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Fractal Brownian Motion

Layers noise at multiple frequencies to create richer natural variation.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Procedural Generation
Difficulty: Intermediate
Family: Coherent Noise
Tier: Core
Status: Verified
Review: Source Checked
Sources: 1
Formulas: 1
Relationships: 6
Code example: Not ready
Visualization: Ready
Aliases: fBm

Overview

Fractal Brownian Motion sums several octaves of coherent noise with decreasing amplitude and increasing frequency.

Core Concepts

generated structuresmooth noise fieldmulti-scale detailcoherent noiseseeded variationrule expansionspatial structure

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(o)

Average

O(o)

Worst

O(o)

Space

O(1)

When to Use

Use Fractal Brownian Motion when you need to sample several noise octaves.
Use it for terrain detail with inputs like noise function.
Use it when repeatable content can be produced from compact rules, parameters, and seeds.
Use it when the Coherent Noise tradeoff is acceptable for the problem size.

When Not to Use

Avoid it when authored control matters more than variation or replayability.
Avoid it when the required output is not layered noise value or field.

What It Does

Samples several noise octaves
Combines them into multi-scale detail

Use Cases

Terrain detail
Cloud textures
Procedural materials

Inputs

Noise function
Octave count
Frequency and amplitude settings

Outputs

Layered noise value or field

Key Formulas (1)

Octave sum

value = ∑(amplitude_i · noise(frequency_i · point))

value = sum(amplitude_i * noise(frequency_i * point))

Adds multiple noise layers at different scales.

Pseudocode

1.Start with amplitude and frequency
2.Sample the base noise function
3.Add the weighted sample to the total
4.Increase frequency and reduce amplitude
5.Repeat for each octave

Canonical Example

Input: seed = 42, size = 8x8
Output: generated map, pattern, or noise field
Explanation: Fractal Brownian Motion: The algorithm expands a small set of rules and random choices into structured content.

Implementation Notes

Keep the input contract explicit: Noise function; Octave count; Frequency and amplitude settings.
Expose seed and parameters so results can be reproduced and tuned.
Store seed, parameters, and validation results with generated output so artifacts can be reproduced.

Common Pitfalls

Persistence and lacunarity control how rough the result feels.
Letting random choices create disconnected, invalid, or impossible-to-use output.
Handle empty, invalid, and boundary inputs before trusting layered noise value or field.
Changing a seed or constraint weight can create artifacts that are hard to reproduce without recorded parameters.

Interactive Mechanism Walkthrough

Spatial Primitive & Sweep-Line Canvas

Show smooth noise layers combining into detailed texture.

Step 1 of 5: Start with amplitude and frequency

noise-octaves

Notes

Fractal Brownian Motion operates in O(o) time and O(1) space within the Coherent Noise family. Key governing relation: value = sum(amplitude_i * noise(frequency_i * point)). Often compared with Perlin Noise and Simplex Noise.