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Mandelbrot set appreciation thread

No.10646178 ViewReplyOriginalReport
Whether you like math or not, you must concede that the Mandelbrot set is pretty cool. Despite being calculated from a very simple formula, it's literally infinite and endless. Even after countless zooming videos are posted on youtube every day, the total amount of set explored will always be 0%.
The set was never invented, it was discovered. It always existed, but we can only see it now thanks to computers, and despite being known and studied since the 80s, there are still some mysteries surrounding it. For example it is known that the set is connected, and it is conjectured that the set is locally connected, but this has never been proven.
Famous science fiction writer Arthur C. Clarke was fascinated by it and even made a documentary about it and fractals in general, going as far as adding a reference to the set in it's novel "The Ghost from the Grand Banks".

Feel free to post images and facts about this wonderful set of complex numbers.