Slope Formula Tutorial for UltraFractal - Page 1



The slope formulas provide a way to create realistic looking 3D textures and lighting effects similar to what can be obtained by ray tracing. Most slope formulas can be used with any coloring method. To obtain the 3D effects one of the lighting formulas must be used (Damien Jones' Lighting ucl, 3D Texturizer Enhanced III, or Direct Color Slope). The strange attractor slope formulas can only be used with one of the lighting coloring formulas. Examples will be provided to aid in understanding how the various formulas can be used. 

Most slope formulas have the following parameters:

Most of the non-attractor formulas have the parameter

Depending upon the formula, attractor slope formulas generate 2D, 3D and 4D strange attractors. They have the following parameters in common with the other slope formulas:

In addition they have the following parameters:

The 3D attractor slope formulas have the following additional parameters:

The 4D attractor slope formulas have the following additional parameters:

Several of the slope formulas for convergent fractals have the parameter

A brief discussion of three additional formulas that use slope techniques will be at the end of the tutorial. The formulas are Slope Apollonian Gasket, Indra's Pearls and Landscape. Slope Apollonian Gasket is a circle inversion formula and Indra's Pearls is a Kleinian Group formula. Separate tutorials for circle/sphere inversion formulas will be available soon.

Most formulas will have formula specific parameters.

Page 2