Exercise: Finding order in chaos
Part 1. Finding patterns in the Mandelbrot set

Although the Mandelbrot set, like many fractals, displays a frightening amount of complexity, it also overlays that with an overall pattern. Try the following:

1) Open the following fractals from the favourites folder:

3) arms.fx
4 arms.fx
5 arms.fx
6 arms.fx

2) On the Location menu, click View Location.

Notice that these four images are quite neatly lined up along the large cardiod (pear shaped thing) in the Mandelbrot set. As you move from one bulb to the next along the edge of the cardiod, the number of arms in major structures gradually increases. You can get any numbers of arms that you want (well, no less than three).

3) Find the bulbs that have three arms and four arms, respectively.

Notice that there is another smaller bulb inbetween these two arms.

4) Zoom in on this smaller bulb.

Notice that it has seven arms -- the sum of three and four. Isn't that weird?

This pattern repeats itself all over the Mandelbrot set, at every level. How does it keep all these rules straight? Remember that all of this is produced by an incredibly simple formula.