Glossary
- Belousov–Zhabotinsky (BZ) reaction :
-
is a term applied to a group of chemical reactions in which an organic substrate (typically malonic acid) is oxidized by bromate ions in the presence of acid and a one electron transfer redox catalyst (e.g., ferroin, or the light-sensitive ruthenium complex). During the BZ reaction, there are three major interlinked processes – firstly the reduction of the inhibitor (bromideions) via reaction with bromate ions, secondly autocatalysis in bromous acid and the oxidation of the redox catalyst, and finally reduction of the redox catalyst and production of the inhibitor (bromide ions) via a reaction with the organic substrate and its brominated derivative. The reaction produces oscillations in well-stirred reactors and traveling waves in thin layers, which may be visualized if the redox behavior of the catalyst is accompanied by a change of color (e.g., the color is changed from orange to blue when ferroin is oxidized to ferriin).
...
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
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 Model 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 (2015) Binary full adder, made of fusion gates, in a subexcitable Belousov-Zhabotinsky system. Phys Rev E 92(3):032811
Adamatzky A, De Lacy Costello BPJ (2002a) Experimental logical gates in a reaction-diffusion medium: the XOR gate and beyond. Phys Rev E 66:046112
Adamatzky A, De Lacy Costello B (2002b) Experimental reaction-diffusion pre-processor for shape recognition. Phys Lett A 297:344–352
Adamatzky A, De Lacy Costello BPJ (2002c) Collision-free path planning in the Belousov–Zhabotinsky medium assisted by a cellular automaton. Naturwissenschaften 89:474–478
Adamatzky A, De Lacy Costello B (2007) Binary collisions between wave-fragments in a subexcitable Belousov-Zhabotinsky medium. Chaos Solitons Fractals 34:307–315
Adamatzky A, Teuscher C (eds) (2006) From Utopian to genuine unconventional computers. Luniver Press, Beckington
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, Asai T (2005) Reaction diffusion computers. Elsevier, Amsterdam
Adamatzky A, de Lacy Costello B, Skachek S, Melhuish C (2006) Manipulating objects with chemical waves: open loop case of experimental Belousov–Zhabotinsky medium coupled with simulated actuator array. Phys Lett A 350(3):201–209
Adamatzky A, Bull L, De Lacy Costello B, Stepney S, Teuscher C (eds) (2007) Unconventional computing 2007. Luniver Press, Beckington
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 (eds) (2007) Unconventional computation: 6th international conference, UC 2007, Kingston, 13–17 Aug 2007, Proceedings. Springer
Berlekamp ER, Conway JH, Guy RL (1982) Winning ways for your mathematical plays, vol 2. Academic Press, New York
Blum HA (1967) 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, Oxford
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 B, 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 (2004a) 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 (2004b) 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 (2009) Implementation of glider guns in the light-sensitive Belousov-Zhabotinsky medium. Phys Rev E 79(2):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
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
Hwang YK, Ahuja N (1992) A potential field approach to path planning. IEEE Trans Robot Autom 8:23–32
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 (1986a) Photochemische Manipulation von chemischen Wellen. Naturwissenschaften 76:96–97
Kuhnert L (1986b) 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 JW (2008) The nature of the extended analog computer. Physica D 237(9):1235–1256
Motoike IN, Adamatzky A (2004) Three-valued logic gates in reaction-diffusion excitable media. Chaos Solitons Fractals 24:107–114
Motoike I, 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, Tóth A (2001) Biophys Chem 92:47
Rambidi NG (1997) Biomolecular computer: roots and promises. Biosystems 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 N (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 GY (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
Sendiña-Nadal I, Mihaliuk E, Wang J, Pérez-Muñuzuri V, Showalter K (2001) Wave propagation in subexcitable media with periodically modulated excitability. Phys Rev Lett 86:1646–1649
Shirakawa T, Adamatzky A, Gunji YP, 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) Chemical wave logic gates. 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
Tóth A, Showalter K (1995) Logic gates in excitable media. J Chem Phys 103:2058–2066
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
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
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Science+Business Media, LLC, part of Springer Nature
About this entry
Cite this entry
Adamatzky, A., De Lacy Costello, B. (2018). Reaction-Diffusion Computing. In: Adamatzky, A. (eds) Unconventional Computing. Encyclopedia of Complexity and Systems Science Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6883-1_446
Download citation
DOI: https://doi.org/10.1007/978-1-4939-6883-1_446
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-6882-4
Online ISBN: 978-1-4939-6883-1
eBook Packages: Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics