Difference between revisions of "Harmonic Warping"

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Revision as of 12:41, 23 June 2009

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

Harmonic Warping

This image is a tiling based on a harmonic warping


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




Teaching Materials

There are currently no teaching materials for this page. Add teaching materials.

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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Leave a message on the discussion page by clicking the 'discussion' tab at the top of this image page.