1I wonder if Dr. Mandelbrot knows that Jonathan Coulton made this song about him, Mandelbrot Set. Here are the lyrics to the chorus:
Take a point called Z in the complex plane
Let Z1 be Z squared plus C
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Z’s should always stay
Close to Z and never trend away
That point is in the Mandelbrot Set