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Can Pure Math Grow a Diamond Snowflake?
Fractals & patterns

Can Pure Math Grow a Diamond Snowflake?

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BEHIND THE WORK

Can a single mathematical line grow an intricate hexagonal ice crystal with zero human intervention? Governed by D6 dihedral crystal invariants and self-similar dendritic branching at exact 60-degree intervals, this diamond snowflake traces tiered chevron needles, intermediate star spurs, and faceted spearheads in one continuous unbroken trajectory with exact 0.000mm periodic closure.

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

#MathArt #Snowflake #Fractal #Geometry #Crystallography #GenerativeArt #Blender3D #Shorts #Mathematics

THE MATHEMATICAL RULE

Sector replication and linear edge interpolation\text{Sector replication and linear edge interpolation}Rk=(cos⁡(kπ/3)−sin⁡(kπ/3)0sin⁡(kπ/3)cos⁡(kπ/3)0001),k=0,…,5R_k=\begin{pmatrix}\cos(k\pi/3)&-\sin(k\pi/3)&0\\\sin(k\pi/3)&\cos(k\pi/3)&0\\0&0&1\end{pmatrix},\quad k=0,\ldots,5Qk,j=RkPj,Pj∈stored sector vertices\mathbf Q_{k,j}=R_k\mathbf P_j,\quad\mathbf P_j\in\text{stored sector vertices}q(λ)=(1−λ)Qi+λQi+1,0≤λ≤1\mathbf q(\lambda)=(1-\lambda)\mathbf Q_i+\lambda\mathbf Q_{i+1},\quad0\leq\lambda\leq1

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