Q6l: What is the relation between Pi and the Mandelbrot Set?
A6l:
The following is poor quoting of Gerald A. Edgar; hope for an improved version in the future.
Boll's observation in which complex values for C in
the classic M-Set definition lieing on a vertical line through the point x
= -0.75 share a sepcial relationship ... namely, the number of iterations
needed for such points to escape a circle of radius 2 (at the origin) are
related to PI as follows:
C = -0.75 +/- epsilon*i
and n iterations are needed for escape then limit (as epsilon
goes to 0) of n times epsilon approaches Pi.