# This is why the Mandelbrot sets are amazing!

Mandelbrot set is a special set of complex numbers that has fascinating properties. It consists of all complex numbers \( c \) for which the sequence \( z_{n+1} = z_{n}^{2} + c, z_{0} = 0 \) is bounded.

If we visualize all such complex numbers in the complex plane, such that we associate with them a color representing
the number of iterations before they diverge, we get a fascinating plot. The shape is so intricate that we can
always zoom-in and never go out of finer detail. In fact, the boundary of the *Mandelbrot set* is a *fractal:*
it means it has an infinite perimeter and finite area. It also means it is nowhere differentiable.

Using *Python* and *Matplotlib's* Animation API, we implement and visualize the convergence
of the *Mandelbrot set* as the number of iterations increases. This is illustrated in the animation below:

The source code related this visualization can be found in this Python Notebook. For more information, please follow me on Twitter.

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