Microscopic Snowflake Crystal

High-magnification microscopic ice crystal growth exhibiting 6-fold cyclic C6 rotational symmetry, primary hexagonal basal spines, and self-similar 60-degree secondary dendritic side prongs.

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60 FPS • Canvas 2D

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Live Parameters

Crystallization Speed 0.6

Stefan phase-change growth cycle rate

Dendrite Branching Order 5

Number of secondary side-prong pairs

Mathematical Formulation

86 chars high

Analytical Equation

r(\theta, t) = r_0(t) + \sum_{k=1}^K A_k(t) \cos(6 k \theta), \quad \mathbf{p}_{\text{prong}}(s) = \mathbf{p}_{\text{spine}} + s \begin{bmatrix} \cos(\pm\pi/3) \\ \sin(\pm\pi/3) \end{bmatrix}

Compact Formula

main_spine = L*(0.3 + 0.7*growth), prong = spine_pos + [cos(±π/3)*len, sin(±π/3)*len]

Renderer Logic

const mainArmLen = crystalRadius * (0.3 + 0.7 * growth);
const ux = branchPos + Math.cos(Math.PI / 3) * branchLen;
const uy = -Math.sin(Math.PI / 3) * branchLen;
const lx = branchPos + Math.cos(-Math.PI / 3) * branchLen;
const ly = -Math.sin(-Math.PI / 3) * branchLen;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#snowflake #microscopic #crystals #ice #geometry #hexagonal #fractal #symmetry

Author: Math Art Core Target: 60 FPS

Microscopic Snowflake Crystal

Live Parameters

Mathematical Formulation

Mathematical Tags

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