Perlin noise explained

01Why plain randomness looks wrong

Ask a computer for random numbers and draw them as a line, and you get static: every value jumps with no relation to the one before. Nature doesn't look like that. A coastline, a cloud or a mountain ridge changes gradually, with large shapes and small details at the same time.

What we want is randomness that is smooth: nearby points get similar values, distant points get unrelated ones. That is exactly what Perlin noise gives.

02Ken Perlin and Tron

Ken Perlin worked on the computer graphics of the film Tron (1982) and was frustrated by how machine-like computer images looked. In 1983 he developed a noise function to give surfaces a natural texture, and published it in 1985. In 1997 he received an Academy Award for Technical Achievement for it.

Since then it has been used for clouds, fire, marble, terrain and water in countless films and games, and it is built into creative coding tools such as Processing and p5.js.

03How it works: gradients on a grid

Imagine a grid laid over space. At every grid point the function picks a random direction, a gradient. To get the value at any point in between, it looks at the nearby grid points, measures how far the point lies along each of their directions, and blends those numbers with a smooth curve.

Because the blending is smooth, the result has no jumps. Because the directions are random, it has no visible pattern. And because the same coordinates always give the same value, the noise can be computed again at any time, identically.

fade(t) = 6t⁵ − 15t⁴ + 10t³

04Octaves: large shapes and fine detail

One layer of Perlin noise gives gentle hills. Real landscapes have hills, rocks and pebbles at once. So the noise is added up in layers called octaves: each layer twice as fine as the last and, typically, half as strong.

Our program uses four octaves with a falloff of 0.5, so the first layer sets the broad swell of a line and the last adds the slight roughness that makes it look drawn rather than ruled.

noise(x) = Σₖ 0.5ᵏ · perlin(2ᵏ·x),   k = 0…3

05From noise to sound waves

On First Signal, from the Ridges series, each of the 56 lines is one waveform. A Gaussian envelope decides where the signal is loud, a carrier wave makes it oscillate, and two noise layers shape it: one for the slow swell, one for the fine texture. Every line samples the noise at a slightly different row, so neighbouring lines look related but never identical.

Stacked one behind another, with each line hiding the ones behind it, the waveforms read as a mountain range at night.

yᵢ(t) = bᵢ − A·env(t)·(n₁(t)² + |sin(2π·f·t + φᵢ)|³·n₂(t))

06Noise around a circle

On the Orbit posters the same signal is wound into rings. There is a catch: if you sample noise along a straight line and bend it into a circle, the end won't meet the start and the ring breaks. The fix is to sample the noise along a circle in noise space itself, at (cos θ, sin θ), so the values return exactly to where they began.

rᵢ(θ) = Rᵢ + A·env(θ)·noise(cos θ, sin θ, i)

07The same seed, the same picture

Perlin noise looks random but is fully determined by its seed. Our programs fix the seed for each piece, so the same equations and the same seed always draw the same lines. That is why every print of a piece is identical to the image you see on its page.