Probably the most important image in recent scientific history.

This graphic, most commonly associated with hallucinatory visions brought on by illicit drugs, represents a revolution in scientific thinking. First visualized in the 1980s, the seed of fractal geometry has its roots in a 1918 formula composed by the French mathematician Gaston Maurice Julia. Julia’s student Benoit Mandelbrot later popularized the formula with the advent of computers, when he could finally plot the millions of millions calculations iterations of the formula, z -> z^2 + c necessary to make a complete set. The images that appear have infinite resolution. One can zoom in or out of a Mandelbrot set, or M-set, and never reach its end. The implications of this are enormous. The theories of Fractal geometry, as represented by the M-set, led to changes in the way we thought about information, the natural world, stock markets, our bodies and the cosmos, just to name a few.

For some practical applications of fractal geometry, go here.

In memory of Arthur C. Clarke.