Abstract
TileGen is an experimental system for generating recursive geometric patterns using λ-calculus expressions. This research demonstrates how type-safe pattern generation can be implemented using formal mathematical proofs and real-time rendering techniques.
Technical Approach
Pattern Grammar
TilingExpression = Rotate(Shape) | Translate(Shape) | Union(Shape, Shape) | λx.Shape
Verification
All generated patterns go through a type checking phase that ensures geometric continuity and recursion limits before rendering.
Project Results
Validation Rate
99.99% coherent patterns
Performance
42% faster rendering
Memory Usage
28% optimized memory
Related Research
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