Noise

Noise Generation

Random values are extremely common and important in procedural generation. Functions like Math.random() are the common go-to for choosing random values, but in many situations they are hard to work with. Psuedo-random number generators are designed to provide independent, unpredictable, and evenly-distributed values. If we want related or repeatable random values we have to do extra work. If we want random variation with specific aesthetic characteristics we also have to do extra work.

Noise functions are an alternative source of random values. Unlike the random() function however, noise functions provide related, repeatable, and “good looking” random variation.

There are several common noise functions, each with different characteristics. The most widely known noise function is probably Perlin Noise, developed by Ken Perlin while working on visual effects for the amazing 1982 motion picture Tron. Ken later developed a similar but faster version called simplex noise. Other noise functions include Worley noise, developed by Steven Worley, and the simpler value noise.

Noise functions provide a “cloud” of random values that can be used in a wide variety of ways. Noise functions are frequently used in procedural texture generation and terrain generation, but their applications are not at all limited to those areas. Noise functions can be thought of as a lookup table of pre-generated random values that can be used in place of random() in many cases. Noise functions are particularly well suited to adding small variations to create more natural feeling output.

Ken Perlin

Tron, 1982

Ken Perlin developed Perlin Noise while working on the feature film Tron with the goal of producing natural-appearing textures on computer-generated surfaces for motion picture visual effects.

Ken Perlin on Procedural TexturesEssayTron (1982)IMDB

Emily Xie

Dunes, 2016

Creative coding project in p5.js that explores "behavior that is at once organic yet systematic".

DunesProject Pagexie-emily.comArtist Site

RGBA + TBC

Elevated 4K Demo, 2011

A landscape generated using Value Noise.

Elevated 4kDemoBehind ElevatedTech Presentation

Tyler Hobbs

Return Zero, 2021

Flow fields printed on large canvas.

tylerxhobbs.comArtist SiteFlow FieldsEssay

Yasai

Perlin Noise Painter, 2019

Yasai created an interface that allows users to "paint" with Perlin noise.

Perlin Noise PainterProject Pagewangyasai.github.ioArtist Site

Eddie Lee

Open CL Perlin Particles, 2011

Controlling 2-million particle movements using a 2D Perlin height map as a vector field. Each particle travels along the vector field to give this smokey behavior.

OpenCL Perlin ParticlesVideoEddie LeeVimeo

Red Blob Games

Displacement Terrain, 2015

Interactive tutorial showing how to generate maps using noise functions.

Terrain TutorialTutorial

Noise vs. Random

Consider the code you would write to draw the blue squares above. You would need to provide several values for each square: horizontal position, vertical position, width, height, and color.

Where do those values come from? They could come from a few places.

Both random() and noise() provide a source of variation, but noise() provides much more control. The values from random() the sizes of the boxes won’t be related at all. With noise() we can control how quickly the size changes horizontally, vertically, and over time. If we sample a small area of the noise function the variation will be subtle and gradual. If our samples are far apart the variation will be be drastic, unpredictable and look a lot like random().

Random()

This example draws a big circle, and a line of smaller circles. Variation is created with the random() function, which allows control over the amount of variation, and global (and fragile) repeatability via the random seed.

Noise(x)

This example uses the noise() function to create variation. It control over the amplitude, frequency, and character of the variation. It also provides independent (and robust) repeatability.

Compare the code and results of the two examples above.

Benefits of Noise

Noise Looks Good

The p5 noise(x) function returns values sampled from Perlin Noise. Perlin Noise provides random values with a particular aesthetic arrangement. The variation in Perlin Noise is band-limited: the frequency of values is predictable and even, without flat or noisy areas. The variation is also visually isotropic: it looks the same at different rotations. These characteristics make it a useful basis for many applications that require natural-feeling variation.

Other noise functions—like Worely and Value Noise—offer different aesthetic qualities, and it is quite possible to create your own noise function that looks the way you want. Most of the time you don’t need to create your own noise function to get a particular look. You can tweak the aesthetics of a noise functional by manipulating its values with math. The Terrain from Noise article on Red Blob Games is a good place to see some common techniques for shaping noise.

Noise is Repeatable

Noise functions take one or more coordinate arguments. These arguments specify a location in the noise cloud and the function returns the value found at that location.

This makes getting repeated results easy: every time you call noise(x) with a particular argument, you get the same value back. This can be very useful. For example, in an animation you often need a value to stay the same from frame to frame.

• random() does not accept coordinate arguments and returns a different random value every time.
• noise(x) requires an coordinate argument and returns the same random value every time it is called with that argument.

Noise is Controllable

By controlling what you pass to noise(x), you can control the frequency of change in the returned values. This can be used to control how quickly values vary in space and time. With p5s Perlin Noise, you can also adjust the character of noise(x) using noiseDetail(). You can scale and shift the values returned from noise(x) to the range you need in the same way you shift values from random().

1D Noise Example

1D, 2D, + 3D Noise

Many noise functions are multidimensional. The noise function in most programming libraries can take 1, 2, 3, or even more parameters. You can think of these parameters as specifying a multidimensional address in a “cloud” of values.

noise(x)

noise(x, y)

noise(x, y, z)

Building Noise Functions

The noise() function models an infinite cloud of predetermined random values. When you call noise(x), you are asking for the value in the cloud at the coordinate x. To create a noise function you need to build two things:

1. a way to associate random values with each integer coordinate in the cloud
2. a way to interpolate between these values if fractional coordinates are requested.

Different noise functions solve these problems in different ways.

Working with Noise

Calling the Noise Function

The noise() function takes up to three parameters: noise(x,y,z). These parameters allow you to request values arranged in a three dimensional “cloud” of pseudo-random values.

When you call noise(x) you have to pass in at least one parameter. This parameter specifies the location in the cloud of the value to return. You can think about noise(x) as a lookup table: noise(1) provides one value in the table and noise(2) provides another.

Choosing appropriate parameter values takes some getting used to. You can pass in frameCount or millis() to get values that change over time. You can pass in XYZ coordinates to get values that change over space. These are very common cases, but really you can pass values from any range into noise() and it will provide random values in return.

Controlling the Frequency

You can control the frequency of returned values by scaling the values you pass in for x, y, and z.

// get a value that changes over time
n = noise(seconds);

// get a value that changes over time more slowly
n = noise(seconds * 0.1);

// get a value that changes over time more quickly
n = noise(seconds * 10);

Controlling the Amplitude and Range

Noise functions typically return values in the range of 0 to 1. Use multiplication and addition to shift values to the range you need. Be aware that while random() provides evenly-distributed values, noise values are biased towards the middle. Also check the documenation for your noise function to understand the range it provides. In p5.js the range will differ depending on how you have configured it with noiseDetail().

// scale values to sit between 10 and 20;
n = noise(frameCount) * 10 + 10;

You could also use map():

// map noise(frameCount) from the range [0,1) to the range [10 to 20)
n = map(noise(frameCount), 0, 1, 10, 20);

Controlling the Detail

The noiseDetail() function allows you to control the “roughness” or “detail” of the noise returned. Detailed noise is achieved by adding layers of noise together.

Typically, each layer of noise is twice as detailed (higher frequency) and half as prominent (lower amplitude). These layers are sometimes refered to as “octaves” because their frequncies double each time, like musical octives.

Controlling the Seed

By default, every time you restart your sketch the noise cloud is regenerated with a randomized seed. The noiseSeed() allows you to manually set the seed used for the noise cloud. This allows you to get the same values from noise() after restarting your sketch.

Study Examples

The following study examples demonstrate using noise to introduce variation. Compare these examples to their counterparts in the Random Values chapter.

Skyline

Using noise to determine the height of the buildings creates a skyline with tall and short buildings clustering together.

Circle Grid

This example draws circles of varying sizes. Explore how passing different values to noise() impacts what is drawn.

Grass

Using noise to control the lean of each blade of grass leads to a nice, natural-looking wind effect.

Explore