The Mandelbrot Set and Julia Sets

Scalings in the Mandelbrot Set

Hurwitz-Robucci scaling - Universal Function Scaling Relation

Now we find a scaling relation for the g_n(e).

Recall r_n = 4ⁿ/6.

gn+1(4e) = fn+1(-2 + 4e/rn+1)

= fn+1(-2 + e/rn)

= (fn(-2 + e/rn))2 + (-2 + e/rn)

= (gn(e))2 - 2 + e/rn

Taking the limit as n -> infinity, we obtain

g(4e) = g(e)² - 2

Return to Hurwitz-Robucci scaling.