artismathicThe archive
ENKOJA
YouTube ↗
← Back to the archiveSHORT / 087
How 28 Math Chambers Carve a 3D Nautilus
Logarithmic forms & biomathematics

How 28 Math Chambers Carve a 3D Nautilus

BEHIND THE WORK

How do 28 mathematical chambers carve the living architecture of a 3D Nautilus shell? By expanding a logarithmic golden spiral into volumetric 3D elliptical septa, each chamber breathes with negative space and organic rhythm. An internal siphuncle axis weaves back through the core in a single continuous stroke, achieving exact 0.000mm periodic closure.

Playlist: Bio-Mathematics & Natural Growth

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

#MathArt #NautilusShell #GoldenRatio #BioMathematics #Fibonacci #Geometry #3DArt #Mathematics #Blender3D #Shorts

THE MATHEMATICAL RULE

Logarithmic spine before chamber offsets\text{Logarithmic spine before chamber offsets}θ(u)=0.6+5πu,r(u)=0.16e0.165θ(u),0≤u≤1\theta(u)=0.6+5\pi u,\quad r(u)=0.16e^{0.165\theta(u)},\quad0\leq u\leq1s(u)=(rcos⁡θ,rsin⁡θ,0)\mathbf s(u)=(r\cos\theta,r\sin\theta,0)
Watch the drawing↗

WATCH IT COME TO LIFE

Watch the drawing

YouTube loads only after you press play.