Here's an example of chaos: Start with x = 0.3 and iterate x = 2 * x * (1 - x). The next two value of x are 0.42 and 0.4872. Iterate a few more times, and x will go to 0.5 and stay there for all subsequent iterations. Try it again with an initial x of 0.301, or any value between 0 and 1, and the final result will be 0.5. Now, try the same thing with x = 4 * x * (1 - x), just replacing the 2 with 4. If you compare the x sequence starting with 0.3 with the x sequence starting at 0.301 (or any other value close to 0.3), then you'll see that the difference between the two sequences starts out small, grows rapidly, and after maybe 20 or 30 iterations, the two sets of numbers seem to have nothing to do with each other. The first process is not chaotic, and leads to a limit point. The second is chaotic: small differences between states lead to large differences over time. In other words, there's sensitive dependence to initial conditions. This is a property of dynamical systems, not images. In the typical fractal plot for this formula, the idea of sensitive dependence on initial conditions can be seen in the fine detail around the boundary of the Mandelbrot set. One pixel may be inside the set, an adjacent pixel could be outside, and another nearby pixel could be on the boundary. The small differences in pixel location (initial condition) lead to large differences in the orbits of their corresponding points--convergent, divergent, or chaotic. In the context of math/science, a system maybe chaotic if it is governed by fixed rules. If a system's dynamics are chaotic, then they can often be visualized with fractals. Kerry