Slope (Julia, Mandelbrot, Newton)

The Slope formulas are modifications of the classic Mandelbrot, Julia, and Newton fractals that can create various 3D lighting effects. They are available as fractal formulas in Standard.ufm and as a fractal formula plug-in in Standard.ulb.

In plug-in form, Slope uses a plug-in parameter to select which fractal formula to use, so it is not just limited to Mandelbrot, Julia or Newton fractal types. See Example 1 - Formula plug-ins for more information.

Slope should be combined with the Lighting coloring algorithm. For each pixel, the Slope formula calculates a "height" value that is passed to Lighting, which performes the final lighting calculations.

For best results, use a black-to-white gradient such as Lighting in Standard.ugr. This will create a grayscale image with highlights and shadows. You can then combine this with other layers to add colors while retaining the 3D effect. For the merge mode of the layer with the Slope formula, try Soft Light or Hard Light.

The following parameters are provided:

Fractal Formula	Selects the fractal formula to use for the lighting effect. (Plug-in version of Slope only.)
Orbit Separation	To determine proper lighting for a particular point, the Slope formulas test two orbits that are close together. This parameter specifies how close they should be. Smaller values give better results, especially for zoomed-in images. Avoid to use values that are too small for the current precision range.
Height Value	Specifies how the apparent height of each pixel will be calculated. Smooth images can be obtained with potential and distance estimator. The other options will produce images with sharper edges.
Height Transfer	This function will be applied to the height value before calculating the slope. It can be used to reduce (log) or exaggerate (exp) certain ranges of height values. The default linear option will not change the height value.
Height Pre-Scale	Scales the height value before it is processed by the transfer function.
Height Post-Scale	Scales the height value further after it has been processed by the transfer function. When zooming in, you should reduce this to make sure the highlights and shadows do not become too large.
Every Iteration	If selected, the height value is calculated every iteration, which is much slower. This is only necessary if you are combining the Slope formula with a coloring algorithm that processes every iteration, such as Orbit Traps. The normal Lighting algorithm does not need this option.

For the non-plug-in version of the Slope fractal formulas, the other parameters are described in the topics for the regular (non-Slope) formulas.