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The Noise node generates smoothly varying random values, based on an input value.

This is useful for many things, like creating random textures, or randomizing values over time.

The noise can be generated in one to four dimensions.

Let's start off by looking at its simplest form, the 1D mode. Here,

the noise is generated based on a single value input, the W field.

If we look at the Color output of the noise with a given W value,

we see a constant color. Changing this input smoothly varies the color.

The Noise node also gives us a Factor output, which is a single random value. We can use this

to our advantage, and animate the W parameter, to generate values that randomly change over time.

It's difficult to see the shape of the noise in this way, so instead, we can feed it an

input that varies throughout space. Here we see the noise varying over the X axis.

There are a few parameters that allow us to change the noise characteristics.

The scale parameter, simply multiplies the W input, changing its slope, and therefore

the size of the noise. It's notable that because the scale multiplies the input,

the resulting texture will be smaller at higher scales,

and larger at lower scales. We covered this inverse relationship in the Vector Math chapter.

To understand the detail parameter, we have to look at how the noise is generated.

Setting the detail to zero reveals a smooth noise, and this smooth noise is actually the

only thing the noise function can generate. Rougher noise textures are generated by

overlaying multiple of these smooth noises of different scales on top of each other.

The detail parameter controls how many of these noises are generated and overlaid.

Each unit of Detail corresponds to one additional noise level. Each level has a scale parameter that

is twice that of the previous level, meaning that each level is half as big as the previous one.

When gradually increasing the detail, between integer values, the next level of detail gets

gradually stronger, from no influence to its full influence when reaching the next integer value.

Note that each additional level of noise makes the computation heavier,

so you always want to use as low a detail level as you can, while still getting the effect you want.

Additionally to each level being smaller than the previous,

each level also has a progressively smaller amplitude, which is controlled by the roughness

value. The default value of 0.5 means that each level will have half the amplitude of

the previous level. Setting this higher gives more and more influence to the smaller noise levels,

until reaching one, where all levels have the same influence. Conversely, lowering the roughness

gives less influence to the smaller levels, until reaching zero, where only the very first level has

any impact on the noise, resulting in effectively the same thing as setting the Detail to zero.

Lastly, the Distortion parameter distorts the result by adding a noise to the input value,

before feeding it back into the main noise function. It's like calculating a noise

based on a noisy input. This pre-noise, consists of only the lowest noise level,

meaning that it acts as a noise with the same scale as the main noise, but with the Detail

set to zero. Personally, I don't find the distortion parameter particularly useful,

as in most cases, when distortion is desired, adding another custom noise to the input is a

better option, giving more control, and allowing the distortion noise to have different parameters.

As for the other noise modes, setting it to 2D, changes the W input to a Vector. This gives us

a noise that varies along two axes. Note that only the X and Y components of the vector will be taken

into account, so applying this to a 3D object will result in a constant output along the Z axis.

Note that this is the texture coordinate's Z axis, which doesn't have to be aligned with the scene

or object space Z axis. You can always rotate the coordinates before passing them to the Noise node.

Changing it to 3D will cause the noise to vary along all three Vector axes. This is probably the

most common mode of the Noise node, as Blender is a 3D application after all, so this is also

the default mode. There is something special to note. If we apply a 3D noise onto a 2D object,

like a plane, the Z coordinate seems redundant, as we get the two required axes of variation from

the 2D mode just as well. However, if we want to animate the noise, so that it changes over time,

but without moving in a particular direction, we can just animate the Z axis.

Think of it as if the plane is taking a slice of a noise that exists in 3D space.

Like a cross sectional view of the noise. We can see this well if we apply the noise to a 3D object

and move it along the Z axis. Notice how on the sides of the cube the noise is simply

moving vertically, while on the top, the noise is morphing, without moving in any

particular direction, as the surface is perpendicular to the direction of motion.

This is very useful for animated noise, but what if we want to animate a noise on a 3D object?

Well, that's why we have the 4D mode. Just like the plane was a slice of a 3D noise,

in this mode, our 3D object represents a slice of a noise that exists in 4D space. We control this

fourth dimension with an additional W parameter, which allows us to make an animated 3D noise.

Taking a closer look at the noise's Color output, we find that it's just

composed of a separate noise pattern for each channel. And it's also good to note

that the Factor output is actually just the noise pattern generated for the Red channel.