Circle Inversion

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Circle Inversion Examples

Fractal: Circle Inversion

Circle Inversion 01
Circle Inversion 01

Fractal: Circle Inversion

Circle Inversion 02
Circle Inversion 02

The Circle Inversion examples are used to generate a Circle Inversion fractal.

Circle Inversion fractals are described on the Circle Inversion Fractals page on Yale University's Fractal Geometry site.

Change the Circle Inversion Properties

Select the equation's properties page:

General
    Orbital / IFS / Strange Attractor
        Orbital Equation: Circle Inversion
            Properties

Play with the equation's properties.

Change the Transformation

You can apply a transformation to the fractal.

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 fractal, select the Identity transformation's page:

General
    Orbital / IFS / Strange Attractor
        Transformation 1
            Identity

Set the Based On property to one of the available transformations, select the transformation's properties page (found under the transformation in the page hierarchy), and play with the properties found there.

Mobius transformations work especially well in these examples because they preserve circles; i.e., circles are mapped to circles.

To use a Mobius transformation, set the Based On property to one of the following transformations:

  • Mobius Transformation
  • Mobius Transformation - Elliptic
  • Mobius Transformation - Hyperbolic
  • Mobius Transformation - Loxodromic
  • Mobius Transformation - Parabolic
  • Disc Automorphism - Elliptic
  • Disc Automorphism - Hyperbolic
  • Disc Automorphism - Parabolic
  • Disc Automorphism - General
  • Half-Plane to Disk
  • Circle To Circle
  • Poincare Disk
  • Mobius Group

Note that the default for most of these transformations is the identity transformation (which does nothing) so you will need to select the properties page found under the transformation and change the properties in the section labeled Transformation Control.

 

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