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Pólya's Space-Filling Curve
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
THINGS TO TRY
Gamepad Controls
Automatic Animation
SNAPSHOTS
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.
RELATED LINKS
Fractal
(
Wolfram
MathWorld
)
Right Triangle
(
Wolfram
MathWorld
)
Space–Filling Function
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Pólya's Space-Filling Curve
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/PolyasSpaceFillingCurve/
Contributed by:
Robert Dickau
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