The program on the previous page renders the Mandelbrot set as it appears in a particular rectangular window on the complex plane; specifically, the rectangle . We can change this window by panning and by zooming in and out. In the following program, setting frame to 2 (or 3 or 4) creates a frame for zooming in or out by a factor of 2 (or 3 or 4).¹ When zooming in, the frame expands to become the the window; when zooming out, the window contracts to fill the frame. To pan, drag the frame to a new location. Press Go to apply your choices.

Exploring the Mandelbrot set

The boundary of the Mandelbrot set is a fractal curve. To see this, repeatedly zoom in on a region containing a section of boundary. Although the set’s fractal structure persists to any magnification, our program magnifies only to a power of about due to its finite precision.