We can zoom in on the above graphic forever,
literally FOREVER;

and as we zoom further inward, an endless series
of new shapes and patterns will arise.

Amazingly, as we continue to move inward,
one distinctive shape will appear, disappear
and then appear again - it is this one


image credit

This shape has been called "the thumbprint of God"
and "an island of order in a sea of chaos".

It is the strangely familiar shape that defines the
mathematical phenomenon called The Mandelbrot Set.

The Mandelbrot Set is essentially a set of points in
a series of planes that is generated by the repeated
application of this relatively simple formula:  

        
where c is a complex parameter - wikipedia.


We may not be able to grasp the mathematics of the
Mandelbrot Set, but we can taken great pleasure in
pondering it as it unfolds in the video below





The above is an excerpt from Arthur C. Clarke's
Fractals: The Colors of Infinity.