Difference between revisions of "Harmonic Warping"

Harmonic Warping
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

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

Here

Here

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.