Chained Marble 

Chained Marble ExamplesThe Chained Marble examples apply a Circle Orbit Trap to a Newton Fractal based on various Fractal Equations. The coloring is achieved by mapping the trap's dwell (i.e., orbit index value) to 1 of 4 gradients and then mapping the trapped point's magnitude into a gradient to select the color. Then the color is blended with a Perlin noise based pattern to give it a stonelike appearance. Note the following:
In the remaining sections, when I refer to the equation, I will use Newton 2, but you should use the equation 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. Remember that as you Zoom In, you may need to increase the Max Dwell property found in the Orbit Trap Orbit Generation section of the General page. Play with the Fractal Equation's PropertiesYou can change the equation's properties for more variations. Select the equation's properties page:
General Play with the equation's properties. Explore the Julia FractalsFor the Mandelbrot Fractal examples, 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 the Julia ConstantFor the Julia Fractal examples, you can generate other Julia Fractals based on the same equation. Select the Fractal Equation:
General Uncheck the Julia checkbox, 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. Alternatively, you can change the Julia Constant property on the Fractal Equation page, and then click the Preview Fractal toolbar button on the Properties Window to generate a preview of your change in the Preview Window. Change the Fractal EquationYou can change the Fractal Equation used to generate the fractal. Select the Fractal Equation:
General Change the Based On property to one of the following Fractal Equations:
Then 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 Preview Julia Support for details. Remember to navigate to the properties page for the equation (found under the equation in the page hierarchy) and play with the different properties found there. Many of the equations support properties that can be used to generate lots of different variations. Change the Orbit TrapYou can try out different Orbit Traps. Select Instructions: Circle:
General Change the Based On property to one of the following 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. There are several orbit traps not given in the above list since they are standalone fractals or are too complex to display in this context. 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. Change the TransformationYou can apply a transformation to the initial orbit point, or to each orbit point prior to passing it to the orbit trap. 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 initial orbit point, 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:
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. To change the transformation applied to each orbit point prior to passing it to the orbit trap, 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. Play with ColorTo play with color, select the color controller's properties page:
General Change the Power, Factor, and Offset properties in the Value Map section to control how colors are mapped onto the image. 
Copyright © 20042017 Hilbert, LLC 