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Three Spheres Trap an Infinite Void
Fractals & inversion

Three Spheres Trap an Infinite Void

BEHIND THE WORK

What happens when four spheres kiss in 3-dimensional space? Governed by Descartes' 4-Sphere Theorem, the 3D Apollonian Spherical Foam packs mutually tangent spheres into a cosmic tetrahedral cage. Trapped at the center lies the sacred Soddy void, an impossible inner sphere touching every boundary simultaneously. Traced through exact mathematical tangency points in one unbroken line with 0.000mm periodic closure.

Related Video: How Infinity Fits Inside a Circle (Longform Documentary LF_011) Playlist: Fractal Geometry & Conformal Inversions

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

#MathArt #ApollonianGasket #DescartesTheorem #Fractal #Geometry #3DArt #Blender3D #GenerativeArt #Mathematics #Shorts

THE MATHEMATICAL RULE

Sphere geometry before path construction\text{Sphere geometry before path construction}Cj∈12{(1,1,1),(1,−1,−1),(−1,1,−1),(−1,−1,1)}\mathbf C_j\in\frac1{\sqrt2}\{(1,1,1),(1,-1,-1),(-1,1,-1),(-1,-1,1)\}∥x−Cj∥=1,rinner=3/2−1\|\mathbf x-\mathbf C_j\|=1,\quad r_{\mathrm{inner}}=\sqrt{3/2}-1∥x∥=rinner,Pij=Ci+Cj2\|\mathbf x\|=r_{\mathrm{inner}},\quad\mathbf P_{ij}=\frac{\mathbf C_i+\mathbf C_j}{2}
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WATCH IT COME TO LIFE

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