Mandelbrot fractal. Computer graphic showing a fractal image derived from the Mandelbrot Set. Fractals geometry is used to derive complex shapes as often occur in nature. The Mandelbrot Set, named after the mathematician Benoit B. Mandelbrot, is a group of complex numbers. Each point is assigned a color depending upon its behaviour plotted under a series of simple but repeated mathematical operations or mappings. Generated on a computer screen, fractals are used to create models for real-world non-linear phenomena such as stock market prices, weather forecasting, plant growth, erosion of coastlines and fluid turbulence.