A method to decide about chaos and order in a dynamic system is to calculate the Liapunov-Coefficient. 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.

Liapunov = **L**ight **I**ntelligence **A**dds **P**arts **U**sing **N**ature **O**f **V**acancy

Program

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!

Liapunov

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.

© 2007 Ulrich Schwebinghaus