Harmonic Triangle Fractals in Base-12 and Base-10: Integer Precision and the 10368 Lattice

© 2025 Andrew Delph. All rights reserved. Licensed under the Apache License, Version 2.0.

This preprint examines the behavior of recursively subdivided harmonic triangles in base-12 and base-10 numerical systems, using the highly composite number 10368 (2^7 × 3^4) as a harmonic lattice. The study compares integer-preserving subdivisions in base-12—where factors 2, 3, 4, 6, 8, 9, 12, and others yield exact lengths—against base-10, where many common factors produce repeating decimals. Results highlight base-12’s advantage for precise, resonant fractal geometry with potential applications in acoustics, crystalline modeling, and wave-based design. This work establishes a timestamped reference for the 10368 lattice method in harmonic fractal generation.