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Fractal Brownian motion (fBm)

Programming På svenska → Updated: 2026-10-25

Stack several layers of noise — each at double the frequency and half the amplitude — until the result has detail at every scale.

A single layer of Perlin or simplex noise is smooth and dull. Sum five or six octaves instead, each one finer and fainter than the last, and you get the self-similar roughness of mountain ranges, clouds and coastlines. The technique borrows its name and idea from Benoît Mandelbrot's fractional Brownian motion.

Two knobs set the character: lacunarity (how much the frequency grows per octave) and gain or persistence (how fast the amplitude falls off). Small changes separate a soft hill from a jagged cliff, which makes fBm the workhorse behind procedural heightmaps and terrain.

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