FBM sums octaves at doubling frequency and halving amplitude — more octaves add finer natural detail across scales

Fractal Brownian Motion (FBM) is a technique for generating noise with detail at multiple scales simultaneously, matching how natural surfaces appear: rough at a large scale and rough again at a smaller scale. The algorithm sums several octaves of noise, where each successive octave has double the spatial frequency (finer grain) and half the amplitude (lower contribution). Adding more octaves increases fine detail but is computationally more expensive. The result looks natural because natural phenomena (terrain, clouds, wood grain) share this self-similar multi-scale roughness. FBM is the go-to choice when plain single-frequency noise looks too smooth or too simple.

Examples

GLSL FBM with 5 octaves: fbm(p) = noise(p) + 0.5*noise(p*2) + 0.25*noise(p*4) + 0.125*noise(p*8) + 0.0625*noise(p*16). Each term adds finer detail at lower amplitude.

Assessment

A texture looks too smooth and uniform. The developer is using a single noise layer. Identify the specific technique to add multi-scale natural detail, describe the two parameters that change with each octave, and predict what changing the octave count from 3 to 8 will look like.