3. The Mandelbrot Set and Julia Sets

3. F.Scalings in the Mandelbrot Set

The sequence of discs attached immediately to the left of the main cardioid correspond to a stable 2-cycle, 4-cycle, 8-cycle, ..., and so is called the period-doubling cascade. Here we measure the diameters of the components in order to discover a pattern in how the components shrink. The limit of the ratios of the diameters of successive compnents is an instance of the Feigenbaum scaling. The Hurwitz-Robucci scaling is an interesting example because it scaling equation can be solved exactly and the scaling ratio derived. Return to the Mandelbrot set and Julia sets.