The Julia set is a nice example of self-similarity and of how tiny perturbations in the initial conditions can lead to significant changes in the behavior of a complex system. A simple iteration in the complex plane is investigated with respect to the parameters causing convergent or divergent behavior respectively. The colors are related to the number of iterations needed to reach a certain threshold above which the parameter is regarded as causing divergence. The animation shows a zoom into the Julia set and consists of 1,200 individual pictures. The final magnification is about 21,000,000,000.
