The credit goes to Benoit Mandelbrot for discovering the fractals. He gave them the present name in 1975 though mathematicians have known about them as long as the 17th century. A Fractal is a pattern which is repeated at every scale. This concept of self similarity was first mentioned by the mathematician, Lebinz.
As the knowledge about fractals increased, computer programmes for making these started to come into existence and these were started being used as an art form and a background for web pages.