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An interactive 2D simulator comparing three rectangular constructions under iterative square-cutting (Gauss map) with different scaling parameters (λ = √2, φ, π). The visualization demonstrates that only λ = φ produces a geometrically self-similar rectangle where the continued fraction ratio returns to itself at every depth. All three panels use identical computation — no hard-coding — with uniform floating-point error correction across all known constants. The closure of φ emerges from pure arithmetic: φ − 1 = 1/φ, the unique fixed point of the Gauss map among real numbers greater than 1. Built in vanilla JavaScript with Canvas 2D rendering, synchronized animation, and real-time ratio tracking. Part of the Captain Cookie Face Universe (CCFU) framework deriving geometric structure from C₂ algebraic symmetry.
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Title C₂ in algebra · Closure in geometry
An interactive 2D simulator comparing three rectangular constructions under iterative square-cutting (Gauss map) with different scaling parameters (λ = √2, φ, π). The visualization demonstrates that only λ = φ produces a geometrically self-similar rectangle where the continued fraction ratio returns to itself at every depth. All three panels use identical computation — no hard-coding — with uniform floating-point error correction across all known constants. The closure of φ emerges from pure arithmetic: φ − 1 = 1/φ, the unique fixed point of the Gauss map among real numbers greater than 1. Built in vanilla JavaScript with Canvas 2D rendering, synchronized animation, and real-time ratio tracking. Part of the Captain Cookie Face Universe (CCFU) framework deriving geometric structure from C₂ algebraic symmetry.
Work type Script
Tags φ, the golden point on ℍ¹, captain cookie face
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Identifier 2604245382358
Entry date Apr 24, 2026, 12:22 PM UTC
License All rights reserved
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Author 100.00 %. Holder Captain Cookie Face Universe. Date Apr 24, 2026.
Information available at https://www.safecreative.org/work/2604245382358-c2-in-algebra-closure-in-geometry
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