Power Fractal Shader v3

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Power Fractal Shader v3


Overview[edit]

The Power Fractal Shader is one of the most important and fundamental shaders used in Terragen. Based on a choice of fractal formulas, it provides the user with the ability to create and control the distribution and displacement of many functions in any Terragen project. The fractal detail provided by this shader is user-defined and adaptable to any scale required, ranging between the order of magnitude of a tiny grain of sand, up to planetary structures.

Usually, the Power Fractal Shader is sourcing information to other shaders, such as a surface shader or cloud shader, which then interpret the fractal information provided, relative to the functions these other shaders perform.

Fractals can be used for displacement or for colour, or for both displacement and colour. When we refer to the amplitude of a feature, this is related to the "displacement amplitude" when used for displacement or the "colour contrast" when used for colour. The colour generated by a shader is often interpreted in other ways when connected to other shaders. Examples are the density of a cloud layer or the fractal breakup applied to another surface layer.

Scale is measured in texture space, which is not the same as the "tallness" of a feature. For example, you can have a feature scale of 100 km but its features only 10 metres tall.

The default scene contains a Power Fractal Shader which has been renamed "Base Colors". This shader provides color to the planet surface. To be precise, it provides a fractal distribution of colors, ranging from grey to black, at a certain fractal detail, contrast and color roughness. Under its Displacement Tab, the “Apply displacement” checkbox has been disabled so as not to provide additional 3D structure to the planet surface.

Settings

  • Name: This setting allows you to apply a descriptive name to the node, which can be helpful when using multiple Power fractal shader nodes in a project.
  • Enable: When checked, the node is active and the settings below will affect the surface. When unchecked, the node is ignored.
  • Seed: This setting controls the noise pattern generated. Each seed value generates a slightly different pattern. You can either set the value manually or use the Random Seed button at right to generate a random value.
  • Random seed: Clicking this button will randomly choose a new value for the “Seed” setting.
    The Seed value and Random seed button can be used to generate variations of the fractal pattern without having to change any of the other settings.
  • Mask by shader: When checked, the Power fractal shader is masked by the shader or function nodes assigned to this setting. Whiter parts of the masking shader show more of the image map. Shades of grey control the opacity of the image map.
  • Fit mask to this: When checked, the masking shader or function nodes are remapped to fit into the area of the image map shader. When unchecked, the masking shader determines the area to which the mask is applied.
  • Invert mask: When checked, the shader or function nodes assigned to the Mask by shader input are inverted. For example, light parts become dark and vice versa.

Scale Tab[edit]

Scale Tab


  • Feature scale: The dominant features in the fractal pattern occur at the "feature scale", therefore any positive value may be used. Features that are smaller than the feature scale have a reduced amplitude, that is, the amplitude continues to diminish as the scale gets smaller, at a rate that depends on the roughness parameters.
    Feature scale values on terrain at 1500, 5000, and 12500 metres.
    Feature scale values on cloud layer at 500, 1500, and 5000 metres.
    Feature scale values on planet at 10,000 metres, 100,000 metres, and 1,000,000 metres.


  • Lead-in scale: This setting should always be the largest feature that is visible in the texture. Any positive value may be used. With clouds, for example, the lead-in scale allows you to create variations that occur over large areas of the sky, even if you want more prominent features at a smaller scale.
    Lead-in scale values on terrain at 5000, 25000, and 100000 metres.
    Lead-in scale values on cloud at 7500, 50000, and 100000 metres.
    Lead-in scale value on planet at 250000, 1 million, and 5 million metres.


  • Smallest scale: This setting may be any positive value, and sets the fractal pattern’s limit for producing detail, so that the shader does not calculate detail to an infinite level. The fractal does not create detail below this scale. If this is the only fractal in your surface or texture, then it will be smooth below this scale.
    Smallest scale values on terrain at 0.1, 100 and 1000 metres.
    Smallest scale value on cloud layer at 0.1, 1000 and 1,500 metres.


  • Noise octaves: This setting controls the number of layers which are combined to make up the noise pattern. The noise in each additional layer is twice the frequency of the previous layer. This has the effect of adding finer detail to the noise pattern.
    Noise octave values on terrain ranging between 2 and 20.
    Noise octave values on cloud layer ranging between 2 and 20.
    Noise octave values on planet ranging between 2 and 20.


  • Obey downstream smoothing filters: This setting allows the shader to take into consideration the Smoothing scale setting value of any Smoothing filter shaders located downstream from its position in the node network. The Smoothing filter forces the Power Fractal shader not to generate features smaller than its Smooth scale value thereby smoothing the output of the Power Fractal shader..
    The Smoothing scale setting on Smoothing filter shaders downstream from the Power fractal shader limits the feature size generated by the Power fractal shader.
    The Smoothing scale setting on Smoothing filter shaders downstream from a cloud layer limits the feature size generated by the Power fractal shader.
    The Smoothing scale setting on Smoothing filter shaders downstream from the Power fractal shader limits the feature size generated by the Power fractal shader.


  • Noise stretch XYZ: This setting stretches, or scales, the noise pattern along the XYZ axis.
    The fractal noise pattern can be stretched along any or all of its axis via the Noise stretch XYZ setting.
    The fractal noise pattern can be stretched along any or all of its axis via the Noise stretch XYZ setting.
    The fractal noise pattern can be stretched along any or all of its axis via the Noise stretch XYZ setting.


Colour Tab[edit]

Colour Tab

The settings on this tab allow you to tweak the color information generated by the fractal, which in turn impacts the functions or nodes reading the information from this shader.

For example, a Power fractal shader with a colour range from black to white might be assigned to the Colour function parameter of a Surface layer in order to create variations of the colour defined by its Apply colour setting.

A Power fractal shader assigned to the Colour function setting of a Surface layer.


Or, a Power fractal shader might be used to tint a tree population, changing their folliage from green to autumnal colours.

A Power fractal shader assigned to the Diffuse tint colour setting of a population.


  • Apply high colour: When checked, the colour value to the right determines the high end of the power fractal’s colour range. The Power fractal shader generates a range of colours between this setting and the Apply low colour setting. When unchecked, the colour values defined by other shaders upstream from this shader are passed through.
    When the Apply high colour setting is unchecked, colour values from upstream shaders are passed through.


  • Apply low colour: When checked, the colour value to the right determines the low end of the power fractal’s colour range. When unchecked, the colour values defined by other shaders upstream from this shader are passed through.
    When the Apply low colour setting is unchecked, colour values from upstream shaders are passed through.
    When the Apply high colour and Apply low colour settings are checked, the shader generates colour values between the two colour swatches.


  • Colour contrast: This setting adjusts the contrast between the colors generated by the fractal.
    Contrast between the colour values generated by the power fractal can be adjusted via the Colour contrast setting.


  • Colour offset: This setting is used to adjust the bias between the Apply high colour and Apply low colour values. At the default value of zero the two colours are considered “in balance”. Lowering the value below 0 strengthens the effect of the Apply low colour, while increasing the value above 0 strengthens the effect of the Apply high colour.
    The Colour offset setting can be used to shift the colours towards the high or low colour value.
    The Colour offset setting can be used to shift the colours towards the high or low colour value.


  • Colour roughness: This setting controls the transitions between the colour values. The lower the value the smoother the transition, and the higher the value the sharper and more abrupt the transition.
    The Colour roughness value controls the transition between colour values in the fractal.
    The Colour roughness value controls the transition between colour values in the fractal.


  • Clamp high colour: The Power Fractal shader generates values above white or 1.0. When checked, this setting stops the fractal from generating values greater than 1.0.
    The Clamp high colour setting ensures that colour values output by the shader do not exceed a value of 1.0.


  • Clamp low colour: The Power Fractal shader generates values below black or 0.0. When checked, this setting stops the fractal from generating values below 0.0.
    The Clamp low colour setting ensures that colour values output by the shader are 0.0 or greater.


Displacement Tab[edit]

Displacement Tab

Displacements are one of the two main functions of the Power Fractal Shader. When displacement is enabled in this shader, the color information generated by the fractal is interpreted as elevations; where the high color equals maximum elevation, and the low color is the minimum elevation. The elevation information is independent of the color chosen in the Colour tab of the Power Fractal Shader. In fact, colors can be completely disabled in the Power Fractal Shader and displacement information is still generated for use by other shaders and functions.

  • Apply displacement: When checked, the shader will generate displacement. This popup menu contains five options which allow you to choose the direction that displacement is applied in. Options in the popup list that have "(requires computed normal)" require that there be a Compute Terrain or Compute Normal connected somewhere above the node in the network to work properly.
    Apply displacement options

    Along vertical: Displacement happens along the original normals of the underlying object (i.e. the planet or a model) prior to any displacement having been applied.
    Along normal: Displacement happens along the current surface normal.
    Vertical only (requires computed normal): Displacement only happens along the normal of the underlying object (i.e. the planet or a model). The displacement is scaled by the difference between the object normal and the surface normal. Displacement is reduced as the angle between the normals approaches 90°.
    Lateral only (requires computed normal): Displacement only occurs in the lateral plane, or in other words perpendicular to the normal of the underlying object.
    Lateral normalized (requires computed normal): This is the same as Lateral only but the normal is normalised, that is scaled so it has a length of 1.

    Apply displacement options


  • Displacement amplitude: This setting determines the amplitude of the displacement. For example, how high and low the maximum terrain features can be when the power fractal is used to displace a terrain.
    Displacement amplitude ranging from none to 1000.


  • Displacement offset: This value is added to the displacement values, offsetting the displacement by a set amount along the displacement direction. Positive values push the displacement out so it looks almost as if it was sitting on a plinth. Negative values will sink the displacement back into the surface. It doesn't reverse the displacement, it's more like creating a hole in the surface and then applying the displacement to the bottom of the hole.
    Displacement offset ranging from 0 to 1000 metres, illustrating how the Apply displacement mode affects the offset direction.


  • Displacement roughness: This setting controls roughness of the displacements. Values less than 1 reduce the roughness of the displacement.
    Displacement roughness ranging between 0 and 1


  • Displacement spike limit: This setting prevents individual noise elements from becoming too high in amplitude. It works similarly to a gradient limit, putting a damper on how steep the noise features can get. Without damping, the fractal can end up with very steep and spikey features caused by high roughness, high displacement or high variation settings. While you might want to use these high roughness values to drive steeper and rougher terrain at small scales, you still need a way to stop the roughness getting out of hand in some places due to amplitude variations.
    Displacement spike limit limits the amplitude of the noise features.


  • Continue spike limit: When unchecked, the Displacement spike limit only limits the amplitude of each octave independently. When checked, whenever some noise element is affected by spike limit it remembers the reduction in amplitude and applies that reduction to further (smaller scaller) octaves that overlap the same region. This allows roughness and noise variation to continue to have effects on smaller scales even on parts of the fractal where the amplitude is being limited, and in most cases results in a smoother, yet more varied, appearance of steep surfaces where larger scale octaves were producing excessive amplitude.
    Continue spike limit checked.


  • Adjust coastline: When checked, displacements will be smoothed by the Coastline altitude and Coastline smoothing settings below.


  • Coastline altitude: This setting controls the altitude where the smoothing effect begins.
    Coastline altitude at various heights.


  • Coastline smoothing: This setting determines the amount of smoothing. A value of 0 results in no smoothing.
    Coastline altitude = -100.  Coastline smoothing from 0 - 40.


Tweak Noise Tab[edit]

Tweak Noise Tab

This tab has settings which let you control the "noise" pattern used for the fractal. In relation to fractals, "noise" is a pseudo-random, space-filling texture primitive. The actual look of the generated texture changes by choosing a different seed from which the noise functions begins to calculate. Think of "noise" as a way to add pseudo-random variation to a fractal, which by definition is self-similar over all magnitudes. So "noise" combined with the structures pre-defined by a fractal produces a multi-dimensional density function, which Terragen uses for things like procedural terrain generation and clouds, as well as masking, displacements, colouring of structures, etc. The most fundamental characteristics of the final density function generated by a Power Fractal are determined by the flavour of noise chosen in this tab.


  • Noise Flavor: This popup has seven options which support the following different flavours of noise:
    Noise flavor options
    Perlin
    Perlin billows
    Perlin ridges
    Perlin mix 1
    Perlin Mix 2
    Voronoi billows
    Voronoi ridges

    These example images use a single octave of noise, aside from the two Perlin mix flavours which use two octaves. This helps to show the underlying pattern more clearly. The "billows" and "ridges" patterns are variations of their basic flavour. "Billows" patterns are a bit like a whole lot of bubbles. Generally speaking they have smooth rounded tops dropping down to quite sharp joins between different blocks of the pattern. In fact the voronoi billows pattern looks a lot like bubbles. You might also think of "billows" as rounded hills separated by steep sharp gullies. The "ridge" patterns are the opposite of the "billows" patterns. It's the same overall pattern but inverted. This means it has narrow sharp ridges which drop down to rounded bottoms. The two "Perlin mix" flavours are a combination of the other Perlin flavours.


  • Ridge smoothing: This setting controls smoothing of the ridges generated by the fractal. A value of 0 means ridges are at their sharpest. Higher values make ridges smoother and smoother. This parameter is only available for some noise flavours.
    Ridge smoothing values from 0.1 to 1.0


  • Gully smoothing: This setting controls the smoothing of the low gullies created in "billows" patterns. A value of 0 means gullies are at their steepest. Higher values makes the gullies less steep and have an effect rather like they were being filled in. This parameter is only available for some noise flavours.
    Gully smoothing values from 0.1 to 1.0


  • Noise variation: Sets the overall noise variation. At value 0, the noise generated shows an even distribution of small and large texture components. At higher values, the noise varies more unevenly, creating a noise texture with an uneven amount of large and small features.
    Profile of terrain at different Variation values.
    Variation = 0
    Variation = 1.5 Variation = 4


  • Variation method: This popup menu provides three options for applying the "Variation" to the fractal noise pattern.
    Variation method options
    Profile of variation methods
    Variation method = Clamped multifractal
    Variation method = Unclamped multifractal
    Variation method = Multi-scale modulator


  • Buoyancy from variation: When the "Variation method" is set to Multi-scale modulator, this setting allows the rough peaks of the terrain to rise in height and the valley areas to lower and become smoother. Note, this setting has no effect on Clamped and Unclamped multifractal variation methods.
    Profile of Buoyancy setting at different values.
    Buoyancy = -1.0
    Buoyancy = -0.5
    Buoyancy = 0.0
    Buoyancy = 0.5
    Buoyancy = 1.0


  • Clumping of variation: This setting adjusts the distribution of variation changes. Higher values result in a clumping effect. For example, when the fractal is used for creating a procedural terrain, a high clumping value would account for distinct areas of plains and mountains, especially when combined with a higher than default value for Noise variation.
    Clumping of variation values from 0.1 - 1.0


  • Better colour continuity: When enabled, the shader uses more precise math to remove C1 discontinuities in the chosen Variation method option. A C1 discontinuity is a change in the tangent of a curve, in other words, a kink in the curve. The shader changes how the smoothing of ridges and gullies is performed in Perlin Ridges, Perlin Billows and Perlin Mix noise flavours to give smoother results.


  • Better displacement continuity: When enabled, the shader uses more precise math to remove C1 discontinuities in the chosen Variation method option. A C1 discontinuity is a change in the tangent of a curve, in other words, a kink in the curve. The shader changes how the smoothing of ridges and gullies is performed in Perlin Ridges, Perlin Billows and Perlin Mix noise flavours to give smoother results.


Warping Tab[edit]

Warping Tab

The settings on this tab, allow you to warp, or distort, the noise pattern generated by the shader’s previous tabs and settings.


  • Distort by normal: This setting controls how much distortion to apply to the fractal colour, based on the value of its surface normal. A normal value of 0 results in no distortion. This setting has no effect on the fractal’s displacement. In the examples below, as a slope increases from 0 to 90 degrees its normal value increases from 0 to 1.0. As the Distort by normal value increases, the greater the distortion to the fractal colours where the surface normal value is higher. Note that where the slope angle, or normal, is 0 there is no distortion to the fractal colour no matter how high the value of the Distort by normal setting.
    As the slope angle increases its normal value gets closer to 1.0.
    Distort by normal along X axis of power fractal.
    Distort by normal along Z axis of power fractal
    Distort by normal along XYZ axis of power fractal.
    Distort by normal values from 0 - 10


  • Lead-in warp effect: This popup menu has two options and allows the internal noise pattern to either be warped or left unwarped.
    Lead-in warp effect options

    None: Does not warp the internal noise pattern.
    1 Octave Perlin Warp: Warps the noise pattern with a single octave noise pattern of the same scale as defined in the Lead-in scale setting under the Scale tab. This introduces large swirl-like patterns to your noise pattern. It affects both the fractal pattern’s colour and displacement.


  • Lead-in warp amount: Controls the amount of warp. A value of 0 is the same as setting the Lead-in warp effect to "None". Higher values create more pronounced swirl-like patterns.
    Lead-in warp amount from 0 - 2, affecting the fractal colour and displacement.


  • Less warp at feature scale: When checked, applies less warping to features of the noise pattern the same scale as defined by the Feature scale setting under the Scale tab. In other words, smaller scale features are less affected by the warping.
    Less warp at feature scale off and on


  • Allow vertical warp: When checked, allows for the internal noise pattern to be warped vertically, in the “Y” axis, as well as the “X” and “Z” axis.
    Allow vertical warp off and on


Animation Tab[edit]

Animation Tab


  • 4D noise: When checked, 4D noise is enabled. 4D noise is always different from 3D noise, so expect deformations to change when this setting is enabled.
  • 4D noise speed: This setting controls how quickly the noise evolves. Higher values generate more rapid change over time; in other words, the higher the value, the greater the change from one frame to the next.
    4D noise speed = 0.1
    4D noise speed = 1.0
    4D noise speed = 0.1
    4D noise speed = 1.0


  • Reference frame number: This is the frame at which changing the 4D noise speed value has no effect. For example, if the reference frame value is 1, then frame 1 will look the same no matter what the 4D noise speed value is set to. All other frames are calculated according to the time difference from this frame. The shape of the noise depends on the time difference multiplied by the 4D noise speed value.


Legacy Example Movies[edit]

Feature scale
FeatureScale.gif

Lead-in scale
LeadInV3Cloud.gifLeadInV3.gif

Smallest scale
SmallestScale.gif

Noise octaves
NoiseOctavesV3.gif

Noise stretch
NoiseStretchV3.gif

"Apply High Color" and "Apply Low Color"
Applycolor.gif

Color Contrast
Colorcontrast.gif

Color Offset
Offsetcolor.gif

Color Roughness
Roughnessscolor.gif

"Clamp High Color" and "Clamp Low Color"
ColorClamp.gif

Displacement direction
DisplacementDirection.gif

Displacement amplitude
DisplacementAmplitude.gif

Displacement offset
OffsetDisplacement.gif

Displacement roughness
Displacement roughness.gif

Displacement spike limit
Displacement spike limit.gif

Coastline altitude
CoastlineAltitude.gif

Coastline smoothing
CoastlineSmoothing.gif

Noise Flavour

Perlin
TweakNoisePerlin.gif

Perlin billows
PerlinBillows.gif

Perlin ridges
PerlinRidges.gif

Perlin mix1
PerlinMix1.gif

Perlin mix2
PerlinMix2.gif

Voronoi billows
VoronoiBillows.gif

Voronoi ridges
VoronoiRidges.gif

Ridge smoothing
Ridgesmoothing.gif

Gully smoothing
Gullysmoothing.gif

Noise variation
NoiseVaraition.gif

Variation Method
VariationMethod.gif

Buoyancy from variation
Buoyancy.gif

Clumping of variation
Clumpingofvariation.gif

Distort by normal

Distortbynormal.gif

Lead-in warp effect

LeadInWarpEffect.gif

Lead-in warp amount

LeadInWarpAmount.gif

Less warp at feature scale

LessWarpAtFeatureScale.gif

Allow vertical warp

AllowVerticalWarp.gif


Literally, to change the position of something. In graphics terminology to displace a surface is to modify its geometric (3D) structure using reference data of some kind. For example, a grayscale image might be taken as input, with black areas indicating no displacement of the surface, and white indicating maximum displacement. In Terragen 2 displacement is used to create all terrain by taking heightfield or procedural data as input and using it to displace the normally flat sphere of the planet.

A shader is a program or set of instructions used in 3D computer graphics to determine the final surface properties of an object or image. This can include arbitrarily complex descriptions of light absorption and diffusion, texture mapping, reflection and refraction, shadowing, surface displacement and post-processing effects. In Terragen 2 shaders are used to construct and modify almost every element of a scene.

A single object or device in the node network which generates or modifies data and may accept input data or create output data or both, depending on its function. Nodes usually have their own settings which control the data they create or how they modify data passing through them. Nodes are connected together in a network to perform work in a network-based user interface. In Terragen 2 nodes are connected together to describe a scene.

A parameter is an individual setting in a node parameter view which controls some aspect of the node.

Literally, to change the position of something. In graphics terminology to displace a surface is to modify its geometric (3D) structure using reference data of some kind. For example, a grayscale image might be taken as input, with black areas indicating no displacement of the surface, and white indicating maximum displacement. In Terragen 2 displacement is used to create all terrain by taking heightfield or procedural data as input and using it to displace the normally flat sphere of the planet.