Fractal Sculpture 

Fractal Sculpture ExamplesThe Fractal Sculpture examples display an Orbit Trap in the context of a symmetry transformation. The fractal is colored using a blend of Perlin Noise and a background pattern. Note the following:
In the remaining sections, when I refer to the symmetry transformation, I will use Transformation Shift  Circular Path, but you should use the symmetry transformation for the example you are working with, and when I refer to the orbit trap, I will use Circle Inversion, but you should use the orbit trap for the example you are working with. Zoom In/OutZoom 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. Explore the Julia FractalsSince these examples are Mandelbrot Fractals, you can use the Preview Julia command to explore the Mandelbrot's many different Julia Fractals. This is a common technique that can be used to generate lots of different Julia fractals from a single Mandelbrot image. Execute the Home command on the View menu of the Fractal Window to reset the Mandelbrot fractal to the default position/magnification, and use the Preview Julia command to explore the Mandelbrot's many different Julia Fractals. See Working with Julia Fractals for details. Change Transformation 1You can change the transformation applied to the orbit point prior to 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 change the transformation applied to the orbit point prior to applying the symmetry transformation, select the transformation's properties page:
General 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. You can also use a different transformation altogether. Select the Composite Function page, and 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 Click the New toolbar button to add a new Identity transformation to the bottom of the list, and then click the Move Up toolbar button to move the new transformation to the desired position in the list. Normally, I move the new transformation to the top of the list, but it can be placed anywhere. See Transformation Array for details. Then select the Identity transformation:
General 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 2You can change the transformation applied 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 change the transformation applied to the orbit point after applying the symmetry transformation, select the transformation's properties page:
General 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. You can also use a different transformation altogether. Select the Composite Function page, and 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 Click the New toolbar button to add a new Identity transformation to the bottom of the list, and then click the Move Up toolbar button to move the new transformation to the desired position in the list. Normally, I move the new transformation to the top of the list, but it can be placed anywhere. See Transformation Array for details. Then select the Identity transformation:
General 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 Transformation within the Symmetry TransformationYou can change the transformation applied to the orbit point within the symmetry transformation. Select the transformation's properties page:
General 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. You can also use a different transformation altogether. Select the Composite Function page, and 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 Properties for the Symmetry TransformationYou can change the properties that control the symmetry transformation. Select the transformation's properties page:
General Change any of these properties to define the symmetry transformation. Change the Symmetry TransformationYou can try a different symmetry transformation. Select the symmetry transformation:
General Change the Based On property to one of the following symmetry transformations:
After selecting one of the symmetry transformations, select the transformation's properties page and change the properties found there. Change the Orbit TrapYou can try out different Orbit Traps. Select Instructions: Circle Inversion:
General Change the Based On property to one of the other Orbit Traps. Each of these programs have properties (on the properties page found under the orbit trap) to manipulate the trap and thereby change the resulting fractal. Note that some of the property settings result in solid polygons/shapes and should be avoided. You can also try out the different optimized orbit traps. To do this, select Orbit Trap Map:
General Change the Type property to one of the following:
Each of these orbit traps have properties (on the page found under the Orbit Trap Map page) to manipulate the trap and thereby change the resulting fractal. 
Copyright © 20042014 Hilbert, LLC 