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Mandelbrot Orbits
by Jeffrey Ventrella

(1) Click and drag inside of the main cartioid.
(2) Explore Elephant Valley (crevice at right).
(3) Click and hold on the bulbs to see orbits.

The Mandelbrot Set is revealed when the function z=z^2+C is iterated in the complex plane C. The value of the number z changes at every iteration. This interactive web page allows you to experience the behavior of z.

If you click and hold anywhere inside of the Set, the value of z establishes an orbit with a particular shape. Notice how clicking anywhere outside of the Set causes the orbit to diverge.

Here are some web pages about orbits