10673
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Knopp's Osgood Curve Construction
Robert Dickau
Arbitrary Curves of Constant Width
Ed Pegg Jr
Schoenberg Plane-Filling Curve
Robert Dickau
Peano Curve Explorer
Robert Dickau
Lebesgue 3D Curves
Robert Dickau
Wunderlich Curves
Robert Dickau
Sierpinski 3D Arrowhead Curve
Robert Dickau
Recursive Exercises V: Nested Triangles
Jaime Rangel-Mondragon
Drilling a Square Hole
Stan Wagon (Macalester College)
Square-Hole Drill in Three Dimensions
Stan Wagon (Macalester College)
Related Topics
Curves
Fractals
Plane Geometry
Triangles
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+