Calculations of the minimal perimeter for N deformable cells of equal area confined in a circle

Candidates to the least perimeter partition of a disk into N planar connected regions are calculated for N ≤43. A Voronoi construction is used to randomly create the candidates and then the perimeter of each is found with the Surface Evolver. Formulae for the perimeter and number of peripheral regions are given, and the candidates classified according to their topology. The simulation technique also provides improved candidates to the unconstrained problem of finding the least perimeter arrangement of N planar regions