Overview
Ridged Multifractal Noise transforms each octave so values near zero become high ridges, then combines octaves into mountainous patterns.
ExtendedSource checked
Ridged Multifractal Noise
Builds sharp ridge-like terrain by inverting and layering noise octaves.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Procedural Generation
- Difficulty
- Intermediate
- Family
- Fractal Noise
- Tier
- Extended
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 3
- Code example
- Ready
- Visualization
- Ready
Core Concepts
noise octaveridge transformfractal layeringterrain height
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(octaves)
Average
O(octaves)
Worst
O(octaves)
Space
O(1)
When to Use
- Use when terrain needs craggy ridges rather than rolling hills.
- Use when mountain terrain is a central requirement.
When Not to Use
- Avoid when smooth clouds or soft blobs are the target style.
- Avoid when the generator cannot enforce the playability, connectivity, or style constraints required.
What It Does
- Samples multiple noise octaves
- Transforms noise into ridge responses
- Combines weighted ridge layers
Use Cases
- Mountain terrain
- Rocky masks
- Planet surface generation
Inputs
- Sample position
- Noise function
- Octave settings
Outputs
- Ridged noise value
Key Formulas (1)
Ridge transform
ridge = (offset − |noisevalue|)2
ridge = (offset - abs(noise_value))^2Turns values near zero into high ridge responses.
Pseudocode
- 1.For each octave, sample base noise
- 2.Convert the sample to a ridge value
- 3.Weight and add the ridge value
- 4.Increase frequency and reduce amplitude
- 5.Normalize the final result
Canonical Example
- Input
- base noise sample = -0.1
- Output
- ridge response = high
- Explanation
- Values near zero become ridge peaks after inversion.
Implementation Notes
- Clamp or normalize the final value before using it as height.
- Expose seed, scale, and constraint parameters so outputs can be reproduced.
- Keep a tiny example with expected output beside the implementation.
Common Pitfalls
- Too many high-frequency octaves can create noisy terrain instead of readable ridges.
- Random-looking output can still contain repeated patterns, dead ends, or invalid regions.
- Not defining boundary, empty, or degenerate inputs before implementation.
Interactive Mechanism Walkthrough
2D Grid Wavefront & TrajectoryShow smooth noise transformed into sharp bright ridge lines over several scales.
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Step 1 of 5: For each octave, sample base noise
generated-gridNotes
Gain and offset parameters strongly control ridge sharpness.
Sources (1)
What each reference supports for this entry.
Texturing and Modeling: A Procedural Approach
BookProcedural texturing reference supporting Ridged Multifractal Noise noise, tiling, terrain, growth, or pattern-generation mechanism.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageOften paired withDomain Warping
Domain warping can add complexity to ridged terrain patterns.
Variant ofFractal Brownian Motion
Ridged multifractal noise modifies layered noise to emphasize ridges.
Related Algorithms
Tags
Procedural GenerationNoiseFractalTerrain