Help File for ldm.ucl
This is the 'help' file for
'Hoops & Tubes', 'Triangles', and 'Thingamajigs' coloring formulas in
ldm.ucl, and for 'Edge Nibbler' transformation in ldm.uxf. In order for the
'blue question mark' help button in UF to work properly, this file should be
saved in a subdirectory named ldm-help in the Formula directory of UF.
Edge Nibbler Transformation
'Edge Nibbler' is a
transformation for use with Ultra Fractal. The purpose of the transformation is
to give fractal images a frayed edge, or 'worn parchment' appearance by turning
the 'Solid Color' on for certain pixels around the border of the fractal. The
'designs' produced are arrived at by calculation of several numeric parameters
but are not fractal in nature. This transformation, admittedly, is not very easy
to use. However, since it is formula and location independent, once a nice
'edge' is found, it can be copied to any fractal.
The following is a
description of the parameters and functions provided by the transformation. The
ranges of values shown have produced satisfactory results. Feel free to try
values outside those ranges. Some of the parameter captions, particularly those
in single quotes, only vaguely describe the effects of the parameter.
'Amplitude', 'Frequency', Scale, and Angle, together, determine the 'pattern' of
the edge. Width, 'Compression', and Offset work together to determine the
'thickness' of the edge, but may also affect the pattern shape. Not all
functions give pleasing results. The most useful seem to be sin, cos, tan,
cotan, sqr, sqrt, log, exp, floor, and ceil. Depending on other parameters, any
function might work well.
'Amplitude': This and the next three
parameters affect the shape of the edge pattern. Useful values range from 0.1 to
1000.
'Frequency': Higher values generally produce greater
complexity. Range: 5 to 10000.
Scale: Higher values increase the
scale of the patterns. Try 2 to 100 for this parameter.
Angle:
'Rotates' the edge pattern. Values around 90° seem to work best.
Width: Varies the width of the edge measured as a percentage of
the width (and height) of the image. See 'Equal Width Edges'.
'Compression': 'Compresses' the pattern away from the edge of the
fractal, among other things. Negative numbers 'expand' the pattern. Values: -100
to 100.
Offset': Works a little like 'Compression' to move the
pattern away from the edge, but also reduces the width of 'filaments' of the
pattern. Negative numbers work here also. Range: -0.5 to 0.5.
Corner
Size: 'Rounds' the corners. Useful for cleaning up.
Randomness: Adds randomness to the patterns. Be careful when
using this parameter on multiple layers that use the transformation. Each
instance will be a little different. (I guess that's why it's called randomness.
;-)
Separate Functions: With this parameter disabled (unchecked),
each of the three functions operate on the pattern for all four sides. When
enabled, Function 1 works the same, Function 2 works on the sides while Function
3 works on the top and bottom. This way the patterns can be different for the
sides and the top/bottom, but not as many different patterns can be produced.
Flip Right, Bottom: Disabled: top and bottom (and right and left)
patterns match but are 'reversed'. Enabled: 'flips' Right and Bottom edges to
mirror Left and Top.
Solid Interior: Turns everything inside the
edge to the Solid Color.
Reverse Mask: Reverses the areas colored
in the Solid Color with those colored normally.
Equal Width
Edges: Unchecked: Edges are proportional to the image dimensions. Checked:
Edges are equal width."
Functions: The three functions contribute
a lot to the shapes of the patterns. Change them!
Hoops and Tubes Coloring
H&T is a coloring formula
for use with Ultra Fractal for the outside and/or inside of fractals. The
following is a description of the parameters and functions provided by the
coloring formula.
Method: The four 'methods' are a combination of
Trap Mode and Flavor Mode used by other coloring formulas. Depending on the
fractal formula, Methods 1 and 3 are sometimes similar, as are 2 and 4. Default
is 1.
Coloring Mode: Eight coloring modes are available. Each
works in a similar fashion to others by the same name. Default is Distance.
Modifier 1: Changes the appearance in unpredictable ways. Any
real number may be used, but negative numbers have an ill effect on most formula
types. I've found 0 to 200 to be a good range, with 20 to 60 being the best.
With certain formulas, the # can go much higher. Default is 20.
Modifier 2: Also changes the appearance, sometimes giving the
effect of zooming, rotating, and 'twisting' the fractal, all in one step. This
variable should be a positive integer between 0 and Maxiter. Zero is the
default.
Power: Again, this variable changes the appearance, but
in a more predictable way, by varying the width of the 'hoops' or 'tubes'. A
real number between 0 and 8 is a good range. This parameter is not used by
Method 4. Default is 1.
Percent Texture: 'Blends' in texture from
0 to 100%.
Texture Type: Four types of 'triangle-based'
texture.
Texture Scale 1 and Texture Scale 2: Together,
these two parameters determine the scale of the texture.
Texture
Density: Works similarly to 'Color Density'. Positive numbers use division.
Negative numbers use modulus, producing a slightly different effect.
Randomness: Adds 'texture' to the fractal. It uses a real number
between 0 and 1, with .05 to .3 being typical. Disk render times may be greatly
extended when using this variable. Default is 0.
Mask: Allows
areas of the fractal above the upper threshold and below the lower threshold
(unless inverted) to be colored with the Solid Color. The 'Re' portion of mask
is the lower threshold, and 'Im', the upper. Each is expressed as a decimal
fraction of maxiter. (0,1) is the default.
Invert Mask: Inverts
the area of the fractal that is colored with the Solid Color, that is,
everything between the two threshold points. Default is disabled.
Functions 1,2,3: 'Front-end' functions applied to the #z
calculation supplied by the fractal formula. These produce wide variations in
the fractal appearance; much more so than the 'modifiers'. The defaults are:
1:acos 2:sqr 3:ident.
Another function: A 'Mid-point' function
applied after the 'flavor' but before the 'trap'. It can change the appearance
as much as functions 1-3, but usually is not as pronounced. Default is ident.
Final #index function: Basically, an additional color transfer
function. It provides more fine tuning to the transfer function. Default is
asin.
Triangles Coloring
Triangles is a coloring formula for
use with Ultra Fractal for the outside and/or inside of fractals. The following
is a description of the parameters and functions provided by the coloring
formula. The parameters requiring numeric input have been placed in descending
order of importance, more or less. The ranges of values shown have produced
satisfactory results. Feel free to try values outside those ranges. The
"triangles" drawn by this formula are not always triangles in the strictest
sense, many have curved sides.
Scale and Power: These two
numbers, together, determine the scale of the triangles. Useful ranges: For
Scale, .01 to 200, depending on the formula type. For Power, -1 to around 8.
When changing 'Method', it may be necessary to re-adjust these parameters.
(After making this formula public I realized that, for many fractals, 'Density'
can have a greater effect on the scale than 'Power'. 'Scale' and 'Density' also
have an inverse relationship - double one while halving the other for similar,
yet different, effects. ;-)
Density: This parameter works
similarly to 'Color Density'. Positive values use division. Negative values use
modulus, producing a slightly different effect, but somewhat tricky to use.
Range: 5 to 500, -1.9, -0.9, etc.
Method: Changes the drawing
method. There may be duplication among the methods, depending on the function
settings. When triangles are turned off with 'Triangle Type':'None', only
methods 'Trapped z' and 'A' through 'J' are in effect; all others are identical
to 'Trapped z'.
Use of Functions: Changes the number of times and
the manner in which the functions are used. As with 'Method', differences
between selections depend on the function settings.
Triangle
Type: Changes the type of triangles drawn. Available choices are Low and
High Contrast, Relief, Solid Color, Blocks, Mesh, None, and Blend. Mesh draws a
mesh or net, the width of which is determined by 'Boundary Width'. 'None' turns
triangles off - again, only methods 'Trapped z', and 'A' through 'J' are valid
with this choice. 'Blend' combines Low Contrast and 'None'. (And, of course,
Blocks aren't triangles. ;-)
'Invert' Triangles: Changes the look
of the triangles in various ways. Low Contrast triangles change from "outies" to
"innies". High Contrast, Relief, and Blocks change triangle orientation. Solid
Color, None, and Blend change coloring methods. This choice has no effect on
'Mesh'.
Trap Method: Changes the trap type. Coloring Mode:
Changes the coloring method.
Boundary Width: Changes the boundary
or border width along two sides of the triangles. This value is expressed as 0
to 100 percent. (Negative values here are treated the same as positive values
for boundary width but invoke an additional use of the functions to remain
compatible with an earlier version.)
Smoothing: Major hard-edged
boundaries sometimes appear rough, especially when using a negative 'Density'.
This parameter 'smooths' that roughness. Lower numbers mean more smoothing. Best
values appear to be 0.1 to 20. A value of 100 will almost certainly ensure no
smoothing.
Contrast and Granularity: Similar parameters,
both of which affect the graininess of the image. Useful values are 0 to 5 for
either. A little goes a long way.
Iterations to Skip: This
parameter is used only with 'Method' 'Old z'. Values can range from 0 to
Maxiter, with 0 meaning that the final value of #z is used.
Randomness: Adds random 'texture' to the fractal. Expressed as a
decimal value between 0 and 1.
Functions: The Real, Imaginary,
and Overall functions are applied to #z or other values to change the appearance
of the fractal. The 'Use of Functions' determines how these functions are
applied. The 'Additional Function' is used with some, but not all, Methods.
Thingamajigs Coloring
'Thingamajigs' is a coloring
formula for use with Ultra Fractal for the outside and/or inside of fractals.
The following is a description of the parameters and functions provided by the
coloring formula. The ranges of values shown have produced satisfactory results.
Feel free to try values outside those ranges.
Trap Mode: There
are two different types of traps: 1 - E and F - N. Modes 1-E generally draw
smooth colored 'blobs' with a '3-D' effect. Five other parameters -
'Expand+|-Contract','Warp Factor', 'Ripple Control', 'Multiplier' and 'Trap
Modes 1-E Fn', affect only these trap modes. Modes F-N often require different
function settings to achieve pleasing results. (In this update, two more traps
of "Type 1-E" have been added -- 'O' and 'P'. All references to "Trap Modes 1-E"
apply to these new ones as well.)
'Flavor': Varies the pre-trap
calculations using the value of #z. 'Flavors' B through H produce the most
variability with Trap Modes 1-E.
Polar Coordinates: Check to
enable. Rectangular Coordinates is the default.
Coloring Mode:
Changes the coloring method.
Mod Iter. Modulus: The modulus value
for Modulated Iteration Coloring. Examples: 0.99, 1.5, 5
Fractal
Offset: A complex number that can be changed to alter the appearance of the
fractal. The range is about -1.5 to 1.5 for both real and imaginary
components.
Texture Offset: A complex number that can be changed
to alter the appearance of the texture, if it is turned on. More on this below.
(The real portion of this number is also used with Trap Modes D and E as
input.)
Texture Mode: There are two groupings of texture - with
'Patterns' and 'Fuzz' in one group, 'Triangles' and 'Blocks' in the other. The
parameters that change the texture can have very different effects on
each group. For the patterns group, the 'Texture Offset' along with 'Texture
Functions' 1-3 determine the general shape of the texture. (Getting the desired
look can be very tricky.) 'Off' is the default.
Texture Amount:
Varies the amount of texture applied to the 'underlying' fractal. Useful values
range from .01 to 10, depending on the fractal formula.
Texture
Scale: Varies the scale of the texture. Larger values increase the
scale of Triangles and decrease the scale of Patterns. Other parameters
and functions will also affect the scale, so it may be necessary to re-adjust
this parameter.
Texture Density: Works similarly to Color Density,
but is applied only to the texture. (Has no effect on
'Blocks'.)
Texture Modifier: Has different effects on Patterns
(try .01 to 5) and Triangles (try .01 to 500)
Fuzz Factor: For
values greater than 1, this parameter gives a less well-defined edge to the
patterns type of texture; with a useful range of .1 to 10, it can affect the
'Scale' (and shape). Too high a value can produce undesirable artifacts with
patterns. For triangles, this parameter might be considered 'Intensity' - Range:
0.1 - 1000
Change Tx Style: This parameter introduces additional
'distortions' to the triangles textures. For patterns, a Texture Offset of (0,0)
and default function values will produce circular patterns with this parameter
enabled.
Iteration Cutoff: A 'multi-purpose' parameter. For
positive numbers, the Whole, or Integer portion of the parameter is the number
of iterations, after which, texture is no longer drawn. For negative
numbers, the Integer portion is the number of iterations reached before
any texture is drawn. The Decimal portion of this parameter is a multiplier that
'blends' Iteration coloring into areas not drawn with
texture.
Solid Color @ IC: Enabling this parameter turns on the
Solid Color for the 'Iteration Cutoff' value. (Usually works better with
negative values for Iteration Cutoff.)
Randomness: Adds 'random'
texture to the fractal. Values range from .01 to
1.
Expand+|-Contract: Used with Trap Modes 1 through E. Generally,
positive values cause the shapes to expand, negative values contract. Sometimes
the outcome is like squeezing a balloon -- some parts contract while others
expand. 'Warp Factor' affects this parameter. Useful range is around -10 to 10.
Warp Factor: Used with Trap Modes 1 through E, this parameter
'warps' the shapes in various ways. The input range is from about -1.5 to 1.5.
This range was chosen to allow the use of the 'Eyedropper' to select the
parameter at low magnifications ( Magn. 1 to 2 will normally cover the full
range of useable values when selecting with the Eyedropper.)
Warp Set
2: Changes the way the Warp Factor works. Disabled: generally produces more
pleasing shapes; small increments produce small changes. Enabled: discontinuous
around zero, less pleasing, but can yield some nice surprises.
'Ripple
Control': Adds 'ripples' to the fractal when using Trap Modes 1 through E. A
few trap modes are unaffected by this parameter. 'Multiplier' value can have a
significant effect on this parameter. Useful range is -50 to
50.
Multiplier: Used only with Trap Modes 1 through E. Typical
values are 1-9.
Iters to Skip: The Integer portion of this
parameter is the number of iterations, after which, trapping is discontinued.
This can be useful for smoothing the grainy appearance of the 'inner' parts of
some fractals. The Decimal portion of this parameter modifies the trapped
values, and works better with Trap Modes F through N.
Soften
Color: Two different approaches to coloring Trap Modes 1-E. At times,
enabling the change may work better than the default.
Mask
Threshold: All values of trapped #z that are less than this parameter are
drawn in the Solid Color. The effective range is .01 to around 2.0. For Julias
and many other formulas, useful values fall into a more narrow range of 0.8 to
1.0 This parameter usually works better with Trap Modes 1-E.
Reverse
Mask: Reverses the areas drawn in the Solid Color with those drawn
normally.
Functions: The 'Initial', 'Real', 'Imaginary',
'Overall', and 'Trap Mode 1-E' functions change the appearance of the fractal.
'Texture Functions' 1-3 alter the texture in various ways. The 'Final #index'
function works similarly to the 'Transfer Function' except it is applied only to
the non-texture part of the fractal. (To see texture only, set this to
zero.)