The Mandelbrot Set and Julia Sets

Scalings in the Mandelbrot Set

Hurwitz-Robucci scaling - Convergence of Rescaled Polynomials

So gn(ε) = fn(-2 + ε/rn) = fn(-2 + 6ε/4n). Here we plot the graphs of the first few gn.

Click the picture to animate.

The animation suggests good convergence of the gn(ε) to some limiting function. Note that with increasing n, the gn(ε) change very little over larger ranges of ε values.

Return to Hurwitz-Robucci scaling.