Harmonic Warping

From Math Images

(Difference between revisions)
Jump to: navigation, search
(New page: {{Image Description |ImageName=Harmonic Warping |Image=Harmonic warp.jpg |ImageIntro=D |ImageDescElem=basic here |ImageDesc=detailed here |other=Single Variable Calculus |AuthorName=Paul C...)
Line 3: Line 3:
|Image=Harmonic warp.jpg
|Image=Harmonic warp.jpg
|ImageIntro=D
|ImageIntro=D
 +
|ImageDescElem=basic here
|ImageDescElem=basic here
-
|ImageDesc=detailed here
+
Look at [[Blue Warp]] for more information to learn how the image that is tiled was created.
 +
 
 +
 
 +
|ImageDesc=
 +
[[Image:HarmonicWarp.png|thumb|]]
 +
Essentially, an equation was used to map the points of
 +
 
 +
 
 +
 
 +
*equation <math>d(x) = 1 - \frac{1}{1+x}</math>, limit is 1
 +
<math>d(y) = 1 - \frac{1}{1+y}</math>, 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
 +
 
 +
 
 +
 
 +
 
|other=Single Variable Calculus
|other=Single Variable Calculus
|AuthorName=Paul Cockshott
|AuthorName=Paul Cockshott

Revision as of 14:55, 22 June 2009

Image:inprogress.png
Harmonic Warping
D

Basic Description

basic here

Look at Blue Warp 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


  • equatio [...]

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




Teaching Materials

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








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

Have questions about the image or the explanations on this page?
Leave a message on the discussion page by clicking the 'discussion' tab at the top of this image page.






Harmonic Warping
Fields: Calculus and Fractals
Created By: Paul Cockshott
Retrieved from "http://mathforum.org/mathimages/index.php/Harmonic_Warping"
Personal tools
Create or Edit a Page