Similarity between the Mandelbrot set and Julia sets

The Mandelbrot setM is “self-similar” about any Misiurewicz pointc in the sense that if we examine a neighborhood ofc inM with a very powerful microscope, and then increase the magnification by a carefully chosen factor, the picture will be unchanged except for a rotation. The corresponding Julia setJc is also “self-similar” in the same sense, with the same magnification factor. Moreover, the two setsM andJc are “similar” in the sense that if we use a very powerful microscope to look atM andJc, both focused atc, the structures we see look like very much the same.