As we showed in [7],
the fact that the orbit of 0 "finds" the
attracting cycle of **F _{c}** (if it exists) allows us to assign a number
to the bulbs or decorations in

The boundary of this region consists of **c** values for which the
magnitude of this derivative is **1**, i.e., for **c**-values
for which

Solving the equations above using this fact yields

which parametrizes a cardioid as **t** runs from **0** to **2 pi**.
Similarly, the large disk to the left of the main cardioid consists of
**c**-values for which **F _{c}** has an attracting cycle of period 2. One
may easily check that this region is bounded by the circle of radius
1/4 centered at

** Figure 2. Periods of the bulbs in M**

The * primary bulbs* in **M** are those decorations that are
directly attached to the main cardioid. In the sequel we will be
mainly concerned with these decorations.

Recall from [7] that we may also read off the period of the primary bulbs by simply counting the spokes of the antenna attached to this decoration. Note that each bulb features a large antenna that contains a junction point from which a number of spokes emanate. It is a fact that the number of these spokes is exactly the period of the bulb. When counting these spokes, it is important to count the main spoke (the spoke that is attached directly to the bulb). For example, in Figure 3 we have displayed several of the primary decorations and their periods.

Period 9

Period 19

**Figure 3.**

There is another way to read off the period of the primary bulbs.
Choose any **c** in the interior of such a bulb and compute **J _{c}**. Of
course,

** Figure 4**

Fractal Geometry of the Mandelbrot Set (Cover Page)

2 Role of the Critical Orbit (Previous Section)