The Mandelbrot Set and Julia Sets
Two Critical Points
The function
z
2
/2 + z
3
/3 + c
has
two critical points
,
z = 0
and
z = -1.
Consequently, we have three plausible definitions for the Mandelbrot set: all c for which
the iterates of z
0
= 0 remain bounded,
the iterates of z
0
= -1 remain bounded, and
the iterates of both z
0
= 0 and z
0
= -1 remain bounded.
Here are pictures of these three Mandelbrot sets. Click each picture to enlarge.
z = 0
z = -1
z = 0 and z = -1
Return to
the Mandelbrot set definition
.