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This image was made using Mathematica®, a program for symbolic and numeric mathematical computation from Wolfram Research, Inc., with some postprocessing with standard image manipulation tools.
The Mathematica notebook (gzip compression) which generates the image is here. Be warned, this notebook does heavy computation! It constructs a web-like image with straight lines, and then transmutes the straight lines into sinusoidal parametric paths. Since it uses the Random[] function in making the straight-line web, don't expect to get the same result every time you run it.