Polypath Iterations

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.

SNAPSHOTS

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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.
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