Introduced to general readers on the cover of the August 1985 Scientific American, the Mandelbrot Set... is now an element of popular culture... In many ways, the Mandelbrot Set is the prototypical fractal: so easy to generate, yet so complex in structure. Despite its algorithmic simplicity, the study of its regular irregularities has generated new and deep mathematics.
Peak, David and Michael Frame. Chaos Under Control: The Art and Science of Complexity. New York: W. H. Freeman, 1994. p.243.