Similarity between the Mandelbrot set and Julia sets
Abstract
The Mandelbrot set M is “self-similar” 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 “self-similar” 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