Fractal geometry: Mandelbrot set. A computer graphics image of the Mandelbrot set, a group of complex numbers plotted using their real and imaginary parts as coordinates. Each point is assigned a color depending upon its behavior under a series of simple, but repeated, mathematical operations or mappings. The patterns are infinitely complicated, but appear to repeat themselves on whatever scale they are viewed. A magnification, however large, of any part of the image, produces an image which looks very similar. The study of such 'chaotic' mathematical behavior is becoming increasingly important is a means of modeling real world processes form stock market prices to population dynamics and fluid turbulence.