The Mandelbrot Fractal Explained!

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The Mandelbrot fractal, or Mandelbrot set as it's sometimes called. Most people have seen its iconic shape and many of us have marveled at its beauty and complexity. It has become somewhat of a poster child for chaos theory and perhaps math in general and it is the go to example for what you can do with 'complex' numbers. It is literally infinitely deep and in my mind, infinitely beautiful. But how does it work? Lets find out!
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