1. INTRODUCTION TO FRACTALS 7 Figure 13. Julia sets. Once we have a parametric set {fc}c of mappings, we can also consider the set of the values of the parameter c for which fc has a certain property. The famous Mandelbrot fractal on Figure 14 is defined as the set of all c C for which 0 belongs to the filled Julia set of fc or, equivalently, for which the Julia set of fc is connected. One more example where infinite iteration arises naturally is the Newton meth- od for finding roots of functions.
Previous Page Next Page