Chapter 6: Escape-time Plots

Some of the most elegant fractals are produced by plots showing in color the number of iterations required for an orbit starting at a particular point to escape beyond some boundary surrounding an attractor. In fact, the famous Mandelbrot set and its associated Julia sets are the best known such examples. This chapter shows a number of other less familiar examples employing the maps and flows in the previous chapters as well as a special map that is a generalization of the usual Julia sets.