Mandelbrot set: orbits (by Fabio Cesari)

Note: this applet requires a Java 1.1.5 compatible browser (such as Netscape 4.5).

In the Mandelbrot set page, we have examined the iteration process that has to be applied to each point of the complex plane in order to see whether or not it belongs to the Mandelbrot set. This applet lets you iterate the formula on selected points of the plane. Let's recall the iteration formula:

Z_n = Z_n-1² + C

Clicking on the image, the orbit (i.e. the values assumed by Z_n during the iteration process) of the corresponding complex number C is shown.

The button "Show Iterations" brings up a window that shows the value of Z_n at each step of the iteration process, along with its distance from the origin (called mod(Z_n)).

To change the maximum number of iterations, insert a new value in the text field labelled "Max Iter" and press ENTER.

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