Interactive demo

Blue Noise

Purely random points form clumps and leave gaps. Blue noise points are still random, but keep a minimum distance from each other, like trees in a forest or cells in the retina. Robert Bridson's algorithm creates them in linear time.

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Every step picks an active point (coral) and tries up to k random positions in the ring around it. Green is accepted, crosses were too close to another point.

Controls

Display

Points
–
Active points
–

Legend

  • Point
  • Active point (may still get neighbors)
  • Current point and rejected tries
  • Accepted new point

Noise types compared

NoiseOutputBuilt fromWork per sampleSmooth
Value NoiseScalar fieldRandom values on a grid4 grid pointsYes
Perlin NoiseScalar fieldRandom gradients on a grid4 grid pointsYes
Simplex NoiseScalar fieldGradients on a triangle grid3 cornersYes
Worley NoiseScalar fieldRandom feature points9 to 25 cellsNo
Blue Noise this pagePoint setRandom candidates around existing pointsUp to 30 tries per point–
Fractal NoiseScalar fieldOctaves of a base noise1 base noise per octaveYes
Diamond-SquareHeightmapDisplaced midpoints of a grid4 neighbors per pointNo
Colors of NoiseSignal or imageWhite noise filtered by frequency1 FFT for all samples–
Domain WarpingScalar fieldFractal noise at warped positionsUp to 5 fractal noisesYes
Curl NoiseVector fieldDerivatives of a noise field4 noise samplesYes
Noise Terrain GeneratorHeightmapStacked noise layersLayers × octaves–

All noise types →

1. Tries around active points

  1. Start with one random point and mark it active.
  2. Pick a random active point and try up to k random positions in the ring between r and 2r around it.
  3. Keep the first position that is at least r away from every point, and mark it active.
  4. If all k tries fail, retire the point. Stop when no active point is left.

2. A grid for the neighbors

To test a position quickly, a background grid with cells of size r/√2 is used. Each cell holds at most one point, so only the 5 × 5 cells around a position need to be checked, no matter how many points there are.

3. Why “blue”

The spectrum of random points is flat, like white noise. Poisson disk points have almost no power at low frequencies, the dark disk in the middle of their spectrum, because they never clump. That is the mark of blue noise, and why it is used for sampling, dithering and stippling.

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