Julia and Mandelbrot Sets

This application allows you to zoom in to get a feeling for the infinitely complex structure of either the Mandelbrot Set M or the Julia Set associated with a particular point k.

Option 1. Select Mandelbrot Set. Place the cursor anywhere in the picture, click and drag to draw a box. The region inside the box is recomputed, and the magnified portion appears in the right panel. You may repeatedly draw boxes in panels alternately to zoom in further and further.

Option 2. Select Julia Sets. In the portion of the complex plane that appears, each point names a complex number k, of the form a + bi, and each point determines a different Julia Set. Click and drag the cross to select a point, whose coordinates appear in the function definition below the right panel. When you release the mouse button, the corresponding Julia Set is drawn in the left panel and you may zoom in as in Option 1.

Option 3. Select M/J relationships. Many of the most interesting Julia Sets are those for points on the boundary of M . To select the point for the Julia Set, place the cursor on the picture of M in the left panel; then shift-click to see the Julia Set for your point choice. You may then zoom in on the resulting Julia Set by drawing rectangles as before. You may also zoom in on M before making your point selection.