The orbit of 0 plays an important role in determining the structure
of **J _{c}**. The following fact was discovered by P. Fatou and G. Julia.

The previous paper in this series
[1] contains additional details about this fact.
It is well known that a Cantor set consists of uncountably many
points, and each connected component of a Cantor set is a point. Thus
the filled Julia sets of **F _{c}** fall into one of two classes, those
that consist of a single piece, and those that consist of uncountably
many disjoint pieces. It is the orbit of 0 that distinguishes which
class

There is a second reason why the orbit of 0 plays a critical role.
Suppose **F _{c}** admits an attracting cycle of period

Here **F _{c}^n** denotes the

If there exists such an attracting cycle for **F _{c}**, then the fact is
that the orbit of 0 must tend to this cycle. As a consequence,

Fractal Geometry of the Mandelbrot Set (Cover Page)

1 Basic Definitions (Previous Section)