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How 3 Frequencies Weave a 3D Crystal Sphere
Chaos & dynamics

How 3 Frequencies Weave a 3D Crystal Sphere

BEHIND THE WORK

What happens when three pure harmonic frequencies collide across 3D space? By tuning a spherical coordinate frame with integer ratios (5:7:3), sixteen continuous braided ribbons fold onto a sphere without breaking. The radial harmonic ripple pulses its surface, carving a celestial crystal sphere with exact 0.000mm periodic closure.

Related Video: Topology & The Impossible 3D Knots (https://youtu.be/0mvqG8cNyOw)

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

#MathArt #Harmonics #Geometry #Lissajous #3DArt #Mathematics #Blender3D #CrystalSphere #Shorts

THE MATHEMATICAL RULE

Individual strands before joining\text{Individual strands before joining}αs=2πs16,θ=5t+αs,s=0,…,15\alpha_s=\frac{2\pi s}{16},\quad\theta=5t+\alpha_s,\quad s=0,\ldots,15ϕ=π2+0.42πsin⁡(7t+αs/2),r=2.40+0.28cos⁡3t\phi=\frac\pi2+0.42\pi\sin(7t+\alpha_s/2),\quad r=2.40+0.28\cos3t(x,y,z)=r(cos⁡θsin⁡ϕ,sin⁡θsin⁡ϕ,cos⁡ϕ),0≤t≤2π(x,y,z)=r(\cos\theta\sin\phi,\sin\theta\sin\phi,\cos\phi),\quad0\leq t\leq2\pi
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