Bubble Cluster
Bubble Cluster is a physical surface model, of constant mean curvature, given by a parametrisation, immersed.
Open Bubble Cluster in the interactive viewer →
aperiodic cmc def-parametric immersed implemented physical
Properties
- Family
- physical
- Given by
- a parametrisation
- Curvature
- constant mean curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
Definition
No chart is stored: soap-film cluster produced by numerical relaxation with Plateau angle conditions; no chart. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- Joseph Plateau, "Statique experimentale et theorique des liquides soumis aux seules forces moleculaires" (1873) -- Plateau's laws for soap films (120-degree triple junctions).
- Young-Laplace law for the pressure jump across a curved film.
- Double Bubble theorem: M. Hutchings, F. Morgan, M. Ritore, A. Ros, "Proof of the double bubble conjecture", Annals of Mathematics 155 (2002), pp. 459-489.
- Triple Bubble theorem: E. Milman, J. Neeman, "The structure of isoperimetric bubbles on R^n and S^n", arXiv:2205.09102 (2022) -- proof of the triple bubble conjecture in R^3 (the standard triple bubble is the least-area partition).
- C. Isenberg, "The Science of Soap Films and Soap Bubbles" (Dover, 1992); D. Weaire & S. Hutzler, "The Physics of Foams" (Oxford, 1999).