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.
“This research was supported by the MSIP (Ministry of Science, ICT & Future Planning), Korea, under the National Program for Excellence in SW (2015-0-00938) supervised by the IITP (Institute for Information & communications Technology Planning&Evaluation)”.
“This work was supported by the faculty research fund of Sejong University in 2019”.
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Notes
- 1.
For the results of Gierer-Meinhardt, refer https://imc.zih.tu-dresden.de/wiki/morpheus/doku.php?id=examples:reaction-diffusion.
- 2.
For the results of Belousov-Zhabotinsky, refer https://en.wikipedia.org/wiki/Belousov-Zhabotinsky_reaction, https://scipython.com/blog/simulating-the-belousov-zhabotinsky-reaction/.
- 3.
These PDE’s correspond to the additive color mixing. Of course, arbitrary color states and the subtractive color mixing can be applicable.
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Han, Dy., Kim, B., Song, Oy. (2019). New Three-Chemical Polynomial Reaction-Diffusion Equations. In: Gavrilova, M., Chang, J., Thalmann, N., Hitzer, E., Ishikawa, H. (eds) Advances in Computer Graphics. CGI 2019. Lecture Notes in Computer Science(), vol 11542. Springer, Cham. https://doi.org/10.1007/978-3-030-22514-8_32
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