Harmonic Warping

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Revision as of 13:41, 23 June 2009

Image:inprogress.png
Harmonic Warping
This image is a tiling based on a harmonic warping
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

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.







If you are able, please consider adding to or editing this page!

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






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