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.