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Pólya's Space-Filling Curve

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Generating Pólya's space-filling curve begins with a right triangle. For each iteration, split each right triangle into two smaller right triangles and join the centers of the resulting smaller triangles.

Contributed by: Robert Dickau (March 2011)
Open content licensed under CC BY-NC-SA

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Details

Snapshots 1, 2: adjusting the opacity of the triangles and the curve highlights the construction

Snapshot 3: for an isosceles right triangle, the Pólya space-filling curve is identical to the Sierpinski curve

H. Sagan, Space-Filling Curves, New York: Springer-Verlag, 1994 pp. 63–67.

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