Sierpinski Variations

The Sierpinski Variations example generates a set of attractors based on a variation of the algorithm used to generate the classic Sierpinski Triangle. A set of points is defined along with a transformation per point. A point is randomly selected and the transformation is used to alter the location of the current orbit point.

Experiment 1

Change the attractor. To do this, select the equation's Point Information properties page:

General
    Orbital / IFS / Strange Attractor
        Orbital Equation: Sierpinski N-gons (Variations)
            Point Information

Change the Example property to 1 of the predefined examples or define your own set of points/transformations using the properties on this page.

The Weight property controls the relative probability of selecting the associated point during orbit processing and can add depth to the resulting image in some situations. Try setting the Weight values for all the points equal to 1 and then set the Weight for one of the points to 4. Very different results are obtained depending on which point you choose.

Experiment 2

Change the number of vertices in the base polygon. To do this, select the equation's General Options properties page:

General
    Orbital / IFS / Strange Attractor
        Orbital Equation: Sierpinski N-gons (Variations)
            General Options

Change the Vertices property to try higher order polygons. You can also change the Reflect, Rotate, and Scale properties which affect the transformations applied to each of the points.

Experiment 3

Change the non-linear transformation applied to each point. To do this, select the transformation's Properties page:

General
    Orbital / IFS / Strange Attractor
        Orbital Equation: Sierpinski N-gons (Variations)
            Transformation Array
                Shape Value
                    Properties

Set the Shape property to 1 of the 167 different shape types. When you change the Shape (or any of the other properties associated with the other experiments for this example), if the image is too dense, try reducing the Radius property. If the image is too sparse, try increasing Radius. Small changes to Radius can result in large changes in the image.

Experiment 4

Change the transformation applied to the base fractal. To do this, select the transformation's Properties page:

General
    Orbital / IFS / Strange Attractor
        Transformation 1
            Composite Function
                Properties

Set the F(z) property to one of the complex functions in the list. You can change some of the other properties on this page for more variations.