Understanding the Noise Node in Blender

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.  

1D Noise - The simplest form is the 1D mode. 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.

• Scale - 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.
• Detail - 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.
• Distortion - 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. 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.