CRT Procedural Generation

Unity / Unreal / Epic Games. CC0.

Game engines spend millions on proprietary procedural generation: Perlin noise with heuristic octaves, hand-tuned biome rules, compute-heavy terrain shaders. CRT approach: every grid cell IS a ring element in Z/214,414,200. Its 7 CRT channels ARE 7 algebraically independent octaves. Its GCD class IS its biome. Coupling to neighbors IS terrain smoothness. No noise functions. No hand-tuning. The ring structure IS the world generator.

How It Works

CRT Terrain Generation Theorem
Every cell at position (x,y) maps to a unique ring element in Z/214,414,200. The 7 CRT channels provide 7 algebraically independent frequency octaves: mod 8 = continental scale, mod 9 = regional features, mod 25 = hills and valleys, mod 49 = fine rock texture, mod 11 = moisture distribution, mod 13 = temperature gradient, mod 17 = vegetation density. These octaves are PROVABLY independent (CRT guarantee), unlike Perlin noise where octave independence is heuristic. GCD classification determines biome type. Coupling between adjacent cells = terrain smoothness. The ring IS the world.
7 octaves
CRT channels
Each channel = one independent frequency layer. Algebraically guaranteed independence.
GCD biome
O(1) classify
gcd(val, N) = biome. No lookup table. No rules engine. The algebra IS the classifier.
7 channels
Independent
7 coprime moduli: 8, 9, 25, 49, 11, 13, 17. Each channel carries one terrain feature.
Deterministic
Reproducible
Same seed = same world. Always. No floating-point drift. No platform variance.

Generate Terrain

World seed:

Generates a 12x10 terrain grid. Each cell = one ring element in Z/214,414,200. Color = biome (GCD classification). Symbol = elevation (CRT-weighted channel sum). Cross-section shows full 7-channel decomposition.

Terrain Map (Canvas)

World seed:

192x144 pixel terrain rendered to canvas via cvs_blit. Each pixel = one terrain cell. Color = biome from GCD classification. Upscaled 3x with pixelated rendering. One bulk call paints 27,648 pixels.

Biome Distribution

400-cell world. Biome classification via gcd(val, 214414200). Each biome maps to a specific algebraic divisibility pattern.

CRT Octave Decomposition

Watch elevation build up as each CRT channel adds its octave. mod 8 = continental. mod 9 = regional. mod 25 = hills. mod 49 = rocks. mod 11 = moisture. mod 13 = temperature.

CRT vs Traditional Procedural Generation

Noise functionPerlin/Simplex: gradient interpolation, heuristic octavesCRT: ring residues = natural octaves. Provably independent.OctavesArbitrary: 4-8 octaves with hand-tuned persistence7 CRT channels: algebraically independent. No tuning.BiomesRule-based: temperature + moisture thresholds (hand-authored)GCD class: gcd(val,N) = biome. Algebraic. Zero rules.SmoothnessGradient interpolation (computationally expensive)Coupling distance: sum of per-channel differences. O(1).DeterminismFloating-point: platform-dependent rounding differencesInteger arithmetic: identical on ALL platforms. Always.Patent statusUnity (SpeedTree), Epic (Nanite), various (noise patents)CC0. Public domain. Forever.

Source code · Public domain (CC0)

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