The Brownian texture is based on Brownian Motion, which is a mathematical model that describes the random motion of particles in a fluid dynamic system. A key element of the model is the "random walk," in which each successive step of a particle is in a completely random direction. Brownian Motion was discovered by the biologist Robert Brown (1773–1858).

In general, the Brownian texture is smoother than other fractal-based textures. As such, the texture can replicate a sandy beach or similar surface. One disadvantage of the Brownian texture, however, is its tendency to produce rendering artifacts when viewed up close. For example, in Figure 5.3, a faint grid is visible on the middle plane.

The distinctive attributes of the Brownian texture follow:

The Volume Noise texture is a 3D variation of the Noise texture. The following attributes are shared by both Volume Noise and Noise:

In addition, the Volume Noise texture has two unique attributes:

Whether a Volume Noise or Noise texture should be selected depends on the nature of the object assigned to the texture's shading network. Since Volume Noise depends on a 3D Placement utility, it is not suited for an object that deforms or is in motion. On the other hand, the Noise texture, which is mapped directly to the surface, is restricted by the quality of the surface UVs. For example, in Figure 5.6 a polygon frog has a Noise and Volume Noise mapped to the Color attribute of an assigned Blinn material. In both cases, the Color Gain and Color Offset attributes of the noise texture are tinted green. Since the frog is split into multiple UV shells (groups of UV points), shell borders are noticeable on the Noise texture version. The Volume Noise version, by comparison, ignores the inherent UV information in favor of the 3D Placement process. Hence, the Volume Noise version renders cleanly with no shell borders. To improve the quality of the Noise version, more time must be spent refining the UVs. To make the Volume Noise version acceptable for animation and deformation, you must use the Convert To File Texture tool or the Transfer Maps window. (Convert To File Texture is described at the end of this chapter; the Transfer Maps window is discussed in Chapter 13.) The same dilemmas occur when choosing between Fractal and Solid Fractal textures.

Figure 5.6. A polygon frog with Noise and Volume Noise textures mapped to the color of the assigned Blinn

On a more technical level, Perlin Noise, and thus Noise and Volume Noise texture variations, are graphic representations of multiple noise functions, each at a different scale (frequency), added together. You can emulate the addition of noise functions in the Hypershade window by connecting two Noise textures to a Plus Minus Average utility. For example, in Figure 5.7 the Out Color attributes of two Noise textures are connected to input3D[0] and input3D[1] of a Plus Minus Average utility. The Operation of the utility is set to Average. To see the result, the utility's output3D is connected to a Layered Texture. The Layered Texture icon reveals a new, more complex noise pattern, which is a combination of Noise1 and Noise2. Noise1's Frequency is set to 3 and Noise2's Frequency is set to 10, guaranteeing that the scale of each noise pattern is different.

Figure 5.7. Two Noise textures are averaged to produce a more complex noise pattern. This shading network is included on the CD as noise_average.ma.

The Solid Fractal texture is a 3D variation of the Fractal texture. Both Solid Fractal and Fractal share attributes with Volume Noise and Noise. These attributes include Amplitude, Threshold, Ratio, Frequency Ratio, and Inflection. For descriptions of each attribute, see the previous section in this chapter. At the same time, Solid Fractal and Fractal share the following unique attributes:

In addition, the Fractal texture carries the Level Min and Level Max attributes. These two attributes control the number of iterations the texture undertakes in its calculations. A high Level Max value will produce finer detail in the resulting noise. Solid Fractal, on the other hand, carries the Ripples and Depth attributes. The Ripples fields, which represent Ripples X, Ripples Y, and Ripples Z attributes, control the fundamental noise frequency of the Solid Fractal. In basic terms, Ripples creates waviness in the texture in the X, Y, and Z directions. A high value in any one of the three fields causes the noise to stretch. High values in all three fields inserts a greater number of dark "holes" into the noise. The Depth fields, which represent Depth Min and Depth Max attributes, set the minimum and maximum number of iterations used in the Solid Fractal calculation. The higher the values, the finer the detail. The lower the values, the blurrier the texture.

The Cloud texture uses Perlin and fractal noise techniques to create soft, wispy noise suitable for smoke or clouds. To create a cloud in a sky, follow these steps:

In addition, you can use the Cloud texture to quickly create a moon or other planetary body. For example, in Figure 5.9 a Cloud texture is mapped to the Incandescence of a Lambert material, which is assigned to a sphere.

Figure 5.9. A Cloud texture is mapped to the Incandescence attribute of a Lambert material, creating a moonlike texture. This scene is included on the CD as cloud_moon.ma.

As for the Cloud texture attributes, Color1 and Color2 are mixed to create the noise. Edge Thresh and Center Thresh control the density of the noise. Low Edge Thresh values create a denser noise pattern along the edges of the 3D Placement box by biasing Color2. High Center Thresh values create a less dense noise pattern at the center of the placement box by biasing Color1. If both Edge Thresh and Center Thresh are low, Color2 is favored in the pattern. Contrast fine-tunes the color mixture. If the Contrast value is 0, the colors are averaged across the entire texture. If the value is 1, the colors maintain a harder separation. Amplitude scales the resulting noise; that is, the noise color values are multiplied by the Amplitude value. The Depth and Ripples fields, which represent the Depth Min, Depth Max, Ripples X, Ripples Y, and Ripples Z attributes, function in the same manner as those belonging to the Solid Fractal texture (see the previous section). Soft Edges, when checked, creates a more gradual transition between Color1 and Color2. This attribute also reduces the amount of contrast and allows more detail to survive. Transp Range controls the rapidity with which the colors transition between each other and become opaque. A low value creates a harsher transition. A high value creates a subtler, tapered transition. Ratio controls the ratio of low- to high-frequency noise. This attribute is identical to the Ratio attribute used by the Noise, Volume Noise, Fractal, and Solid Fractal textures.

The Marble texture creates a stonelike pattern that includes virtual mineral veins. The Marble texture isn't designed to match a specific marble type, nor is the texture capable of replicating a realistic marble by itself. However, if the Marble texture is combined with other 2D and 3D textures, it becomes more convincing. For example, in Figure 5.10 a Marble texture is mapped to the Color of a Blinn material, which in turn is assigned to a cube. When the marble is used by itself, it betrays its procedural origin. When Leather, Noise, Fractal, and Cloud textures are mapped to the Color Gain, Color Offset, Vein Color, and Filler Color attributes of the Marble texture as well as the Bump Mapping attribute of the Blinn, the results become more complex. This technique of combining procedural textures makes any single procedural texture more believable.

Figure 5.10. (Left) Marble texture. (Center) Marble texture with other procedural textures mapped to various attributes. (Right) Reference photo of real marble. This scene is included on the CD as marble.ma.

As for attributes, Filler Color sets the color of the stone's bulk. Vein Color sets the color of the thin veins. Vein Width sets the width of the veins. If the value is high, the veins become large spots. Diffusion controls the color mixture of the stone. Low values produce a high level of contrast between the Filler Color and Vein Color. High values allow the Vein Color to spread and mix into the Filler Color. Contrast increases or decreases the amount of contrast set by Diffusion. A Contrast value of 1 is equal to a Diffusion value of 0. Amplitude controls the complexity of the veins. Higher values create thinner veins with more kinks. You can raise the Amplitude value above the default maximum of 1.5. Ratio controls the ratio of low- to high-frequency noise. This attribute is similar to the Ratio attribute used by the Noise, Volume Noise, Fractal, and Solid Fractal textures. If the Marble texture's Ratio is raised above 0.9, however, detail is removed. The Depth and Ripples fields, which represent the Depth Min, Depth Max, Ripples X, Ripples Y, and Ripples Z attributes, function in the same manner as those belonging to the Cloud and Solid Fractal textures (see the previous section).

The Wood texture replicates the rings found in a cross-section of a tree trunk or a branch. The Wood texture is not well suited for realistic wood. However, the texture can create convincing painted or stained wood when applied as a low-intensity bump map. For example, in Figure 5.11 a Wood texture is mapped to the Bump Mapping attribute of a Blinn material, which in turn is assigned to a flattened polygon cube.

Figure 5.11. A Wood texture applied to a cube as a bump map. This scene is included on the CD as wood.ma.

On a more technical level, Vein Color establishes the color of the rings. Filler Color establishes the color of the wood between rings. Vein Spread determines how far the Vein Color will bleed into the Filler Color. A Vein Spread value of 0 will remove the Vein Color from the texture (with the exception of extremely thin ring lines). Layer Size "zooms" in and out of the pattern. Higher values create fewer rings. Randomness varies the width of each ring. When raised, Age adds more rings. Grain Color and Grain Contrast control the color and intensity of "grains" within the wood. These appear as tiny dots throughout the wood. Grain Spacing controls the distance between individual grain dots. Center sets where the circular heart of the wood is in the U and V directions.

The patterns created by the wood rings are controlled by a set of attributes in the Noise Attributes section of the Wood texture's Attribute Editor tab. Amplitude X sets the strength of noise function in the X direction. Amplitude Y does the same for the Y direction. When the 3D Placement box is at its default position, X direction corresponds with the world X axis and Y direction corresponds with the Y axis. The Ratio, Depth Min, Depth Max, Ripples X, Ripples Y, and Ripples Z attributes are identical to those of the Solid Fractal, Cloud, and Marble textures.

Although the Leather texture is not designed to create realistic animal hide, it can create interesting organic and cellular patterns (see Figure 5.12). Cell Color sets the color of the circular cells. Crease Color sets the color found between the cells. Cell Size determines the size of individual cells. Density determines how closely the cells are packed together. High values create less empty space between the cells and thus less color provided by Crease Color. Spottyness randomly kills off cells. High values create larger areas colored by the Crease Color. Randomness varies the pattern of cells. Low values make the distance between cells and the cell size more consistent. Threshold controls the intensity of the cell growth. High values increase the intensity of the Cell Color.

Figure 5.12. A Leather texture, with default settings, applied as a color and bump map to an assigned Blinn material

The Snow texture places a virtual snow on the areas of a surface that point toward the positive Y axis and do not possess too great a slope. The Snow texture works in conjunction with bump and displacement maps. For example, in Figure 5.13 a Fractal texture is used as a displacement map on a primitive plane. The Snow texture is mapped to the Color attribute of the Blinn connected to the displacement. As a result, all the parts of the surface that point upward are colored white. (For more information on bump and displacement mapping, see Chapter 9.)

Figure 5.13. A Snow texture colors the peaks of a displaced plane. This scene is included on the CD as snow_displace.ma.

You can adjust the Snow texture to emulate fallen dust, dirt, or other debris. For example, in Figure 5.14 a Snow texture is mapped to the Color attribute of a Blinn, which is assigned to a plate and bowl. A Mountain texture is mapped to the Snow Color attribute of the Snow texture, producing white bits of debris instead of solid snow. The Threshold attribute of the Snow texture is set to 0.75, causing the debris to appear only on surface faces whose normals lie roughly between 0 and 22 degrees off the Y axis.

Figure 5.14. A Snow texture creates a debris-like effect over a pair of dishes. This scene is included on the CD as dish_debris.ma.

As for the Snow texture attributes, Snow Color sets the color of the virtual snow. Surface Color sets the color of the surface where the snow does not stick. (In the case of Figure 5.14, Surface Color is set to blue.) You can map this attribute with another texture for more realism. Whether or not snow sticks to a surface face is determined by the Threshold attribute. A value of 0.5 allows the snow to stick to any surface point whose surface normal lies roughly between 0 and 45 degrees off the positive Y axis. A value of 0 allows the snow to stick to any surface point whose surface normal lies roughly between 0 and 90 degrees off the positive Y axis. For example, a value of 0 would cause the snow to appear on the top half of a sphere. Depth Decay controls the transition from snow to lack of snow. High values make the transition fairly hard, and low values make the transition tapered and soft. A Depth Decay value of 0 removes the snow completely. Thickness determines the thickness of the virtual snow. High values make the snow more opaque.

The positive Y axis used by the Snow texture is defined by the Snow texture's 3D Placement box, and not the world axis. If the box is left at its default position, the positive Y axis runs "up" in world space. However, if the box is rotated, the positive Y axis used by the Snow texture changes. When viewing the 3D Placement box, remember that the Y axis runs in the same direction as the small "tail" on the corner diamond icon (see Figure 5.2 earlier in this chapter and Figure 5.29 in the section "Placing Placement Boxes and Projection Icons").

The Rock texture is similar to the Mountain texture in that it creates a hard-edged pattern (see Figure 5.15).

Figure 5.15. (Left) Default Rock texture applied as color and bump. (Right) Default Granite texture applied as color and bump.

Mix Ratio sets the ratio of Color 1 to Color 2. If the Mix Ratio value is below 0.5, Color 2 becomes the grain color. If the Mix Ratio value is above 0.5, Color 1 becomes the grain color. Grain Size controls the size of the individual grains. Diffusion controls the hardness of the grain edges. Higher values blur the grains. If you increase the Grain Size and Diffusion values, you can create a stylized tile (see Figure 5.16).

Figure 5.16. Rock texture with raised Grain Size and Diffusion values applied as a bump map. This scene is included on the CD as rock_tiles.ma.

The Granite texture is similar to the Leather texture in that it creates a series of colored, semicircular cells. At the same time, you can adjust the Granite texture to produce abstract patterns (see Figure 5.17).

Figure 5.17. The Granite texture is adjusted to produce an abstract pattern. This scene is included on the CD as granite_pattern.ma.

On a technical level, the texture combines three sets of cells, the color of which is determined by Color 1, Color 2, and Color 3. Cell Size determines the size of individual cells. Filler Color determines the color of the space between cells. Density controls the intensity of the cell color. High Density values reduce the amount of empty space between cells and therefore decrease the amount of Filler Color visible. Mix Ratio controls the visible ratio of the three cell colors. A value of 0 prevents the use of Color 2 and Color 3 cells. Values between 0.001 and 0.5 create a relatively equal mix of all three cell colors. Values closer to 1 favor Color 1 and Color 3. Spottyness reduces the cell density. Randomness controls the regularity of the cells. A value of 0 will align the cells in a grid. Higher values make the cells more chaotic. Threshold determines the amount of contrast between cells. Lower values reduce the contrast. Creases, when checked, inserts honeycomb-style division lines between the cells, making their shapes more irregular.

The Stucco texture mixes two colors, Channel 1 and Channel 2. The Shaker attribute determines the ratio of the two colors. A high value biases Channel 1. A low value biases Channel 2.

Two Stucco attributes, Normal Depth and Normal Melt, will not function unless the Out Normal attribute of the texture is connected to the Normal Camera attribute of a material. Since this requires a custom connection, the following steps are recommended:

The Normal Depth attribute controls the depth of the bump. The Normal Melt attribute controls the smoothness of the bump. Low Normal Melt values create a rough bump with small detail, and high values create a smooth bump with large features. For information on standard bump mapping, see Chapter 9.

The Crater texture functions in a manner similar to the Stucco texture but adds extra attributes. The Crater texture mixes three colors defined by Channel 1, Channel 2, and Channel 3. The Shaker attribute controls the mixture. Shaker values below 0.1 favor Channel 1. Values from 0.1 to 0.5 favor Channel 1 and Channel 2. Values above 0.5 mix all three colors. When the value is raised above 2, the detail is reduced in scale and Channel 3 is favored. Melt controls the smoothness of the resulting pattern. Low values introduce a greater number of kinks into the threads of color. Balance controls the ratio of the three colors. As the Balance value gets higher, a greater portion of the Channel 2 color is added to the mixture. Frequency controls the scale of detail created by the color mix. High values create a finer, more convoluted pattern. Frequency is similar to the Frequency Ratio attribute of the Noise, Volume Noise, Fractal, and Solid Fractal textures.

The Out Normal attribute of the Crater texture must be connected to the Normal Camera attribute of a material for the Norm Depth, Norm Melt, Norm Balance, and Norm Frequency attributes to work. Norm Depth controls the strength of the resulting bump and is identical to the Normal Depth attribute of the Stucco texture. Norm Melt controls the smoothness of the bump and is identical to the Normal Melt attribute of the Stucco texture. Norm Balance controls the ratio between high and low points on the resulting bump. High values reduce the number of deep pits created by the bump mapping process. Norm Frequency controls the noise frequency used to generate the bump. High values create finer bump detail and introduce a greater variation between high and low points.

Although the default Crater and Stucco textures are quite vivid and match few surfaces in the real world, you can easily adjust their attributes to create a more complex result (see Figure 5.18).

Figure 5.18. Stucco texture (left) and Crater texture (right) applied with custom attribute settings. This scene is included on the CD as crater_stucco_custom.ma. A version with default texture settings is included as crater_stucco.ma.