The image at the top of the post shows the first five generations of the family of curves obtained from the 'scrambler' construction that I described briefly in the last post. These curves are generated by the equations
The curves formed by choosing alternate + and - signs are the ones most closely related to the 'scrambler' that got this started. This choice has each circle turning in the direction opposite to the circle that preceded it, and generates the 'propeller' curves that lie in the center right of the diagram above.
GSP was used for the first few generations, but to look at this for very large n, I resorted to writing a short (surprisingly short) Processing program that gave these pictures for generations 0-7, and 20:
fractal emerges that displays nice self-similarity along each propeller blade.
Update: A post about the leftmost curve on the chart above ("brain fractal") is here.