Fractal dimension of Julia sets
As part of Brud's luser stories I wrote up a lecture/slideshow about the fractal dimension of Julia sets. You can download the PDF: julia-dim.pdf (3.5MB) and there's a page with source code and detailed results tables here: fractal dimension of Julia sets.
The image is resemblant to the familiar Mandelbrot set because any ball around a boundary point of the Mandelbrot set contains a Julia set with dimension approaching arbitrarily close to 2.