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This question mentions that it contains similar shapes. But what I want to know, does the set contains a PERFECT shape of itself. Can I start to zoom and come to a state where I was already?

Mark McClure
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Superluminal
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    No, the Mandelbrot set definitely does not contain any exactly geometrically similar copies of itself. In fact, in his paper The Complex Geometry of the Mandelbrot Set, Bob Devaney calls the Mandelbrot set "the antithesis of a fractal in that almost every tiny area of the boundary has its own identity. That is, using some tools from geometry, we can read off exactly where this boundary point is and, more importantly, exactly what the corresponding dynamical behavior is". – Mark McClure Nov 01 '19 at 09:57
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    From https://en.wikipedia.org/wiki/Mandelbrot_set#Self-similarity: “The Mandelbrot set in general is not strictly self-similar but it is quasi-self-similar ... The little copies of the Mandelbrot set are all slightly different, ...” – Martin R Nov 01 '19 at 09:58

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