Pólya's Space-Filling Curve

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iterations
3
angle
curve opacity
triangle opacity
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.

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.

External Links

Fractal (Wolfram MathWorld)
Right Triangle (Wolfram MathWorld)
Space–Filling Function (Wolfram MathWorld)

Permanent Citation

Robert Dickau
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​"Pólya's Space-Filling Curve"​
​http://demonstrations.wolfram.com/PolyasSpaceFillingCurve/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011