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
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.