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2019 | OriginalPaper | Chapter

New Three-Chemical Polynomial Reaction-Diffusion Equations

Authors : Do-yeon Han, Byungmoon Kim, Oh-young Song

Published in: Advances in Computer Graphics

Publisher: Springer International Publishing

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Abstract

Reaction-diffusion (RD) generates time-varying patterns or noises, used to create beautiful patterned or noisy variations in colors, bumps, flow details, or other parameters. RD can be relatively easily solved on various domains: image, curved surface, and volumetric domains, making their applications popular. Being widely available, most of the patterns from known RD have been well explored. In this paper, we move on this field, by providing a large number of new reaction equations. Among the vast space of new equations, we focus on three-chemical polynomial reactions as the three chemicals can be easily mapped to any colors. We propose a set of new equations that generate new time-varying patterns.

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For the results of Gierer-Meinhardt, refer https://imc.zih.tu-dresden.de/wiki/morpheus/doku.php?id=examples:reaction-diffusion.

For the results of Belousov-Zhabotinsky, refer https://en.wikipedia.org/wiki/Belousov-Zhabotinsky_reaction, https://scipython.com/blog/simulating-the-belousov-zhabotinsky-reaction/.

These PDE’s correspond to the additive color mixing. Of course, arbitrary color states and the subtractive color mixing can be applicable.

Acton, S.T., Mukherjee, D.P., Havlicek, J.P., Bovik, A.C.: Oriented texture completion by AM-FM reaction-diffusion. IEEE Trans. Image Process. 10(6), 885–896 (2001)CrossRef

Barkley, D.: A model for fast computer simulation of waves in excitable media. Physica D: Nonlinear Phenom. 49(1–2), 61–70 (1991)CrossRef

Belousov, B.P.: Radiates. Med. 145 (1959)

Chen, Y., Pock, T.: Trainable nonlinear reaction diffusion: a flexible framework for fast and effective image restoration. IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1256–1272 (2017)CrossRef

Cottet, G.H., Germain, L.: Image processing through reaction combined with nonlinear diffusion. Math. Comput. 61, 659–673 (1993)MathSciNetCrossRef

FitzHugh, R.: Mathematical Models of Excitation and Propagation in Nerve. Publisher Unknown (1966)

Gierer, A., Meinhardt, H.: A theory of biological pattern formation. Biol. Cyberne. 12(1), 30–39 (1972)MATH

Tim, H., Munafo, R., Trevorrow, A., Rokicki, T., Wills, D.: Ready, a cross-platform implementation of various reaction-diffusion systems (2012). https://github.com/GollyGang/ready

Kindlmann, G., Weinstein, D., Hart, D.: Strategies for direct volume rendering of diffusion tensor fields. IEEE Trans. Visual. Comput. Graph. 6(2), 124–138 (2000)CrossRef

10.

Kondo, S., Miura, T.: Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329(5999), 1616–1620 (2010)MathSciNetCrossRef

11.

Lo, K.Y., Li, H., Fu, C.W., Wong, T.T.: Interactive reaction-diffusion on surface tiles. In: 15th Pacific Conference on Computer Graphics and Applications, PG 2007, pp. 65–74. IEEE (2007)

12.

Malevanets, A., Kapral, R.: Microscopic model for Fitzhugh-Nagumo dynamics. Phys. Rev. E 55(5), 5657 (1997)CrossRef

13.

Meinhardt, H.: Models of Biological Pattern Formation. Academic Press, Cambridge (1982)

14.

Murray, J.: Mathematical Biology II: Spatial Models and Biochemical Applications, vol. II. Springer, New York (2003). https://doi.org/10.1007/b98869CrossRef

15.

Gray, P., Scott, S.K.: Autocatalytic reactions in the isothermal, continuous stirred tank reactor: isolas and other forms of multistability. Chem. Eng. Sci. 38(1), 29–43 (1983)CrossRef

16.

Pena, B., Perez-Garcia, C.: Stability of Turing patterns in the Brusselator model. Phys. Rev.E 64(5), 056213 (2001)MathSciNetCrossRef

17.

Sanderson, A.R., Johnson, C.R., Kirby, R.M.: Display of vector fields using a reaction-diffusion model. In: Proceedings of the Conference on Visualization 2004, pp. 115–122. IEEE Computer Society (2004)

18.

Sims, K.: Interactive evolution of dynamical systems. In: Toward a Practice of Autonomous Systems: Proceedings of the First European Conference on Artificial Life, pp. 171–178 (1992)

19.

Turing, A.M.: The chemical basis of morphogenesis. Philos. Trans. Roy. Soc. Lond. B: Biol. Sci. 237(641), 37–72 (1952)MathSciNetCrossRef

20.

Turk, G.: Generating textures on arbitrary surfaces using reaction-diffusion. ACM SIGGRAPH Comput. Graph. 25, 289–298 (1991)CrossRef

21.

Walter, M., Fournier, A., Reimers, M.: Clonal mosaic model for the synthesis of mammalian coat patterns. Graph. Interface 98, 82–91 (1998)

22.

Witkin, A., Kass, M.: Reaction-diffusion textures. ACM SIGGRAPH Comput. Graph. 25(4), 299–308 (1991)CrossRef

23.

Yang, L., Epstein, I.R.: Oscillatory turing patterns in reaction-diffusion systems with two coupled layers. Phys. Rev. Lett. 90(17), 178303 (2003)CrossRef

24.

Zhabotinsky, A.M.: Dokl. Akad. Nauk SSSR 157. 392 (1964)

Title: New Three-Chemical Polynomial Reaction-Diffusion Equations
Authors: Do-yeon Han
Byungmoon Kim
Oh-young Song
Publisher: Springer International Publishing
Book: Advances in Computer Graphics
Print ISBN: 978-3-030-22513-1

Electronic ISBN: 978-3-030-22514-8

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-22514-8_32

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