Overview
Reaction-Diffusion systems update chemical concentrations through diffusion between neighboring cells and local reaction terms.
SpecializedSource checked
Reaction-Diffusion
Creates organic patterns by simulating chemicals that spread and react on a grid.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Procedural Generation
- Difficulty
- Advanced
- Family
- Pattern Simulation
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 1
- Relationships
- 4
- Code example
- Ready
- Visualization
- Ready
Core Concepts
chemical concentrationdiffusionlocal reactionemergent pattern
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(cells)
Average
O(steps * cells)
Worst
O(steps * cells)
Space
O(cells)
When to Use
- Use when organic texture patterns should emerge from local interactions.
- Use when animal-skin patterns is a central requirement.
When Not to Use
- Avoid when exact art-directable shapes are required.
- Avoid when the generator cannot enforce the playability, connectivity, or style constraints required.
What It Does
- Computes pattern simulation within Pattern Simulation workloads (O(steps * cells) time, O(cells) space).
- Works by Creates organic patterns by simulating chemicals that spread and react on a grid.
- Maintains key invariants across chemical concentration, diffusion, local reaction.
Use Cases
- Animal-skin patterns
- Organic textures
- Generative art
Inputs
- Chemical grids
- Diffusion rates
- Reaction parameters
Outputs
- Patterned concentration fields
Key Formulas (1)
Gray-Scott update
Anext = A + (diffA · laplacian(A) − A·B·B + feed·(1−A)) · dt
A_next = A + (diffA * laplacian(A) - A*B*B + feed*(1-A)) * dtShows a common reaction-diffusion update for one chemical.
Pseudocode
- 1.Initialize chemical concentration grids
- 2.For each step, compute diffusion from neighbors
- 3.Apply reaction equations
- 4.Clamp or normalize concentrations
- 5.Render one concentration as a pattern
Canonical Example
- Input
- grid starts with small chemical disturbance
- Output
- pattern = spots after many steps
- Explanation
- Diffusion spreads chemicals while reactions amplify local differences.
Implementation Notes
- Use ping-pong buffers so each update reads the previous state consistently.
- Expose seed, scale, and constraint parameters so outputs can be reproduced.
- Keep a tiny example with expected output beside the implementation.
Common Pitfalls
- Large timesteps can make concentration values unstable.
- 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 spots and stripes emerging from interacting chemical fields.
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Step 1 of 5: Initialize chemical concentration grids
generated-gridNotes
Small parameter changes can switch patterns between spots, stripes, and noise.
Sources (2)
What each reference supports for this entry.
Turing Morphogenesis
PaperOriginal reaction-diffusion reference for activator-inhibitor pattern formation.
Open sourceTexturing and Modeling: A Procedural Approach
BookProcedural texturing reference supporting Reaction-Diffusion 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 pageConceptual neighborCellular Automata
Both evolve grid states through local update rules.
Depends onFinite Difference Method
Grid-based reaction-diffusion simulations often discretize differential equations with finite differences.
Related Algorithms
Tags
Procedural GenerationReaction-DiffusionSimulationCellular Automata