🔬 Research Category Hub
Tag: Fractal Geometry
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ISL Constraint Geometry: Derivation of the Fundamental Shapes of Reality and the Origin of Constant Φ = 120
Derivation of the 21 stable shapes across dimensions under four ISL closure layers. Explaining the sequence 1, 1, ∞, 5, 6, 3, 3…, the 24-cell anomaly, and α⁻¹…
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Fractal Approximations of Classical Curves and the Dimension Discontinuity Phenomenon
Constructive proof that fractal sequences with constant Hausdorff dimension ≈ 1.465 converge to smooth circles with dim = 1.0 at rate O(1/n²), proving Hausdorff dimension is not continuous.
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Code as Geometry: How 21 Universal Shapes Project to 9 Programming Languages
The GeoCode universal intermediate representation: eliminating syntactic syntax tax with 21 universal shapes and a 3-layer Graph IR projecting cleanly into Python, Rust, and C++.
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