Mandelbrot Set

The Mandelbrot set a 2 Dimensional set of complex numbers ($c$) for which the following equation will never diverge:

For example, if $c$ is $-1$, this results in the sequence $0,-1,0,-1 \ldots$ which never escapes this small region of the graph, so the point $-1 + 0i$ is coloured black on the graph. The remaining points are typically coloured based on how many iterations it takes for their sequence to escape some arbitrary distance from the origin of this graph (such as $|z| > 2$). The teal-coloured region comprises points whose sequences grow very quickly, so they take very few iterations. Zooming in to the edge of the mandelbrot set will reveal an intricate fractal pattern that only reveals more and more complex patterns at higher zoom levels.

Use the mouse scroll wheel or pinch gestures to zoom into the image at different points. The most interesting regions are those one the edge of any black region.