Densely packed membrane configurations

We put forth a simple mathematical model of densely packed fluid membranes and solve for packing configurations that minimize their elastic energy. Numerical calculations are facilitated via a finite-difference discretization scheme. Absent topological constraints, energy-minimizing configurations are found to closely follow solutions of the eikonal equation. These typically involve foliations comprising many closed surfaces. We show how allowing for cuts and creases, with an additional minimization over the total crease energy, generates configurations consisting of a densely packed single sheet.