Harmonic Warping

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Look at [[Blue Wash]] for more information to learn how the image that is tiled was created.
Look at [[Blue Wash]] for more information to learn how the image that is tiled was created.
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[[Image:HarmonicWarp.png|thumb|]]
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[[Image:HarmonicWarp.png|thumb|300px]]
Essentially, an equation was used to map the points of
Essentially, an equation was used to map the points of

Revision as of 14:56, 22 June 2009

Image:inprogress.png
Harmonic Warping
D

Basic Description

Look at Blue Wash for more information to learn how the image that is tiled 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


  • eq [...]

Essentially, an equation was used to map the points of


  • equation d(x) = 1 - \frac{1}{1+x}, limit is 1

d(y) = 1 - \frac{1}{1+y}, 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




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Harmonic Warping
Fields: Calculus and Fractals
Created By: Paul Cockshott
Retrieved from "http://mathforum.org/mathimages/index.php/Harmonic_Warping"
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