A method to decide about chaos and order in a dynamic system is to calculate the Liapunov exponent. The calculation takes a long time, because you have to iterate at least a hundred times for every pixel of the image. The pictures could be very impressive, so the patience is payed.
My program Liapu, like the others written in Delphi, creates images as shown here and in the Fractal Gallery. You can order this program only by Email (please send me an aquivalent: ideas, pictures, programs, education-concepts, etc. with your mail). You are allowed to use the program for your own, but not to distribute it to others!
Aleksandr Mikhailovich Lyapunov (1857 - 1918) was a Russian mathematician, mechanician and physicist, who worked on the theory of figures of equilibrium of rotating heavy liquids. In mathematics the Lyapunov exponent of a dynamical system is a quantity that characterizes the rate of chaos.
Remark: There are three different ways writing his name: Lyapunov, Ljapunov and Liapunov.