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.)