Eur. Phys. J. E 6, 133-137 (2001)
Minimum perimeter partitions of the plane into equal numbers of regions of two different areas
M.A. Fortes and P.I.C. TeixeiraDepartamento de Engenharia de Materiais e Instituto de Ciência e Engenharia de Materiais e Superfícies, Instituto Superior Técnico, Avenida Rovisco Pais, P-1049-001 Lisboa, Portugal paulo@ist.utl.pt
(Received 27 June 2001 and Received in final form 29 August 2001)
Abstract
We identify the minimum-perimeter periodic tilings of the plane by equal
numbers of regions (cells) of areas 1 and 
(minimal tilings), with
at most two cells of each area per period and for which all cells of the
same area are topologically equivalent. For close to 1 the
minimal tiling is hexagonal. For smaller values of the minimal
tilings contain pairs of 5/7, 4/8 and 3/9 cells, the cells with fewer sides
having smaller area. The correlation between area fraction and number of
sides in the minimal tilings is approximately linear and consistent with
Lewis' law.
83.80.Iz - Emulsions and foams.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001
