The Mandelbrot set is a fractal defined as the set of points c of the complex plane for which the sequence of complex numbers defined by induction by :
is bounded.
The images of the Mandelbrot set are produced by traversing the complex numbers over a square region of the complex plane and by determining for each of them whether the result tends to infinity or not when a mathematical operation is iterated over it.
We consider the real and imaginary part of each complex number as coordinates and each pixel is colored according to the speed of divergence, or if it does not diverge.
Images of the Mandelbrot set expose an elaborate boundary that gradually reveals ever-finer recursive detail with increasing magnification.
The boundary of the set is made up of smaller versions of the main shape so the fractal property of self-similarity applies to the whole set and not just some parts.
The Mandelbrot set has become popular outside of mathematics as an artistic inspiration and as an example of complex structure coming from the application of simple rules.
It is one of the best-known examples of mathematical visualization.
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