Similarity between the Mandelbrot set and Julia sets
Abstract
The Mandelbrot set M is “selfsimilar” about any Misiurewicz point c in the sense that if we examine a neighborhood of c in M 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 set J _{c} is also “selfsimilar” in the same sense, with the same magnification factor. Moreover, the two sets M and J _{c} are “similar” in the sense that if we use a very powerful microscope to look at M and J _{c}, both focused at c, the structures we see look like very much the same.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 December 1990
 DOI:
 10.1007/BF02098448
 Bibcode:
 1990CMaPh.134..587L