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8 Harmonic Waves Weave 1 Blooming 3D Lotus
Curves & geometry

8 Harmonic Waves Weave 1 Blooming 3D Lotus

BEHIND THE WORK

Can a single mathematical line bloom into a 3-dimensional lotus crown? By extending Viviani's classical sphere-cylinder window into an 8-fold harmonic coordinate system, eight cupped petals flare outward and curl toward the sky. The continuous space curve weaves every petal in an unbroken sequence, creating a radiant floral sculpture 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 #VivianiCurve #Geometry #SacredGeometry #3DArt #Mathematics #Blender3D #FloralArt #Shorts

THE MATHEMATICAL RULE

Petal geometry before joining and framing\text{Petal geometry before joining and framing}W(s)=0.38sin⁡0.65(πs),r(s)=0.30+1.35sin⁡(0.85πs)W(s)=0.38\sin^{0.65}(\pi s),\quad r(s)=0.30+1.35\sin(0.85\pi s)ϕ=kπ4+w,0.06≤s≤0.96, ∣w∣≤W(s), k=0,…,7\phi=\frac{k\pi}{4}+w,\quad0.06\leq s\leq0.96,\ |w|\leq W(s),\ k=0,\ldots,7z=1.40s1.2−0.40+0.15(1−(wmax⁡(10−5,W(s)))2)sin⁡(πs)z=1.40s^{1.2}-0.40+0.15\left(1-\left(\frac{w}{\max(10^{-5},W(s))}\right)^2\right)\sin(\pi s)(x,y)=(rcos⁡ϕ,rsin⁡ϕ)(x,y)=(r\cos\phi,r\sin\phi)
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