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--- graduation_projects [2021/06/06 14:26] – [Nearest-neighbour-preserving sets of space-filling curves (BM)] administrator
+++ graduation_projects [2021/06/06 14:27] – [Quantifying the roughness of space-filling curves (M)] administrator
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-====Quantifying the roughness of space-filling curves (M)====
-A space-filling curve is essentially a continuous, surjective function //f// from the unit interval to some two- or higher-dimensional volume. As //t// goes from 0 to 1, the image //f//(//t//) traces out a curve that eventually visits each point of the higher-dimensional volume. [[http://teachout1.net/village/|Gary Teachout]] considers Gosper's plane-filling curve "one of the most convoluted, yet one of the smoothest fills". It is probably for this reason that Auber et al. use this curve as the basis for visualizations that consist of [[https://ieeexplore.ieee.org/document/6532285|plane-filling curves cut into pieces]]. Can you find an even smoother plane-filling curve? To answer this question, we should start with developing a metric for how smoothly a plane- or space-filling curve fills the plane (or space), and we should calculate the smoothness metric for known space-filling curves. For a deeper understanding of the problem, we may look at physicists' attempts at achieving the opposite: deliberately rough space-filling curves that may serve as a model for DNA molecules.
 ====Sonifying algorithms (BM)====

Herman Haverkort