Fractal Brownian Motion (FBM)
A single noise layer is too uniform — it lacks detail. FBM stacks multiple layers together, each at double the frequency and half the amplitude, producing both large-scale variation and fine surface texture:
What an octave is
Each layer is called an octave. The first octave is low-frequency, large-scale noise (providing the overall shape). The second doubles the frequency and halves the amplitude (adding mid-range detail). Each subsequent octave adds finer and finer detail. Beyond about 6 octaves the added detail becomes imperceptible.
Frequency doubling, amplitude halving
Amplitudes decay by powers of 0.5 (1/2, 1/4, 1/8...), so the infinite sum converges — the total value stays below 1.0.
Three columns in the canvas
Left column shows 1 octave — smooth large patches, like a height-map outline. Middle column shows 3 octaves — medium detail added. Right column shows 6 octaves — the richest detail, like real terrain or a cloud cross-section.
Try changing it
| Change | Effect |
|---|---|
int octaves = 4 → 1 | Only the coarse, large-scale noise layer |
int octaves = 4 → 8 | Very fine high-frequency detail (hard to see improvement beyond 6) |
amplitude *= 0.5 → amplitude *= 0.7 | Higher layers decay slower, more detail, higher contrast |
uv * 3.0 → uv * 6.0 | Double overall frequency, finer texture |
Exercise
Change int octaves = 4 to 1, then 3, then 6, and observe how the amount of surface detail changes with each value.
Answer Breakdown
1 octave: A single smooth noise layer, similar to plain value noise. No fine detail.
3 octaves: Medium-frequency detail appears. Shapes start to feel complex, like condensed cloud or gentle terrain.
6 octaves: Rich detail approaching natural complexity. Tiny surface texture makes the result feel more realistic.
Key pattern: each additional octave contributes half the amplitude of the previous one, so the visual improvement from each new octave is smaller. Beyond 6–8 octaves the difference is essentially invisible.