From Math Images
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|ImageIntro=This image is a tiling based on
|ImageIntro=This image is a tiling based on harmonic warping
at [[Blue Wash]] for more information how the image was created.
Revision as of 14:38, 23 June 2009
|Harmonic Warping of Blue Wash|
Basic DescriptionThis image is an infinite tiling. If you look closely at the edges of the image, you can see that the tiles become smaller and smaller and seem to fade into the edges. This is true, the border of the image is infinite so that the tiling is infinite and the tiles become infinitely smaller. The source image used for this tiling is another image that is mathematically interesting and is also featured on this website. See Blue Wash for more information about how the source image was created.
A More Mathematical Explanation
- Note: understanding of this explanation requires: *Single Variable Calculus
Essentially, an equation was used to map the points of
- equation , limit is 1
, limit is 1
- distance compressing warp
- infinite tiling of Euclidean plane mapped onto a rectangle (or ellipse)
- mapping (x,y) from Euclidean plane unto (d(x),d(y)) in rectangle
Polar Harmonic Warping
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About the Creator of this Image
Paul Cockshott is a computer scientist and a reader at the University of Glasgow. The various math images featured on this page were originally produced for his research.
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