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This applet allows you to

- Compute and view various regions in the Mandelbrot set.
- Select a
**c**-value from the Mandelbrot set and view the corresponding filled Julia set. - Magnify portions of that Julia set.
- View the orbit of 0 in and around the filled Julia set for a
particular value of
**c**.

When you first open the applet, you will see the control panel on your left. You will also be computing the Mandelbrot set on your right. This will take some time, as will each successive magnification/computation. A timer tells you how much longer you have to wait. For people with old computers, either have patience or buy a new computer! On my little Macintosh G3, it takes less than a second to compute the initial images.

The Mandelbrot set is displayed in black in these images. Since much of this set consists of filaments that are too narrow to be seen at typical resolutions, we use a graduated color scheme so that your eye "zeroes in" on the black regions. Colors proceed from red to orange, yellow, green, blue, and then violet in order of increasing number of iterations necessary for escape.

**Magnifying regions in the Mandelbrot set.** To magnify portions
of the Mandelbrot set, click and drag from the center of the region
you wish to enlarge. You see displayed the coordinates of the center
of the new region and the length of a side of the new square. Click
**Compute** if you wish to see the enlargement of the Mandelbrot
set. Otherwise, you may draw a different square.

Click **Previous** to return to the previous image. Only
one previous image is retained in memory. To obtain a more precise
image of the Mandelbrot set, you may increase the number of
iterations. Increasing this number to huge numbers will cause
interminable delays.

Click **Zoom Out** to see a larger portion of the Mandelbrot set at
any stage. Zoom out increases the linear dimensions of the image by a
factor of 2 (so the area increases by 4).

Click **Reset** to return to the original Mandelbrot set image.

**Computing filled Julia sets.** To compute a filled Julia set,
click the **Julia set** button. You will see a control panel that
you can move around on the screen. Double click on a point in the
Mandelbrot set. This selects a particular **c**-value. Click OK
in the Julia set control panel and the filled Julia set for that
**c**-value will be computed. The **c**-value will be displayed
in the window. If the control panel window disappears, simply click on
the Julia set button again. The flashing point roaming around the
Julia set is the orbit of 0. You may enlarge regions in the Julia set
window exactly as the the case of the Mandelbrot set, but now you need
to click **Zoom** in the Julia set window.

In the Julia set image, you will also see the fate of the orbit of 0 displayed as a blinking series of points (unless the orbit of 0 tends to infinity).