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 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 formulas provide the following parameters for the 3D effects:

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 

Orbit Separation

zoomed in images. Avoid to use values that are too small for the current 

precision range

.

Specifies how the apparent height of each pixel will be calculated. 

Smooth images can be obtained with potential and distance 

Height Value

estimator. The other options will produce images with sharper edges.

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 

Height Transfer

of height values. The default linear option will not change the height 

value.

Scales the height value before it is processed by the transfer function.

Height Pre 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 

Height Post Scale

the highlights and shadows do not become too large.

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 

Every Iteration

Traps

. The normal Lighting algorithm does not need this option.

The other parameters are described in the topics for the regular (non Slope) formulas.

See Also

Embossed (Julia, Mandelbrot, Newton)

Standard formulas

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