The Hilbert Curve

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"Crinkly Curves," in the May-June 2013 issue of American Scientist, discusses a family of geometric curves that are so zigzaggy they burst the bonds of one-dimensionality. The simplest example is the Hilbert curve. Successive approximations to this curve are more and more crinkly, and in the infinite limit the curve is all right angles. Presented here are two interactive illustrations that explore the nature of the curve.

Constructing the Hilbert Curve

Mapping Points on a Line to Points in a Square

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