Enhanced
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 formulas listed below. It assumes that the user is
familiar with the Ultra Fractal program and has some understanding of fractal
theory.
The Enhanced
Trap formulas include ideas from Damien Jones, Mark Townsend, Dennis Magar, and
Red
Williams. They were designed to provide multiple texture and
coloring options for the user. There are a large number of options (parameters)
in each formula, which can be confusing without some suggestions and guidance
for their use. The formulas covered by the
tutorial include:
4D Orbit Trap Enhanced
Chip
Orbit Trap Enhanced
CosMartin Orbit Trap Enhanced
Henon Orbit Trap Enhanced
Hopalong Orbit Trap Enhanced
Ikenaga Orbit Trap Enhanced
Liar Orbit Trap Enhanced
Modified Pickover Orbit Trap Enhanced
Quadruptwo Trap Enhanced
ThreePly Trap Enhanced
Except for trap function specific parameters, all formulas have the same set
of parameters.
- Use original version - This is for backwards
compatibility. All subsequent changes to the formulas are managed by a
hidden version parameter.
- 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.
- 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 6 options which change how the final distance is calculated.
- 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 First and
Last.
- Trapping mask - For trap modes Closest,
Smallest and Average 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.
- Pre Function - Applies a user selected
function to the value passed from the fractal formula before calculation of
the trap function.
- Post Function - Applies a user selected
function to the value passed from the fractal formula after calculation of
the trap function.
- Trap Offset - Sets the
offset for the trap function calculation. For
other values, start small and increase the value to see the effect.
- Starting Offset
- Sets the offset for the start of the trap distance calculations. 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.
- Trap rotation - Rotation of the trap in
degrees.
- Trap skew - Skew of the trap in degrees.
The remaining parameters are visible when the Expert
mode box is checked.
This set of parameters will appear in the General
Parameters section.
- Use all iterations - When this box is checked
all iterations are used in calculating the trap. If it is unchecked, four
additional parameters become visible:
- Initial iterations - The default value is
zero. A non-zero value will cause the trap calculations to skip the
first number of iterations indicated by this parameter.
- Iterations to trap - The default value is
zero. By itself it has no effect. If used with Iterations
to skip and/or Pattern repeat, a
selected number of iterations will be trapped, as explained below.
- Iterations to skip - This parameter is
used in conjunction with Iterations to trap. The two parameters together
set a pattern which will repeat as indicated by the Pattern
repeat parameter.
- Pattern repeat - Sets the number of
times the Iterations to Trap/Iterations to skip
combo will repeat. A value of zero will cause the pattern to repeat
until bailout.
This set of parameters will appear in the fBm Texture
parameters section.
- fBM Weight -
Determines how strongly the fBM noise is applied to individual pixels to
distort the image.
- fBM Transfer Function -
Function for applying the fBM noise to the pixels.
- fBM Transfer Weight -
Determines how strongly the pixel distortions are applied to orbit value.
- fBM Offset
- Offset of the fBM noise. This moves the color scale and the noise pattern
around.
- fBM Scale -
Scale of the fBM noise. Larger values are needed for zooms.
- fBM Final Weight -
Determines the total weighting of general noise to trap distortion noise in
the color index.
This set of parameters will appear in the General Texture
Parameters section.
- Texture offset - Affects the texture
pattern
- Texture Weight - Sets
the intensity of the texture.
- Texture Scale
- Sets the size of the texture. Larger values are needed for zooms.
- Texture Modifier -
Primarily affects the detail level of the texture. Smaller values simplify
the texture.
- Texture Power -
Affects general appearance of the texture and how it scales over the trap.
The effect can be very dependent upon the particular fractal.
- Texture Function 1 -
Affects the texture pattern and scale.
- Texture Function 2 -
Affects the texture pattern and scale.
Each of the formulas has a section with trap function-specific parameters.
For example, the Chip Orbit Trap Enhanced formula has a section titled Chip
Parameters:
- Alpha - This is a parameter for the Chip
strange attractor.
- Beta - This is a parameter for the Chip
strange attractor.
- Gamma - This is a parameter for the Chip
strange attractor.
- Scale - This scales the trap function before
an iterations of the trap function.
- Chip iterations - This defines the number of
iterations of the Chip formula before it is used for trapping an orbit.