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Can Infinite Circles Kiss Without Ever Crossing?
Conformal geometry & fractals

Can Infinite Circles Kiss Without Ever Crossing?

BEHIND THE WORK

How do infinite circles kiss in perfect harmony without ever crossing each other? Governed by Descartes' Circle Theorem, the Apollonian Gasket packs recursively tangent circles into every curving void. Traversed by a single continuous line at exact mathematical tangency points, this radiant sacred geometry achieves exact 0.000mm periodic closure.

Playlist: Fractal Geometry & Conformal Dynamics

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

#MathArt #ApollonianGasket #DescartesTheorem #Fractal #Geometry #SacredGeometry #Mathematics #GenerativeArt #Blender3D #Shorts

THE MATHEMATICAL RULE

Nested ring rule used within the circle layout\text{Nested ring rule used within the circle layout}φ=1+52,rk+1=rk/φ\varphi=\frac{1+\sqrt5}{2},\quad r_{k+1}=r_k/\varphiP=C+r0(cos⁡α,sin⁡α)\mathbf P=\mathbf C+r_0(\cos\alpha,\sin\alpha)Ck+1=P−rk+1(cos⁡α,sin⁡α)\mathbf C_{k+1}=\mathbf P-r_{k+1}(\cos\alpha,\sin\alpha)qk+1(t)=Ck+1+rk+1(cos⁡(α+t),sin⁡(α+t))\mathbf q_{k+1}(t)=\mathbf C_{k+1}+r_{k+1}(\cos(\alpha+t),\sin(\alpha+t))
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