Difference between revisions of "Harmonic Warping"

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===Polar Harmonic Warping===
 
===Polar Harmonic Warping===
 +
Here
  
 
===Infinite Poles===
 
===Infinite Poles===
 
+
Here
  
  

Revision as of 09:52, 23 June 2009

Inprogress.png
Harmonic Warping
Harmonic warp.jpg
Fields: Calculus and Fractals
Image Created By: Paul Cockshott
Website: Fractal Art

Harmonic Warping

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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

HarmonicWarp.png

Essentially, an equation was used to map the points of


  • eq [...]

HarmonicWarp.png

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

Polar Harmonic Warping

Here

Infinite Poles

Here




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