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When zooming in on the Mandelbrot set you will very often find replicas of the original zoomed out image. Is it possible to find out how many the entire set includes?

Bernard
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guil.c
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    this link should help you visualise. You'll get your answer in an instant. – sai-kartik Jun 22 '20 at 20:36
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    They are actually not exact copies, but there are infinitely many. – Robert Israel Jun 22 '20 at 20:40
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    It wouldn't be the Mandelbrot set if you didn't find infinite copies within every copy. – fleablood Jun 22 '20 at 20:41
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    further to the other comments, there are only countably infinitely many, because each has a positive area, they do not overlap, and the whole set is contained in a disc of radius 2 – Claude Jun 22 '20 at 20:57
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    Even furthering the comments of @Claude, the answers at https://math.stackexchange.com/questions/743727/does-the-mandelbrot-fractal-contain-countably-or-uncountably-many-copies-of-itse establish that there are a (countable) infinity of "replicas" within the set. It's a good first question, and don't get discouraged. Welcome to site! – Hooked Jun 23 '20 at 06:39

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