Rep-9 Tile

The Rep-9 Tile example displays a Rep-Tile based on up to 9 affine transformations. A symmetry transformation is used to generate 3-way dihedral symmetry from the base tile. The default property settings completely fill the base tile. Options are provided to omit 1 or more of the affine transformations to generate more interesting images.

Experiment 1

Omit 1 or more of the Rep-9 Tile affine transformations. To do this, select the equation's Properties page:

General
    Orbital / IFS / Strange Attractor
        Orbital Equation: Rep-9 Tile
            Properties

Uncheck 1 or more of the 9 checkboxes labeled Include T1 through Include T9. Unchecking 1, 2, or 3 checkboxes works best.

Experiment 2

Change the base Rep-9 Tile. To do this, select the equation's Properties page:

General
    Orbital / IFS / Strange Attractor
        Orbital Equation: Rep-9 Tile
            Properties

Change the Type property to any of the types found there; i.e.,

• Isosceles Trapezium
• 45 Degree Wedge Trapezium
• 60 Degree Wedge Trapezium
• L-Triomino
• Sphinx
• Stellated Fish
• Stellated Bird
• Stellated Ampersand

This changes the base shape used to generate the tile. Note that since 45 Degree Wedge Trapezium and L-Triomino do not have a 60 degree angle at the origin, the symmetry transformation as currently defined, either has gaps (45 Degree Wedge Trapezium) or overlaps parts of the base tile (L-Triomino), but it still looks good! You can change the symmetry transformation to prevent the gaps/overlap in these cases, if required. See the program comments for details.

Experiment 3

Change the transformation applied to the base fractal before the symmetry transformation. 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.

Since this transformation is applied before the symmetry transformation (i.e., the output from this transformation is passed to the symmetry transformation), the resulting image will maintain the 3-way dihedral symmetry defined by the symmetry transformation.

Experiment 4

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

General
    Orbital / IFS / Strange Attractor
        Transformation 2
            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.

Since this transformation is applied after the symmetry transformation (i.e., the output from the symmetry transformation is passed to this transformation), the resulting image will not maintain the 3-way dihedral symmetry defined by the symmetry transformation.