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Applet Tutorials: Mandelbrot

This applet visualises the Mandelbrot set onto a complex plane.

[Def. Mandelbrot set]

The Mandelbrot set M consists of all of those (complex) c-values for which the corresponding orbit of 0 under z^2 + c does not escape to infinity.

Although it is not possible to determine if certain c-values lies in the Mandelbrot set, as the number of iteration increases (to infinite), the closer boundary of M can be plotted.

[For more technical information about the available parameters, click here.]

Most parameters are self-explanatory and you can always see brief description of each parameter by moving the mouse pointer over the wizard.

First of all, define the "Width" and "Height" of the applet area and select a value for "Resolution." Resolution is the magnification rate of the internal image size.

For example, the value 3 gives three times as big image size as the internal image has. So, it works as a zooming parameter.

As for colouring of the boundary of M, 27 palettes are available. Choose a palette number and explore the result.

Look at the bottom of the left picture. Determine "StartX" and "StartY" values. These are the initial values with which recursive calculation of z(n+1)=z(n)^2 + c (z=x+yi) begins.

Xmin and Ymax determine normal XY complex plane scrolling values, while Xmax and Y min give XY magnification rate.

Proceed to the expert menu.