Overview
Gradient noise produces continuous variation by assigning gradients to lattice points and blending their influence inside each cell.
CoreSource checked
Gradient Noise
Generates smooth noise by interpolating dot products with random lattice gradients.
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
- Ready
- Visualization
- Ready
Core Concepts
lattice gradientdot productsmooth interpolationcoherent noise
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(dimensions)
Average
O(samples * dimensions)
Worst
O(samples * dimensions)
Space
O(lattice)
When to Use
- Use when generating terrain needs lattice gradient.
- Use when the input matches the assumptions behind coherent Noise.
When Not to Use
- Avoid when the design needs strict authored control over every generated detail.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Generates smooth noise by interpolating dot products with random lattice gradients
- Uses lattice gradient and dot product to guide the work.
- Produces generated map, texture, layout, or pattern.
Use Cases
- Generating terrain
- Creating textures
- Building levels or natural patterns
Inputs
- Seed
- Generation parameters
- Constraint rules
Outputs
- Generated map, texture, layout, or pattern
Key Formulas (1)
Gradient contribution
value = dot(gradientcorner, point − corner)
value = dot(gradient_corner, point - corner)Measures each corner's influence before interpolation.
Pseudocode
- 1.Initialize the seed, grid, rule set, or generator state
- 2.Choose the next cell, feature, or parameter to update
- 3.Apply constraints, noise, or stochastic choices
- 4.Repeat until the generated structure satisfies the stopping rule
Canonical Example
- Input
- seed = 7 with a small tile set, rule set, terrain grid, or generation parameter
- Output
- Generated map, texture, layout, or pattern
- Explanation
- Gradient Noise applies lattice gradient to produce generated map, texture, layout, or pattern.
Implementation Notes
- Keep the seed and parameters stored with generated output for reproducibility.
- Keep the lattice gradient step separate enough to test independently.
- Store seed, parameters, and validation results with generated output so artifacts can be reproduced.
Common Pitfalls
- Small parameter changes can create large visual or structural differences.
- Test edge cases, not only clean examples.
- Changing a seed or constraint weight can create artifacts that are hard to reproduce without recorded parameters.
Interactive Mechanism Walkthrough
Spatial Primitive & Sweep-Line CanvasShow the generation state evolving from seed values to the final artifact.
Step 1 of 4: Initialize the seed, grid, rule set, or generator state
procedural-generation-mechanismNotes
Gradient Noise should be used with the assumptions and tradeoffs of coherent Noise in mind.
Sources (1)
What each reference supports for this entry.
Texturing and Modeling: A Procedural Approach
BookProcedural-generation reference for Gradient Noise's noise, texture synthesis, and terrain/shape generation use cases.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Has variantsSimplex Noise
Procedural Generation · Core
Simplex Noise belongs to the gradient-noise family.
Compare with thisAlternative toValue Noise
Procedural Generation · Core
Gradient noise interpolates gradients rather than scalar grid values.
Compare with thisRelationships
View full relationship pageGeneralizesPerlin Noise
Perlin Noise is a named gradient-noise method.
Alternative toValue Noise
Gradient noise interpolates gradients rather than scalar grid values.
Related Algorithms
Tags
Procedural GenerationNoiseInterpolationTexture Synthesis