Similarity between the Mandelbrot set and Julia sets

  title={Similarity between the Mandelbrot set and Julia sets},
  author={Tan Lei},
  journal={Communications in Mathematical Physics},
  • Tan Lei
  • Published 1 December 1990
  • Physics
  • Communications in Mathematical Physics
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… 

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