Elliptic Splits IFS

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Elliptic Splits IFS Examples

Fractal: Elliptic Splits IFS

Archangel II
Elliptic Splits IFS 22

Fractal: Elliptic Splits IFS

Forest of Fangorn II
Elliptic Splits IFS 24

Fractal: Elliptic Splits IFS

Elliptic Owl II
Elliptic Splits IFS 25

Fractal: Elliptic Splits IFS

The Wings of Angels
Elliptic Splits IFS 26

Fractal: Elliptic Splits IFS

Angelic Star
Elliptic Splits IFS 27

Fractal: Elliptic Splits IFS

Shangri-La
Elliptic Splits IFS 28

Fractal: Elliptic Splits IFS

Autumn Star II
Elliptic Splits IFS 29

Fractal: Elliptic Splits IFS

Spiral Plume II
Elliptic Splits IFS 30

Fractal: Elliptic Splits IFS

Mayan Bird Deity
Elliptic Splits IFS 31

Fractal: Elliptic Splits IFS

Sea Star
Elliptic Splits IFS 32

Fractal: Elliptic Splits IFS

Embroidered Starburst
Elliptic Splits IFS 33

Fractal: Elliptic Splits IFS

Chrysanthemum
Elliptic Splits IFS 34

Fractal: Elliptic Splits IFS

Cheshire Cat
Elliptic Splits IFS 35

Fractal: Elliptic Splits IFS

Oxygen
Elliptic Splits IFS 36

Fractal: Elliptic Splits IFS

Thorns and Beetles I
Elliptic Splits IFS 37

Fractal: Elliptic Splits IFS

Thorns and Beetles II
Elliptic Splits IFS 38

Fractal: Elliptic Splits IFS

Mayan Shield
Elliptic Splits IFS 39

Fractal: Elliptic Splits IFS

Center of Gravity
Elliptic Splits IFS 41

Fractal: Elliptic Splits IFS

Abstract Fresco
Elliptic Splits IFS 43

Fractal: Elliptic Splits IFS

Diamond in the Rough
Elliptic Splits IFS 44

 

The Elliptic Splits IFS examples are based on the Orbital Equation Elliptic Splits IFS.

The Elliptic Splits IFS equation is based on information given by SaTaNiA on the page Tutorial - Splits elliptic.

Symmetry Transformations

Some of these examples apply a Symmetry Transformation to improve the fractal generation performance.

For example, if a fractal design exhibits reflective symmetry about the X axis (i.e., the fractal image below the X axis is a reflection of the image above the X axis), you can add a Symmetry Transformation that reflects points about the X axis to improve the performance of the fractal processing without altering the fractal image. The reason you need to be aware of this is because you might change something in the example that alters or eliminates the symmetry in the fractal, and if you do not change or remove the Symmetry Transformation, it will continue to inject the symmetry of the original example into the image. Sometimes this can result in an interesting image, but it can also result in a mess, so my rule of thumb is to check if there is a Symmetry Transformation applied to the image, and if so, reset it to the Identity transformation if your experiments seem to be adversely affected.

To check if a Symmetry Transformation is in effect, look for the Identity transformation:

General
    Orbital / IFS / Strange Attractor
        Symmetry Transformation: Identity

If you find the Identity transformation is selected as shown above, then no Symmetry Transformation is in effect. Otherwise, select the properties page for the transformation that is in effect to view the details. To reset the the symmetry transformation to the Identity transformation, select the existing symmetry transformation and change the Based On property to Identity.

Finally, when you apply a transformation to a fractal, you can apply the transformation before applying the symmetry transformation or after applying the symmetry transformation. If no Symmetry Transformation is in effect, then the distinction is irrelevant. However, if a Symmetry Transformation is in effect, the distinction is important.

Zoom In/Out

Zoom In or Zoom Out to examine different parts of the fractal.

Execute the Home command on the View menu of the Fractal Window to reset the fractal to the default position/magnification, and then Zoom In to other areas.

Remember that as you Zoom In, you may need to increase the Max Count property found in the Orbital / IFS / Strange Attractor section of the Orbital / IFS / Strange Attractor page to strengthen the image.

Play with the Orbital Equation's Properties

You can change the equation's properties for more variations.

Select the equation's properties page:

General
    Orbital / IFS / Strange Attractor
        Orbital Equation: Elliptic Splits IFS
            Properties

Change the properties on this page to control the fractal generation.

ColorBits sets the number of colors to 2^ColorBits; i.e.,

ColorBits 1 2 3 4 5 6 7 8
Number of colors 2 4 8 16 32 64 128 256

The rest of the properties control the shape of the fractal. When experimenting with these properties, small changes work best.

Additional information is given in the comment section of the Orbital Equation so select the equation's page and read the comments at the top of the program.

Change Transformation 1

You can apply a transformation to the orbit point before applying the symmetry transformation.

Execute the Home command on the View menu of the Fractal Window to reset the fractal to the default position/magnification before you adjust the transformation. Then change the transformation and Zoom In to interesting areas of the transformed image.

In the following discussion, when I refer to the transformation, I will use Identity, but you should use the transformation for the example you are working with.

To apply a transformation to the orbit point before applying the symmetry transformation, select the Identity transformation's page:

General
    Orbital / IFS / Strange Attractor
        Transformation 1
            Identity

Change the Based On property to select a transformation and then open the transformation's properties page (found under the transformation in the page hierarchy), and play with the transformation's properties. See Transformation Support for details.

To add additional transformations, select Transformation 1:

General
    Orbital / IFS / Strange Attractor
        Transformation 1

Click the New toolbar button to add a new Identity transformation to the bottom of the list. See Transformation Array for details.

Then select the Identity transformation:

General
    Orbital / IFS / Strange Attractor
        Transformation 1
            Identity

Change the Based On property to select a transformation and then open the transformation's properties page (found under the transformation in the page hierarchy), and play with the transformation's properties. See Transformation Support for details.

Change Transformation 2

You can apply a transformation to the orbit point after applying the symmetry transformation.

Execute the Home command on the View menu of the Fractal Window to reset the fractal to the default position/magnification before you adjust the transformation. Then change the transformation and Zoom In to interesting areas of the transformed image.

To apply a transformation to the orbit point after applying the symmetry transformation, select the Identity transformation's page:

General
    Orbital / IFS / Strange Attractor
        Transformation 2
            Identity

Change the Based On property to select a transformation and then open the transformation's properties page (found under the transformation in the page hierarchy), and play with the transformation's properties. See Transformation Support for details.

To add additional transformations, select Transformation 2:

General
    Orbital / IFS / Strange Attractor
        Transformation 2

Click the New toolbar button to add a new Identity transformation to the bottom of the list. See Transformation Array for details.

Then select the Identity transformation:

General
    Orbital / IFS / Strange Attractor
        Transformation 2
            Identity

Change the Based On property to select a transformation and then open the transformation's properties page (found under the transformation in the page hierarchy), and play with the transformation's properties. See Transformation Support for details.

Change the Symmetry Transformation

You can apply a Symmetry Transformation to inject symmetry into the image.

Typically, a Symmetry Transformation is used to improve performance by adding a transformation that mirrors the symmetry inherent in the fractal image already. However, in some cases, you can add a Symmetry Transformation to inject symmetry into an image where none existed before. In either case, the method is the same.

Select the symmetry transformation:

General
    Orbital / IFS / Strange Attractor
        Symmetry Transformation: Identity

Change the Based On property to select a Symmetry Transformation and then open the transformation's properties page (found under the transformation in the page hierarchy), and set the transformation's properties.

Play with Color

To play with color, select the color controller's properties page:

General
    Orbital / IFS / Strange Attractor
        Controllers
            Color Map - Index
                Properties

Change any of the properties on this page except Index Map.

 

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