Fractals are ususally colorful mappings of infinitely repeating patterns that are created use complex numbers.  Benoit Mandelbrot's book, Les Objets Fractals, published in 1975 has the first occurrance of the word "fractal."  However, geometrical figures that can be classified as fractals exist as far back as 1872 with the one-dimensional "Cantor's Dust."  In 1890 Peano published a two-dimensional fractal known as "Peano's curve."  The coast of Britain is considered to be like a fractal, and the first reference listed below uses fractals to reach the conclusion that the length of Britain's coast is infinite.

Author: Eric Libicki

References:
http://www-hs.iuta.u-bordeaux.fr/louvet/history.html

http://www.columbia.edu/~gae4/chaos/cfd.2.3.htm