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How One Quantum Line Can Weave 6D Space
Dimensions & topology

How One Quantum Line Can Weave 6D Space

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BEHIND THE WORK

Where do the extra dimensions of our universe hide? In superstring theory, spacetime curls up six invisible dimensions into a Ricci-flat Calabi-Yau manifold. This 3D real slice traces a 5-fold symmetric geodesic ribbon winding across all five Riemann sheets with exact 0.000mm periodic closure.

Related Video: How Infinity Fits Inside a Circle (Longform Documentary LF_011) Playlist: Calabi-Yau Manifolds & Quantum Topology

Artismathic turns equations into visual art - one function at a time.

#MathArt #CalabiYau #StringTheory #QuantumTopology #6DGeometry #Geometry #3DArt #Blender3D #GenerativeArt #Mathematics #Shorts

THE MATHEMATICAL RULE

Implemented 3D ribbon before normalization\text{Implemented 3D ribbon before normalization}u=5t, v=3t,r1=sgn⁡(cos⁡v)∣cos⁡v∣2/5,r2=sgn⁡(sin⁡v)∣sin⁡v∣2/5u=5t,\ v=3t,\quad r_1=\operatorname{sgn}(\cos v)|\cos v|^{2/5},\quad r_2=\operatorname{sgn}(\sin v)|\sin v|^{2/5}(x1,y1)=r1(cos⁡u,sin⁡u),(x2,y2)=r2(cos⁡(4u/5+t),sin⁡(4u/5+t))(x_1,y_1)=r_1(\cos u,\sin u),\quad(x_2,y_2)=r_2(\cos(4u/5+t),\sin(4u/5+t))x=x1+0.6x2,y=y1−0.6y2x=x_1+0.6x_2,\quad y=y_1-0.6y_2z=1.2sin⁡5tcos⁡2t+0.4(x1y2−x2y1),0≤t<2πz=1.2\sin5t\cos2t+0.4(x_1y_2-x_2y_1),\quad0\leq t<2\pi

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