The Mandelbrot Set and Julia Sets

Scalings in the Mandelbrot Set

Hurwitz-Robucci scaling - Rescaled Polynomials

Instead of using c as a variable, we measure the distance from the accumulation point -2.

Moreover, we magnify the scale by an amount rn depending on n.

That is, we use as our distance measure ε, where

c = -2 + ε/rn.

In terms of the distance ε, we are interested in the zeros of the functions

gn(ε) = fn(-2 + ε/rn).

Once we find the appropriate scaling factor rn, we hope to show gn(ε) → g(ε), a universal function from which all the 0s can be derived.

Return to Hurwitz-Robucci scaling.