Abstract
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 setJ c is also “self-similar” in the same sense, with the same magnification factor. Moreover, the two setsM andJ c are “similar” in the sense that if we use a very powerful microscope to look atM andJ c, both focused atc, the structures we see look like very much the same.
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Lei, T. Similarity between the Mandelbrot set and Julia sets. Commun.Math. Phys. 134, 587–617 (1990). https://doi.org/10.1007/BF02098448
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DOI: https://doi.org/10.1007/BF02098448