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.
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.
Wolfram Demonstrations Project
Published: March 7 2011