Overview
Perlin Noise assigns gradients to grid points and blends their influence to create coherent noise.
FoundationSource checked
Perlin Noise
Generates smooth random-looking variation over space.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Procedural Generation
- Difficulty
- Intermediate
- Family
- Coherent Noise
- Tier
- Foundation
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 1
- Relationships
- 8
- Code example
- Not ready
- Visualization
- Ready
- Aliases
- Gradient Noise
Core Concepts
gradient latticesmooth interpolationnoise octaveseeded fieldgenerated structuresmooth noise fieldrendered imagecoherent noise
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(1)
Average
O(1)
Worst
O(1)
Space
O(g)
When to Use
- Use it when smooth, repeatable pseudo-random variation is needed.
- Use it for terrain, textures, clouds, and procedural animation parameters.
- Use multiple octaves when richer fractal detail is desired.
When Not to Use
- Avoid it when white-noise independence is required.
- Avoid it when authored control matters more than procedural variation.
- Avoid visible grid artifacts by choosing scale and interpolation carefully.
What It Does
- Creates smooth noise values
- Blends local gradient contributions
Use Cases
- Terrain generation
- Texture variation
- Natural-looking animation
Inputs
- Coordinate
- Gradient grid
- Scale or frequency
Outputs
- Noise value
Key Formulas (1)
Interpolation
value = lerp(dot(g0, d0), dot(g1, d1), fade(t))
value = lerp(dot(g0, d0), dot(g1, d1), fade(t))Blends gradient dot products with a smooth fade curve.
Pseudocode
- 1.Find the grid cell containing the coordinate
- 2.Get gradients at the cell corners
- 3.Compute each corner's influence
- 4.Smoothly interpolate the influences
- 5.Return the blended noise value
Canonical Example
- Input
- coordinate = (2.3, 4.7), seeded gradient grid
- Output
- a smooth noise value
- Explanation
- The value blends gradient influences from the corners of the containing grid cell.
Implementation Notes
- Find the lattice cell containing the query point.
- Hash cell corners to deterministic gradient vectors.
- Interpolate corner influences with a smooth fade function.
Common Pitfalls
- Using a scale that makes grid structure visible.
- Forgetting to seed or hash gradients deterministically.
- Adding octaves without controlling amplitude, frequency, and range.
Interactive Mechanism Walkthrough
Spatial Primitive & Sweep-Line CanvasShow smooth grayscale noise forming from grid gradients.
Step 1 of 5: Find the grid cell containing the coordinate
coherent-noiseNotes
Layering octaves of Perlin noise creates fractal-looking variation, but the output range should be normalized if downstream code expects bounds.
Sources (2)
What each reference supports for this entry.
Perlin Image Synthesizer
PaperOriginal Perlin reference for coherent procedural noise and solid textures.
Open sourceTexturing and Modeling: A Procedural Approach
BookProcedural-generation reference for Perlin Noise's noise, texture synthesis, and terrain/shape generation use cases.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Alternative toSimplex Noise
Procedural Generation · Core
Both produce coherent gradient-based noise.
Compare with thisAlternativesWorley Noise
Procedural Generation · Core
Worley Noise produces cellular patterns rather than smooth gradient noise.
Compare with thisUsed byFractal Brownian Motion
Procedural Generation · Core
fBm often layers Perlin-style noise across octaves.
Compare with thisGeneralizesGradient Noise
Procedural Generation · Core
Perlin Noise is a classic gradient-noise construction.
Compare with thisRelationships
View full relationship pageGeneralizesGradient Noise
Perlin Noise is a classic gradient-noise construction.
Alternative toSimplex Noise
Both produce coherent gradient-based noise.
Related Algorithms
Tags
Procedural GenerationNoiseGraphics