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What If a Wave Beats Like a Heart in 3D Space?
Differential geometry & surfaces

What If a Wave Beats Like a Heart in 3D Space?

BEHIND THE WORK

What happens when a non-linear wave breathes in 3-dimensional space without ever dissolving? Governed by the sine-Gordon field equation, the Breather surface is a pseudospherical manifold of constant negative Gaussian curvature (K = -1). Exactly 53 harmonic waves weave across 40pi angular cycles to sculpt dual trumpet spires and an undulating pulsating disk in one unbroken line with exact 0.000mm periodic closure.

Playlist: Differential Geometry & Minimal Surfaces

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

#MathArt #DifferentialGeometry #Soliton #SineGordon #Topology #Mathematics #3DArt #Blender3D #GenerativeArt #Shorts

THE MATHEMATICAL RULE

Base trajectory before orientation and framing\text{Base trajectory before orientation and framing}w=0.9, b=1−w2, u=13cos⁡(106πt), v=40πt,0≤t≤1w=0.9,\ b=\sqrt{1-w^2},\ u=13\cos(106\pi t),\ v=40\pi t,\quad0\leq t\leq1d=b[(wcosh⁡(bu))2+(bsin⁡(wv))2]d=b\left[(w\cosh(bu))^2+(b\sin(wv))^2\right]X=−u+2w2cosh⁡(bu)sinh⁡(bu)dX=-u+\frac{2w^2\cosh(bu)\sinh(bu)}dY=2wcosh⁡(bu)[−wcos⁡vcos⁡(wv)−sin⁡vsin⁡(wv)]dY=\frac{2w\cosh(bu)[-w\cos v\cos(wv)-\sin v\sin(wv)]}dZ=2wcosh⁡(bu)[−wsin⁡vcos⁡(wv)+cos⁡vsin⁡(wv)]dZ=\frac{2w\cosh(bu)[-w\sin v\cos(wv)+\cos v\sin(wv)]}d(x,y,z)=(Y,Z,X)(x,y,z)=(Y,Z,X)
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