Polypath Iterations

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

A polypath is the result of repeatedly folding an isosceles trapezoidal quadrilateral along its diagonal. The folding transforms the four vertices , represented by complex numbers, into , where is the complex conjugate. This Demonstration shows the possible variations of a polypath as you change the coordinates of the two defining vertices of the original trapezoid. This is achieved by dragging the corresponding locator points.

Contributed by: Erik Mahieu (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

While dragging the locators, hold down the ALT key or the CTRL and ALT keys to fine-tune the image.

The best images are obtained by dragging the locators with, for example, 10 folds until a pleasing figure is reached. Then switch to a higher number of folds. Or you can simply start with a random trapezoid.

The polypath idea comes from M. Trott, The Mathematica GuideBook for Programming, New York: Springer–Verlag, 2004 pp. 639–643.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send