Wolfram Demonstrations Project

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

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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.

Fractal (Wolfram MathWorld)

Right Triangle (Wolfram MathWorld)

Space–Filling Function (Wolfram MathWorld)

"Pólya's Space-Filling Curve" from the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/PolyasSpaceFillingCurve/

Contributed by: Robert Dickau

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Pólya's Space-Filling Curve

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