How One Quantum Line Can Weave 6D Space

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.

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THE MATHEMATICAL RULE

\text{Implemented 3D ribbon before normalization}

u=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}

(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=x_1+0.6x_2,\quad y=y_1-0.6y_2

z=1.2\sin5t\cos2t+0.4(x_1y_2-x_2y_1),\quad0\leq t<2\pi

WATCH IT COME TO LIFE

Watch the drawing

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