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An interactive 3D simulator visualizing the complete algebraic chain from the minimal memory recurrence C₂: x(n+1) = x(n) + x(n-1) to the Kepler triangle and pyramid geometry. The simulator offers two synchronized views — Mathematical and Human — of the same structure, with independently toggleable layers and mouse/touch rotation.
The Mathematical view builds the chain in six layers: the parent space sig(3,2) on R⁵ with dim = 5 = Δ(C₂); the Minkowski slice sig(3,1) with null cone; the hyperbolic space H³ embedded as the upper hyperboloid t² − r² = 1; the golden point (√φ, φ) lying on H³, verified by φ² − φ = 1; the Kepler right triangle with sides 1 : √φ : φ and angle arctan(√φ) = 51.83°; and the pyramid whose face slope equals the Kepler angle.
The Human view shows the same pyramid and Kepler triangle from a ground-level perspective, with spatial axes replacing signature labels.
All geometric values — φ = (1+√5)/2, √φ, the Kepler angle, the hyperboloid embedding — are computed live from C₂ data. No values are hard-coded independently. The pyramid height √φ and base half-width 1 produce slope arctan(√φ) = 51.827°, matching the measured face angle of the Great Pyramid of Giza within archaeological precision.
Built in vanilla JavaScript with Canvas 2D rendering, perspective projection, and smooth layer interpolation. Part of the Captain Cookie Face Universe (CCFU) framework deriving geometric structure from C₂ algebraic symmetry.
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Title From C₂ to Pyramid
An interactive 3D simulator visualizing the complete algebraic chain from the minimal memory recurrence C₂: x(n+1) = x(n) + x(n-1) to the Kepler triangle and pyramid geometry. The simulator offers two synchronized views — Mathematical and Human — of the same structure, with independently toggleable layers and mouse/touch rotation.
The Mathematical view builds the chain in six layers: the parent space sig(3,2) on R⁵ with dim = 5 = Δ(C₂); the Minkowski slice sig(3,1) with null cone; the hyperbolic space H³ embedded as the upper hyperboloid t² − r² = 1; the golden point (√φ, φ) lying on H³, verified by φ² − φ = 1; the Kepler right triangle with sides 1 : √φ : φ and angle arctan(√φ) = 51.83°; and the pyramid whose face slope equals the Kepler angle.
The Human view shows the same pyramid and Kepler triangle from a ground-level perspective, with spatial axes replacing signature labels.
All geometric values — φ = (1+√5)/2, √φ, the Kepler angle, the hyperboloid embedding — are computed live from C₂ data. No values are hard-coded independently. The pyramid height √φ and base half-width 1 produce slope arctan(√φ) = 51.827°, matching the measured face angle of the Great Pyramid of Giza within archaeological precision.
Built in vanilla JavaScript with Canvas 2D rendering, perspective projection, and smooth layer interpolation. Part of the Captain Cookie Face Universe (CCFU) framework deriving geometric structure from C₂ algebraic symmetry.
Work type Script
Tags light-space, ccf simulator, captain cookie face, light-matter
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Registry info in Safe Creative
Identifier 2605125630446
Entry date May 12, 2026, 2:08 PM UTC
License All rights reserved
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Author 100.00 %. Holder Captain Cookie Face Universe. Date May 12, 2026.
Information available at https://www.safecreative.org/work/2605125630446-from-c2-to-pyramid
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