Here is one of my favorite images, a very tiny portion of the Mandelbrot set, which mimics the overall shape of the set itself. It's one of the classics of fractal mathematics, which studies objects of fractional dimension. It was first conceived by Poincare, but not until Benoit Mandelbrot harnessed the power of computers was the full complexity of these objects realized. The Mandelbrot set is simply derived by iterating the equation Z(n+1) = Z(n)^2 +Zo for every point in an area of the X-Y plane and determining if the sequence created for each point converges to a fixed value or diverges to infinity. The black area in the center represents those points which converge (the Mandelbrot set), and the points around it are colored differently, depending on how fast the corresponding sequence diverges.