Yin and Yang 

Yin and Yang ExamplesThe Yin and Yang examples are Newton Fractals based on the equation Carlson  Newton 2. They support 3D shading based on the sample point's angle to create what looks like a 3D relief projecting from the fractal surface. 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 Generation section of the General page. Change the Julia ConstantYou 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. Important: The Mandelbrot fractal will be displayed in grayscale but when you use the Preview Julia command, the resulting Julia Fractal will be in color. 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 Working with Julia Fractals for details. Important: The Mandelbrot fractal will be displayed in grayscale but when you use the Preview Julia command, the resulting Julia Fractal will be in color. 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 TransformationYou 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 change the transformation applied to the fractal, 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. Play with ColorTo play with color, select the color controller's General Options properties page:
General
Set Colors to the number of colors you want to use.
Then click the Color Map to set the colors. Set
Roots to the number of roots associated with the Fractal Equation
you are using, and then for each root index, set the Color
Index and Offset Angle properties. The
Color Index is the index into the
Color Map used for the given root and sets the
color for areas associated with that root. Offset Angle
is used to invert the 3D relief for a given root. You will need to experiment
with these selections to find the best combination for a given Newton (Julia)
fractal. 
Copyright © 20042016 Hilbert, LLC 