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 This email address is being protected from spambots. You need JavaScript enabled to view it.
(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
