Overview
Diffusion-limited aggregation repeatedly releases walkers that wander until they touch the cluster, producing organic branching forms.
ExtendedSource checked
Diffusion-Limited Aggregation
Generates branching clusters by letting random walkers stick to an existing structure.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Procedural Generation
- Difficulty
- Intermediate
- Family
- Growth Model
- Tier
- Extended
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 1
- Relationships
- 1
- Code example
- Ready
- Visualization
- Ready
Core Concepts
random walksticking rulecluster growthbranching pattern
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(walkers)
Average
O(walkers * steps)
Worst
O(walkers * steps)
Space
O(grid)
When to Use
- Use when generating terrain needs random walk.
- Use when the input matches the assumptions behind growth Model.
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 branching clusters by letting random walkers stick to an existing structure
- Uses random walk and sticking rule 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)
Stick rule
attach walker if neighbor is occupied
attach walker if neighbor is occupiedAdds a particle to the cluster once it touches existing growth.
Pseudocode
- 1.Prepare the inputs and state needed for Diffusion-Limited Aggregation.
- 2.Apply the random walk step while the stopping condition has not been met.
- 3.Update intermediate state and discard invalid candidates.
- 4.Return generated map, texture, layout, or pattern.
Canonical Example
- Input
- Diffusion-Limited Aggregation input with a small representative case
- Output
- Generated map, texture, layout, or pattern
- Explanation
- Diffusion-Limited Aggregation applies random walk to produce generated map, texture, layout, or pattern.
Implementation Notes
- Keep the seed and parameters stored with generated output for reproducibility.
- Keep the random walk step separate enough to test independently.
Common Pitfalls
- Small parameter changes can create large visual or structural differences.
- Forgetting to check edge cases can make Diffusion-Limited Aggregation look correct on only ideal inputs.
Interactive Mechanism Walkthrough
Spatial Primitive & Sweep-Line CanvasShow the generation state evolving from seed values to the final artifact.
Step 1 of 4: Prepare the inputs and state needed for Diffusion-Limited Aggregation.
procedural-generation-mechanismNotes
Diffusion-Limited Aggregation should be used with the assumptions and tradeoffs of growth Model in mind.
Sources (2)
What each reference supports for this entry.
Diffusion-Limited Aggregation
PaperOriginal DLA reference for random-walk particle aggregation and branching clusters.
Open sourceProcedural Content Generation in Games
BookProcedural-generation reference supporting Diffusion-Limited Aggregation constraint solving, constructive generation, terrain, dungeon, or stochastic content workflow.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageUsesDrunkard's Walk
Diffusion-limited aggregation grows clusters from random walks that stick to existing particles.
Related Algorithms
Tags
Procedural GenerationGrowth ModelRandom WalkParticles