Fractal geometry: computer graphics representation of part of 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. Here, the real part is plotted on the horizontal axis and the imaginary part on the vertical axis. The Mandelbrot set, named after 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. Mathematically, the image describes the graph: X(n) = [X(n-1)]2 + C