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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Adamatzky A (1994) Reaction-diffusion algorithm for constructing discrete generalized Voronoi diagram. Neural Netw World 6:635–643
Adamatzky A (1996) Voronoi-like partition of lattice in cellular automata. Math Comput Modelling 23:51–66
Adamatzky A (2001) Computing in nonlinear media and automata collectives. IoP Publishing, Bristol
Adamatzky A (ed) (2002) Collision-based computing. Springer, London
Adamatzky A (2004) Collision-based computing in Belousov–Zhabotinsky medium. Chaos Solitons Fractals 21:1259–1264
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
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
Adamatzky A, De Lacy Costello BPJ (2002c) Experimental reaction-diffusion pre-processor for shape recognition. Phys Lett A 297:344–352
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
Adamatzky A, Teuscher C (Eds) (2006) From utopian to genuine unconventional computers. Luniver Press, Beckington, UK
Adamatzky A, Tolmachiev D (1997) Chemical processor for computation of skeleton of planar shape. Adv Mater Opt Electron 7:135–139
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
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
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
Adamatzky A, De Lacy Costello B, Asai T (2005b) Reaction diffusion computers. Elsevier, New York
Adamatzky A, Bull L, De Lacy Costello B, Stepney S, Teuscher C (eds) (2007) Unconventional computing 2007. Luniver, Beckington, UK
Agladze K, Obata S, Yoshikawa K (1995) Phase-shift as a basis of image processing in oscillating chemical medium. Physica D 84:238–245
Agladze K, Aliev RR, Yamaguhi T, Yoshikawa K (1996) Chemical diode. J Phys Chem 100:13895–13897
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
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
Berlekamp ER, Conway JH, Guy RL (1982) Winning ways for your mathematical plays, vol 2. Academic Press, New York
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
Blum H (1973) Biological shape and visual science. J Theor Biol 38:205–287
Calabi L, Hartnett WE (1968) Shape recognition, prairie fires, convex deficiencies and skeletons. Am Math Mon 75:335–342
Courant R, Robbins H (1941) What is mathematics? Oxford University Press, New York
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
De Lacy Costello BPJ, Adamatzky A (2003) On multitasking in parallel chemical processors: experimental findings. Int J Bifurcat Chaos 13:521–533
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
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
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
Dupont C, Agladze K, Krinsky V (1998) Excitable medium with left–right symmetry breaking. Physica A 249:47–52
Field RJ, Winfree AT (1979) Travelling waves of chemical activity in the Zaikin–Zhabotinsky–Winfree reagent. J Chem Educ 56:754
Fredkin F, Toffoli T (1982) Conservative logic. Int J Theor Phys 21:219–253
Fuerstman MJ, Deschatelets P, Kane R, Schwartz A, Kenis PJA, Deutch JM, Whitesides GM (2003) Langmuir 19:4714
Hwang YK, Ahuja N (1992) A potential field approach to path planning. IEEE Trans Robot Autom 8:23–32
Gorecka J, Gorecki J (2003) T-shaped coincidence detector as a band filter of chemical signal frequency. Phys Rev E 67:067203
Gorecki J, Yoshikawa K, Igarashi Y (2003) On chemical reactors that can count. J Phys Chem A 107: 1664–1669
Gorecki J, Gorecka JN, Yoshikawa K, Igarashi Y, Nagahara H (2005) Phys Rev E 72:046201
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
Klein R (1990) Concrete and abstract Voronoi diagrams. Springer, Berlin
Kuhnert L (1986b) Photochemische manipulation von chemischen Wellen. Naturwissenschaften 76:96–97
Kuhnert L (1986a) A new photochemical memory device in a light sensitive active medium. Nature 319:393
Kuhnert L, Agladze KL, Krinsky VI (1989) Image processing using light-sensitive chemical waves. Nature 337:244–247
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
Lemmon MD (1991) 2-degree-of-freedom robot path planning using cooperative neural fields. Neural Comput 3:350–362
Margolus N (1984) Physics-like models of computation. Physica D 10:81–95
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
Motoike IN, Adamatzky A (2004) Three-valued logic gates in reaction-diffusion excitable media. Chaos Solitons Fractals 24:107–114
Motoike IN, Yoshikawa K (1999) Information operations with an excitable field. Phys Rev E 59:5354–5360
Motoike IN, Yoshikawa K (2003) Information operations with multiple pulses on an excitable field. Chaos Solitons Fractals 17:455–461
Motoike IN, Yoshikawa K, Iguchi Y, Nakata S (2001) Real-time memory on an excitable field. Phys Rev E 63:036220
Nakagaki T, Yamada H, Toth A (2001) Biophys Chem 92:47
Rambidi NG (1997) Biomolecular computer: roots and promises. Biosyst 44:1–15
Rambidi NG (1998) Neural network devices based on reaction-diffusion media: an approach to artificial retina. Supramol Sci 5:765–767
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
Rambidi NG, Yakovenchuk D (2001) Chemical reaction-diffusion implementation of finding the shortest paths in a labyrinth. Phys Rev E 63:026607
Rambidi NG, Shamayaev KR, Peshkov G Yu (2002) Image processing using light-sensitive chemical waves. Phys Lett A 298:375–382
Saltenis V (1999) Simulation of wet film evolution and the Euclidean Steiner problem. Informatica 10:457–466
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
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
Sielewiesiuk J, Gorecki J (2001) Logical functions of a cross junction of excitable chemical media. J Phys Chem A 105:8189–8195
Sienko T, Adamatzky A, Rambidi N, Conrad M (eds) (2003) Molecular computing. MIT Press, Cambridge, MA
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
Steinbock O, Tóth A, Showalter K (1995) Navigating complex labyrinths: optimal paths from chemical waves. Science 267:868–871
Steinbock O, Kettunen P, Showalter K (1996) J Phys Chem 100(49):18970
Tolmachiev D, Adamatzky A (1996) Chemical processor for computation of Voronoi diagram. Adv Mater Opt Electron 6:191–196
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
Tóth A, Showalter K (1995) Logic gates in excitable media. J Chem Phys 103:2058–2066
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
Zaikin AN, Zhabotinsky AM (1970) Concentration wave propagation in two-dimensional liquid-phase self-oscillating system. Nature 225:535
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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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DOI: https://doi.org/10.1007/978-3-540-92910-9_56
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