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16 Golden Rings Weave a 4D Stargate | Centennial
Higher dimensions & 4D geometry

16 Golden Rings Weave a 4D Stargate | Centennial

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BEHIND THE WORK

What does four-dimensional space look like when woven from pure light? In topology, the Hopf fibration maps the 3-sphere (S³) onto the 2-sphere (S²), decomposing 4D space into an infinite family of linked circles. Stereographically projected into three dimensions, exactly 16 golden Villarceau circles glide across the Clifford torus, forming a celestial stargate with exact 0.000mm periodic closure.

Related Video: How Infinity Fits Inside a Circle (Longform Documentary LF_011) Playlist: Higher Dimensions & 4D Geometry

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

#MathArt #HopfFibration #4DGeometry #Topology #HigherDimensions #Geometry #3DArt #Blender3D #GenerativeArt #Mathematics #Shorts

THE MATHEMATICAL RULE

Implemented 4D curve and projection before framing\text{Implemented 4D curve and projection before framing}η=π/2,ϕ=16t,ξ=2t,0≤t≤2π\eta=\pi/2,\quad\phi=16t,\quad\xi=2t,\quad0\leq t\leq2\pix1=cos⁡(η/2)cos⁡(ϕ+ξ/2),x2=cos⁡(η/2)sin⁡(ϕ+ξ/2)x_1=\cos(\eta/2)\cos(\phi+\xi/2),\quad x_2=\cos(\eta/2)\sin(\phi+\xi/2)x3=sin⁡(η/2)cos⁡(ϕ−ξ/2),x4=sin⁡(η/2)sin⁡(ϕ−ξ/2)x_3=\sin(\eta/2)\cos(\phi-\xi/2),\quad x_4=\sin(\eta/2)\sin(\phi-\xi/2)(X,Y,Z)=(x1,x2,x3)1−0.65x4(X,Y,Z)=\frac{(x_1,x_2,x_3)}{1-0.65x_4}

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