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- W4311255392 abstract "We introduce an algorithm for a search of extremal fractal curves in large curve classes. It heavily uses SAT-solvers—heuristic algorithms that find models for CNF boolean formulas. Our algorithm was implemented and applied to the search of fractal surjective curves $$gamma :[0,1]rightarrow [0,1]^d$$ with minimal dilation $$begin{aligned} sup _{t_1<t_2}frac{Vert gamma (t_2)-gamma (t_1)Vert ^d}{t_2-t_1}. end{aligned}$$ We report new results of that search in the case of Euclidean norm. We have found a new curve that we call “YE”, a self-similar (monofractal) plane curve of genus $$5times 5$$ with dilation $$5+{43}/{73}=5.5890ldots $$ In dimension 3 we have found facet-gated bifractals (which we call “Spring”) of genus $$2times 2times 2$$ with dilation $$<17$$ . In dimension 4 we obtained that there is a curve with dilation $$<62$$ . Some lower bounds on the dilation for wider classes of cubically decomposable curves are proven." @default.
- W4311255392 created "2022-12-25" @default.
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- W4311255392 date "2022-12-03" @default.
- W4311255392 modified "2023-09-27" @default.
- W4311255392 title "Search of Fractal Space-Filling Curves with Minimal Dilation" @default.
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- W4311255392 doi "https://doi.org/10.1007/s00454-022-00444-2" @default.
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