Fractal geometry: computer graphics representation of a detail from the Mandelbrot Set, plotted from complex number coordinates. A number is described as complex when it is made up of two parts, historically called real and imaginary. The Mandelbrot set, named after the mathematician Benoit B. Mandelbrot, is a form of fractal geometry, the mathematical study of forms having a fractional dimension. Fractal patterns demonstrate order and presence of pattern in apparently highly irregular systems. For example, fractals have been applied to model coastlines.