**Polar
Traps Tutorial for UltraFractal - Page 1
**

**Introduction**

This tutorial is intended to provide examples and explanations to aid the user in the creation of fractal art using the formula Polar Traps Enhanced. This is a general coloring formula with 31 trap types and 9 variants for each function. It assumes that the user is familiar with the Ultra Fractal program and has some understanding of fractal theory.

The Polar Trap formulas include ideas from Damien Jones, Mark Townsend, Toby Marshall and Michèle Dessureault. It was designed to provide multiple texture, coloring, and shape options for the user. The formula has an expert mode which hides the more advanced options from the beginning user. Some of the expert options will be discussed towards the end of the tutorial. Only the parameters which are visible when the expert mode box is unchecked are listed below.

- Version number - Use the default value. If and old upr does not appear correctly, select "0".
- Expert mode - Because of the large number of parameters available, the more advance parameters are hidden unless the Expert mode box is checked.

The following parameters are in the General Parameters section:

- Trap mode: These are the modes for trapping
an orbit during iteration of the fractal formula. They are:
- Closest - The trapped value is the orbit value closest to the trap function and is less than the trap width.
- First - The trapped value is the first one that has a trap distance less than the trap width. If no value of the orbit is less than the trap width, the pixel is colored with a solid color.
- Last - The trapped value is the last orbit value that has a trap distance that is less than the trap width. If no value of the orbit is less than the trap width, the pixel is colored with a solid color.
- Smallest - The trapped value the orbit value with the smallest absolute value.
- Average - A running average of the distance between the orbit value and the trap function is calculated. The trapped value is the minimum average value.
- Farthest - The trapped value is the greatest distance that is less than the trap width. If no value of the orbit is less than the trap width, the pixel is colored with a solid color.
- Sum - This trap mode is like First, except that the trapped distance values are summed. If no value of the orbit is less than the trap width, the pixel is colored with a solid color.
- Weighted Sum - This trap mode is like First, except that the trapped distance values are a weighted sum. If no value of the orbit is less than the trap width, the pixel is colored with a solid color.
- Weighted Sum 2 - This trap mode is like First, except that the trapped distance values are a second variant of a weighted sum. If no value of the orbit is less than the trap width, the pixel is colored with a solid color.
- Weighted Sum 3 - This trap mode is like First, except that the trapped distance values are a third variant of a weighted sum. If no value of the orbit is less than the trap width, the pixel is colored with a solid color.
- Sum 2 - This trap mode is like Last, except that the trapped distance values are summed. If no value of the orbit is less than the trap width, the pixel is colored with a solid color.
- Weighted Sum 4 - This trap mode is like Last, except that the trapped distance values are a weighted sum. If no value of the orbit is less than the trap width, the pixel is colored with a solid color.
- Weighted Sum 5 - This trap mode is like Last, except that the trapped distance values are a second variant of a weighted sum. If no value of the orbit is less than the trap width, the pixel is colored with a solid color.
- Weighted Sum 6 - This trap mode is like First, except that the trapped distance values are a third variant of a weighted sum. If no value of the orbit is less than the trap width, the pixel is colored with a solid color.

- Coloring Mode
- The coloring mode determines how the color is calculated.
- Distance: The color index is proportional to the distance between the orbit value and the trap function
- Iteration: The color
index is proportional to the number of iterations to reach the trapped
orbit. This has two options.
- Normal - This is the "classical" iteration mode used by most trap formulas
- Discrete colors - This is a special mode that takes the modulus of the iteration value and colors accordingly. The modulus is an additional integer parameter, called # of iteration colors.

- Magnitude: The color index is proportional to the absolute magnitude of the trapped orbit.
- Real: The color index is proportional to the absolute magnitude of the real component of the trapped orbit.
- Imaginary: The color index is proportional to the absolute magnitude of the imaginary component of the trapped orbit.
- Angle: The color index is proportional to the angle of the trapped orbit.
- Trap Magnitude: The color index is proportional to the absolute magnitude of the trap function for the trapped orbit.
- Trap Real: The color index is proportional to the absolute magnitude of the real component of trap function for the trapped orbit.
- Trap Imaginary: The color index is proportional to the absolute magnitude of the imaginary component of trap function for the trapped orbit.
- Trap Angle: The color index is proportional to the angle of trap function for the trapped orbit.
- Exp Iter: The color index is proportional to the product of the trap magnitude and the exponentially smoothed value of the trap function.
- Exp Iter 2: The color index is proportional to the exponentially smoothed value of the trap function.

- Trap variants - This parameter has a pull down list with 9 options which change how the final distance is calculated.
- Trap modulator - Modifies the imaginary component of z before any trap calculations
- Trap width - This parameter sets the distance between the orbit and the trap function that is used for calculating which pixel should be colored with a solid color or the trap color. This is used automatically for trap modes for all modes except Closest and Smallest.
- Distance modulator - Modifies the distance calculated from the trap.
- Distance type - Determines whether, in calculating the trap distance, the final value is the absolute value of the sum (option Abs total) or the sum of the absolute values (option Abs parts).
- Solid background - This is a check box which is displayed for all modes except Closest and Smallest.
- Trapping mask - For trap modes Closest and Smallest this parameter is visible. It has a pull down list with three options: None, Normal and Reverse for mask usage

The next set of parameters are in the Trap Parameters section.

- Trap Type - There are 31 trap types.
- Polar Parameter - Visible for all trap types except Cycloid. It affects the shape of the trap.
- 2nd Polar Parameter - Visible for some trap types. It affects the shape of the trap.
- Trap rotation - Rotation of the trap in degrees.
- Trap skew - Skew of the trap in degrees.
- Trap Offset - Sets the offset for the trap function calculation. For other values, start small and increase the value to see the effect.
- Move Trap Offset - This moves the trap offset relative to the pixel value being calculated. If this is checked, a new parameter becomes visible, called Move Amount, which determines the relative move.