Rectangles attempting to be circles, (and mostly succeeding)
Rectangles attempting to be circles (and mostly succeeding).
Rectangles attempting to be circles (and mostly succeeding).
More reaction diffusion fun.
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Reaction diffusion + normal flow. No smoothing.
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I want to make sure the reaction diffusion system responds when the domain expands and contracts.
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A nice one.
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These are the Grey-Scott Equations:
𝑑𝑑𝑡𝑢=𝐷𝑢(△𝑢)+𝐹(1−𝑢)−𝑢𝑣2
𝑑𝑑𝑡𝑣=𝐷𝑣(△𝑣)+𝑢𝑣2−𝑣(𝐹+𝑘)
Kim's solution involved solving a polynomial derived from rearranging the reaction so that u is in terms of v which results in a polynomial, probably to avoid the matrix inversion required by the multi-variable Newton solve. 3/n
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These are the Grey-Scott Equations:
𝑑𝑑𝑡𝑢=𝐷𝑢(△𝑢)+𝐹(1−𝑢)−𝑢𝑣2
𝑑𝑑𝑡𝑣=𝐷𝑣(△𝑣)+𝑢𝑣2−𝑣(𝐹+𝑘)
Kim's solution involved solving a polynomial derived from rearranging the reaction so that u is in terms of v which results in a polynomial, probably to avoid the matrix inversion required by the multi-variable Newton solve. 3/n
#mathart #GenerativeArt #GenArt #algoart #algorithmicart #sculpture #algorithmicsculpture
#mathart #generativeart #genart #algoart #algorithmicart #sculpture #algorithmicsculpture
The problem with using an implicit Diffusion solve is that it tends to knock out all of the high order frequencies, so some of the wild oscillating behavior goes away.
@TheodoreKim proposed a solution to the problem here:
http://www.cs.unc.edu/~geom/SARD/stable_ard_kim_lin.pdf
The idea is to use operator splitting and Newton Solve solve the reaction equation.
2/n
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Life trajectory so far, seemingly, starting from the center and spiraling outward.
This one is amusing to me.
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This is the bound bunny with tangent-point repulsion on the curves. It got to ~200k vertices which ground the solver to a halt.
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Pinball wizard
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Have a nice weekend
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I'm feeling indulgent so here are a few more.
I'm really pleased with how this turned out.