Complex Analysis (Identity)	Complex Analysis (Bipole)

The Complex Analysis example is not a fractal but illustrates how the Fractal Science Kit can be used for visualizing complex transformations.

Complex Analysis (Identity) is the base image with no transformation applied. As you can see, each of the 4 quadrants are displayed with a different color, shaded so that the color gets darker as it approaches the axes. On top of the quadrants, a grid is displayed where the color represents the angle of the associated point.

Complex Analysis (Bipole) shows the results of applying the Bipole() function which is defined as:

Bipole(z) = 1/(z+1) + 1/(z-1)

To change the transformation applied to the base image, select the transformation's Properties page:

General
    Mandelbrot / Julia / Newton
        Transformation
            Composite Function
                Properties

Set the F(z) property to one of the complex functions in the list.

If you want to test a complex transformation not found in the list, select the Composite Function properties page:

General
    Mandelbrot / Julia / Newton
        Transformation
            Composite Function

Change the Based On property from Composite Function to the Identity transformation (the 1^st entry in the list).

Now, click on the  editor pane labeled Instructions at the bottom of the properties page and type the transformation you want to try into the Editor. The transformation should be given as an assignment statement to the variable z.

For example, to use the same transformation as above, type:

z = 1/(z+1) + 1/(z-1)