Fields, noise, and flow
Blue Noise
A point distribution that avoids clumps and regular lattice artifacts.
What it is
Blue noise describes a sampling pattern whose low spatial frequencies are suppressed: on a large scale it lacks obvious waves, clusters, or grid. Remaining variation is concentrated at finer scales, where it is commonly less perceptually distracting. The term describes spectral behaviour, not one algorithm.
Poisson-disk sampling is a practical route to a blue-noise-like distribution. It places points with a hard minimum separation, producing random-looking placement with controlled spacing. [1]
Mathematical construction
For domain D and radius r, a Poisson-disk set S satisfies ||p − q|| ≥ r for every distinct pair in S. Larger r means fewer, more separated points. Bridson’s method uses a background grid with cell width r/√n in n dimensions, then tests annular candidates around active samples; local neighbour lookups make it expected linear time for a fixed candidate count. [2]
A Fourier view supplies the complementary test: desirable blue-noise patterns have depleted power around the spectrum’s origin and avoid the sharp directional peaks of a square lattice. A minimum-distance constraint is useful but not identical to a complete spectral definition.
Reading the distribution
The exclusion disks in the diagram show the radius constraint. The left pattern is not perfectly even—local irregularity remains—but it prevents very near pairs and broad empty voids. The lattice at right has even spacing, yet its repeated axes produce strongly directional spectral peaks. Candidate count, edge handling, and varying radius all change an actual sampler’s result.
Structural use
- Sampling and anti-aliasing. Move error away from coherent low-frequency artifacts in rendering, stippling, and halftoning.
- Seed placement. Start marks, particles, cells, or paths with bounded crowding and non-periodic variation.
- Spatial allocation. Express material clearance, collision distance, drill spacing, or density limits.
- Variable density. Concentrate samples where detail is needed while relaxing them elsewhere.
Algorithmics note. A blue-noise seed map and a field that shapes marks are separate systems: distribution decides where events begin; a scalar or vector field decides how they vary.