One of the most intricate and beautiful images in all of mathematics is the Mandelbrot set, discovered by Benoit Mandelbrot in 1980.
Most people within the mathematics community, and many people outside of the discipline, have seen this image and have marveled at its geometric intricacy.
The Mandelbrot set is a particular mathematical set of points,
whose boundary generates a two-dimensional fractal shape.
Images of the Mandelbrot set display an elaborate boundary that reveals progressively ever-finer recursive detail at increasing magnifications.
The "style" of this repeating detail depends on the region of the set being examined.
This application, the iPad version of Mandelbrot, lets you enter in the Mandelbrot set, and repeatedly zoom in it, to generate many wonderful and spectacular images.