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Procedural Generation

Algorithms that create structured content from rules and randomness.

Procedural generation algorithms build textures, terrain, layouts, or patterns from compact rules instead of hand-authored data.

Procedural GenerationO(1)

Perlin Noise

Generates smooth random-looking variation over space.

IntermediateFoundationFormula8 links
Procedural GenerationNoiseGraphics
Procedural GenerationO(1)

Simplex Noise

Generates coherent noise using simplex-shaped grid cells.

AdvancedCoreNo formula3 links
Procedural GenerationNoiseGraphics
Procedural GenerationO(c r)

Wave Function Collapse

Generates layouts by repeatedly choosing low-uncertainty cells and propagating constraints.

AdvancedSpecializedNo formula6 links
Procedural GenerationConstraint SolvingStochastic
Procedural GenerationO(n log n)

Binary Space Partitioning Dungeon Generation

Builds dungeon rooms by recursively splitting space into partitions.

IntermediateExtendedNo formula3 links
Procedural GenerationDungeon GenerationTree
Procedural GenerationO(t n)

Cellular Automata Cave Generation

Creates cave-like maps by smoothing random grids with neighbor rules.

BeginnerExtendedNo formula4 links
Procedural GenerationCellular AutomataDungeon Generation
Procedural GenerationO(n)

Diamond-Square Algorithm

Generates fractal height maps by alternating square and diamond averaging steps.

IntermediateExtendedNo formula4 links
Procedural GenerationTerrainFractalRandomness
Procedural GenerationO(o)

Domain Warping

Distorts sampling coordinates with another noise field before evaluating procedural patterns.

IntermediateCoreFormula3 links
Procedural GenerationNoiseGraphics
Procedural GenerationO(s)

Drunkard's Walk

Generates paths or caves by moving a random walker through a grid.

BeginnerExtendedNo formula4 links
Procedural GenerationRandomnessDungeon Generation
Procedural GenerationO(o)

Fractal Brownian Motion

Layers noise at multiple frequencies to create richer natural variation.

IntermediateCoreFormula6 links
Procedural GenerationNoiseFractal
Procedural GenerationO(n g)

L-System

Generates structures by repeatedly rewriting symbols with grammar rules.

BeginnerExtendedNo formula5 links
Procedural GenerationGrammar GenerationFractal
Procedural GenerationO(neighbor cells)

Worley Noise

Generates cellular patterns from distances to nearby feature points.

IntermediateCoreFormula3 links
Procedural GenerationNoiseGraphicsSpatial Sampling
Procedural GenerationO(1)

Value Noise

Creates smooth noise by interpolating random values stored on a grid.

BeginnerCoreFormula3 links
Procedural GenerationNoiseGraphicsInterpolation
Procedural GenerationO(octaves)

Ridged Multifractal Noise

Builds sharp ridge-like terrain by inverting and layering noise octaves.

IntermediateExtendedFormula3 links
Procedural GenerationNoiseFractalTerrain
Procedural GenerationO(steps * cells)

Hydraulic Erosion

Shapes terrain by simulating water carrying and depositing sediment.

AdvancedSpecializedFormula3 links
Procedural GenerationTerrainErosionSimulation
Procedural GenerationO(iterations * cells)

Thermal Erosion

Smooths steep terrain by moving material from unstable slopes to lower neighbors.

IntermediateSpecializedFormula2 links
Procedural GenerationTerrainErosionSimulation
Procedural GenerationO(iterations * points * branches)

Space Colonization Algorithm

Generates branching structures by growing toward nearby attraction points.

AdvancedSpecializedFormula2 links
Procedural GenerationPlant GrowthSpatial SamplingSimulation
Procedural GenerationO(steps * cells)

Reaction-Diffusion

Creates organic patterns by simulating chemicals that spread and react on a grid.

AdvancedSpecializedFormula4 links
Procedural GenerationReaction-DiffusionSimulationCellular Automata
Procedural GenerationO(samples * dimensions)

Gradient Noise

Generates smooth noise by interpolating dot products with random lattice gradients.

IntermediateCoreFormula6 links
Procedural GenerationNoiseInterpolationTexture Synthesis
Procedural GenerationO(n)

Midpoint Displacement

Generates rough terrain or curves by recursively displacing midpoints.

BeginnerCoreFormula3 links
Procedural GenerationTerrainFractalNoise
Procedural GenerationO(samples * sites)

Voronoi Terrain Generation

Builds terrain regions from distances to seed points or Voronoi cells.

IntermediateCoreFormula2 links
Procedural GenerationTerrainVoronoiSpatial Sampling
Procedural GenerationO(tokens)

Markov Chain Text Generation

Generates text by choosing each token from probabilities conditioned on recent tokens.

BeginnerCoreFormula1 links
Procedural GenerationMarkov ChainText GenerationProbabilistic Model
Procedural GenerationO(output size)

Grammar-Based Generation

Generates structures by expanding grammar symbols into rules.

IntermediateCoreFormula4 links
Procedural GenerationGrammar GenerationGrammarConstraint Solving
Procedural GenerationO(exponential)

Constraint-Based Generation

Generates content by searching for assignments that satisfy design constraints.

AdvancedCoreFormula4 links
Procedural GenerationConstraint SolvingSearchGeneration
Procedural GenerationO(n)

Poisson Disk Object Placement

Places objects with a minimum spacing so distributions look natural but not clumped.

IntermediateCoreFormula3 links
Procedural GenerationSpatial SamplingPoisson DiskSampling
Procedural GenerationO(iterations * samples)

Fault Formation Terrain

Creates terrain by repeatedly raising one side of random fault lines.

BeginnerExtendedFormula2 links
Procedural GenerationTerrainErosionFractal
Procedural GenerationO(steps * cells)

Tectonic Plate Terrain Generation

Generates large terrain features from simulated plate regions and interactions.

AdvancedSpecializedFormula1 links
Procedural GenerationTerrainSimulationVoronoi
Procedural GenerationO(walkers * steps)

Diffusion-Limited Aggregation

Generates branching clusters by letting random walkers stick to an existing structure.

IntermediateExtendedFormula1 links
Procedural GenerationGrowth ModelRandom WalkParticles
Procedural GenerationO(output size)

Shape Grammar Generation

Generates geometry by repeatedly applying spatial rewrite rules to shapes.

AdvancedExtendedFormula3 links
Procedural GenerationGrammar GenerationGeometryGeneration
Procedural GenerationO(cells * patterns)

Wave Function Collapse Overlapping Model

Generates grids by enforcing local pattern compatibility learned from overlapping examples.

AdvancedSpecializedFormula3 links
Procedural GenerationConstraint SolvingTexture SynthesisGeneration
Procedural GenerationO(n)

Simple Tiled Model

Simple Tiled Model uses rules, noise, or constraints to synthesize repeatable generated content.

IntermediateCoreNo formula3 links
Procedural Generation
Procedural GenerationO(n)

Recursive Backtracking Maze Generation

Recursive Backtracking Maze Generation uses rules, noise, or constraints to synthesize repeatable generated content.

IntermediateCoreFormula2 links
Procedural Generation
Procedural GenerationO(n)

Prim Maze Generation

Prim Maze Generation uses rules, noise, or constraints to synthesize repeatable generated content.

IntermediateCoreNo formula1 links
Procedural Generation
Procedural GenerationO(n)

Kruskal Maze Generation

Kruskal Maze Generation uses rules, noise, or constraints to synthesize repeatable generated content.

IntermediateCoreFormula1 links
Procedural Generation
Procedural GenerationO(n)

Growing Tree Maze Algorithm

Growing Tree Maze Algorithm uses rules, noise, or constraints to synthesize repeatable generated content.

IntermediateCoreNo formula1 links
Procedural Generation
Procedural GenerationO(n)

Perlin Worms

Perlin Worms uses rules, noise, or constraints to synthesize repeatable generated content.

IntermediateCoreFormula1 links
Procedural Generation
Procedural GenerationO(n)

Agent-Based City Generation

Agent-Based City Generation uses rules, noise, or constraints to synthesize repeatable generated content.

IntermediateExtendedNo formula1 links
Procedural Generation
Procedural GenerationO(n)

Road Network L-System

Road Network L-System uses rules, noise, or constraints to synthesize repeatable generated content.

IntermediateSpecializedNo formula2 links
Procedural Generation
Procedural GenerationO(n log n)

Wang Tiles

Generates tiled patterns by matching edge colors between neighboring tiles.

IntermediateCoreNo formula4 links
Procedural Generation
Procedural GenerationO(n log n)

Truchet Tiles

Generates decorative patterns by rotating or selecting simple tile motifs.

IntermediateCoreNo formula3 links
Procedural Generation
Procedural GenerationO(n!) generated permutations

Heap's Algorithm

Generates permutations by recursively swapping elements.

IntermediateExtendedNo formula2 links
Procedural Generation
Procedural GenerationO(n!) generated permutations

Steinhaus-Johnson-Trotter Algorithm

Generates permutations so adjacent outputs differ by one adjacent swap.

IntermediateExtendedNo formula2 links
Procedural Generation
Procedural GenerationO(2^n) for all subsets; O(3^n) for nested mask/submask enumeration

Bitmask Subset Enumeration

Enumerates subsets by treating integers as bit masks.

IntermediateExtendedNo formula1 links
Bit LevelProcedural Generation