambidi NG, Shamayaev KR, Peshkov G Yu (2002) Image processing using light-sensitive chemical waves. Phys Lett A 298:375–382

    Article  Google Scholar 

  • Saltenis V (1999) Simulation of wet film evolution and the Euclidean Steiner problem. Informatica 10:457–466

    MATH  Google Scholar 

  • Sendin̋a-Nadal I, Mihaliuk E, Wang J, Pérez-Mun̋uzuri V, Showalter K (2001) Wave propagation in subexcitable media with periodically modulated excitability. Phys Rev Lett 86:1646–1649

    Article  Google Scholar 

  • Shirakawa T, Adamatzky A, Gunji Y-P, Miyake Y (2009) On simultaneous construction of Voronoi diagram and Delaunay triangulation by Physarum polycephalum. Int J Bifurcat Chaos 19(9):3109–3117

    Google Scholar 

  • Sielewiesiuk J, Gorecki J (2001) Logical functions of a cross junction of excitable chemical media. J Phys Chem A 105:8189–8195

    Article  Google Scholar 

  • Sienko T, Adamatzky A, Rambidi N, Conrad M (eds) (2003) Molecular computing. MIT Press, Cambridge, MA

    MATH  Google Scholar 

  • Skachek S, Adamatzky A, Melhuish C (2005) Manipulating objects by discrete excitable media coupled with contact-less actuator array: open-loop case. Chaos Solitons Fractals 26:1377–1389

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Steinbock O, Kettunen P, Showalter K (1996) J Phys Chem 100(49):18970

    Article  Google Scholar 

  • Tolmachiev D, Adamatzky A (1996) Chemical processor for computation of Voronoi diagram. Adv Mater Opt Electron 6:191–196

    Article  Google Scholar 

  • Toth R, Stone C, Adamatzky A, de Lacy Costello B, Bull L (2009) Experimental validation of binary collisions between wave-fragments in the photosensitive Belousov-Zhabotinsky reaction. Chaos Solitons Fractals 41(4):1605–1615

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Yokoi H, Adamatzky A, De Lacy Costello B, Melhuish C (2004) Excitable chemical medium controlled by a robotic hand: closed loop experiments. Int J Bifurcat Chaos 14:3347–3354

    Article  MATH  Google Scholar 

  • Zaikin AN, Zhabotinsky AM (1970) Concentration wave propagation in two-dimensional liquid-phase self-oscillating system. Nature 225:535

    Article  Google Scholar 

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Adamatzky, A., Costello, B.D. (2012). Reaction–Diffusion Computing. In: Rozenberg, G., Bäck, T., Kok, J.N. (eds) Handbook of Natural Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92910-9_56

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