Is there a space-filling curve that has the same properties of a hilbert curve (two points close in 1D are close in 2D) but grows in a circular shape instead of a rectangular one?
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1Related to http://math.stackexchange.com/questions/29578/is-there-a-way-to-represent-the-interior-of-a-circle-with-a-curve – mvw Mar 16 '15 at 15:12
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I am not aware of a such curve construction, but the next best thing is probably using a suitable mapping between square and circle disc and then transform the square based hilbert curve onto a circle.
Maybe something like this: Conformal mapping circle onto square (and back)
