Soap Bubble Cluster

Plateau's laws govern bubble clusters: surfaces meet at 120°, edges meet at ~109.47° (tetrahedral angle). The cluster minimizes total surface area.

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Plateau's Laws

1. Surfaces are smooth minimal surfaces

2. Interfaces have constant mean curvature

3. Surfaces meet in threes at 120°

4. Edges meet in fours at arccos(−1/3) ≈ 109.47°

Young-Laplace

ΔP = 4γ/R

κ = ½(κ₁+κ₂)
ΔP = 2γκ

Energy ∝ Area
→ minimize!