Nestled within the Mandelbrot Set, you can find this image.  (Credit to Dr. Wolfgang Beyer)

Each and every pixel of this image represents a complex number, graphed on the complex plane, which has been iterated repeatedly through a mathematical equation.  The points colored black give values which remain bounded, even after an infinite number of iterations, and are properly part of the Mandelbrot Set.  The colored points “escape” and leave the set -- and the different colors reflect how quickly or how slowly those points diverge.

The more math you understand, the more you can begin to appreciate the wonders of an image like this.  It reveals itself more and more to people with a knowledge of Algebra, and the Distributive Property.  Of working with complex numbers, and the properties of the number “i.”  Of two-dimensional graphing in the complex plane.  Of logarithmic functions and mathematical interpolation, to provide smooth gradients of colors . . .

And above and beyond that -- to see this particular piece of the set requires a magnification factor of over one million . . .

Seriously.  How cool is that?