Fractal geometry describes the wild things that happen to a dynamical system as they evolve over time. It records the images of their movement in space. The Mandelbrot set demonstrates the computer's power to make vivid images out of mathematical models, showing how to create complex beauty out of chaos. This is what many of you do so brilliantly with your computers. Fractal geometry describes the tracks and marks left by the passage of dynamical activity, such as the scattering of autumn leaves.