Harmonic Warping

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Harmonic Warping
D
Harmonic Warping
Fields: Calculus and Fractals
Created By: Paul Cockshott

Contents

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

Polar Harmonic Warping

Here

Infinite Poles

Here




Teaching Materials

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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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