The term "fractal" was coined by Benoit Mandelbrot in 1975. It comes from the Latin fractus , meaning an irregular surface like that of a broken stone. Fractals are non-regular geometric shapes that have the same degree of non-regularity on all scales. Just as a stone at the base of a foothill can resemble in miniature the mountain from which it originally tumbled down, so are fractals self-similar whether you view them from close up or very far away.
"Fractal Geometry plays two roles. It is the geometry of deterministic chaos and it can also describe the geometry of mountains, clouds and galaxies." - Benoit MandelbrotMandelbrot set images are made by sampling complex numbers and determining for each whether the result tends towards infinity when a particular mathematical operation is iterated on it. Treating the real and imaginary parts of each number as image coordinates, pixels are colored according to how rapidly the sequence diverges, if at all.
The Mandelbrot set has its place in complex dynamics, a field first investigated by the French mathematicians Pierre Fatou and Gaston Julia at the beginning of the 20th century. The first pictures of this fractal were drawn in 1978. On 1 March 1980, at IBM's Thomas J. Watson Research Center, Benoit Mandelbrot first saw a visualization of the set.