To each point of the complex plane there belongs a Julia set
. This set is connected iff the parameter point belongs to the Mandelbrot set
. It is a circle iff the parameter is 0. So I chose a curve that starts at 0, and then runs both inside and outside the Mandelbrot set before returning to 0. Polygonal approximations of the Julia sets belonging to the points of the curve were computed for 13 backwards iterations, stacked, and the whole thing was thickened so that it is printable.
A version where the curve is shorter, doesn't return 0 and thus reveals a more interesting fractal boundary is available here
A version where the interior of the Julia sets is not included is available here