Orthocenter Examples
Barbed Nautilus |
Jeweled Crown |
Samurai Armor |
Starlit Pagoda |
Japanese Lantern |
Metal Sculpture |
Samurai Armor II |
The Orthocenter examples are based on a Triangle Metric called Orthocenter.
For each iteration in the orbit, I form a triangle from the last 3 orbit points and compute the Orthocenter of the triangle. I keep track of the Orthocenter with the Minimum Value over the entire orbit, and use this point to color the sample point.
Note the following:
| Example | Fractal Type | Fractal Equation |
| Orthocenter 01 | Julia Fractal | Mandelbrot |
| Orthocenter 02 | Julia Fractal | Mandelbrot |
| Orthocenter 03 | Julia Fractal | Mandelbrot |
| Orthocenter 04 | Julia Fractal | Mandelbrot |
| Orthocenter 05 | Mandelbrot Fractal | Mandelbrot |
| Orthocenter 06 | Mandelbrot Fractal | Mandelbrot |
| Orthocenter 07 | Julia Fractal | Mandelbrot |
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 Dwell property found in the Orbit Generation section of the General page.
Explore the Julia Fractals
For 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 Constant
For the Julia Fractal examples, you can generate other Julia Fractals based on the same equation.
Select the Fractal Equation:
General
Mandelbrot / Julia /
Newton
Fractal Equation: Mandelbrot
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 Equation
You can change the Fractal Equation used to generate the fractal.
Select the Fractal Equation:
General
Mandelbrot / Julia / Newton
Fractal Equation: Mandelbrot
Change the Based On property to one of the other 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, Zoom In or Zoom Out to examine different parts of the fractal, and use the Preview Julia command to explore the Mandelbrot's many different Julia Fractals. See Working with Julia Fractals 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 Triangle Metric
You can change the Triangle Metric on which the fractal is based.
Select the Triangle Metric page:
Change the Triangle Metric property in the p1 section. You can change the other properties on this page too. See Triangle Metric for details.
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.
Note the following:
- Orthocenter 01 applies the Identity transformation.
- Orthocenter 02 applies the Identity transformation.
- Orthocenter 03 applies the Identity transformation.
- Orthocenter 04 applies the Disc Automorphism - General transformation.
- Orthocenter 05 applies the Composite Function transformation.
- Orthocenter 06 applies the Composite Function transformation.
- Orthocenter 07 applies the Identity transformation.
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 fractal, select the Identity transformation's page:
General
Mandelbrot / Julia / Newton
Transformation
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:
General
Mandelbrot / Julia / Newton
Transformation
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
Mandelbrot / Julia / Newton
Transformation
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.