Porous surfaces

In fractal modeling, porous surfaces in the plane are usually described as the residual setE of a packing by connected open domains (C_n) . In the case whereE is nonempty, we investigate the relationships between the dimensionality ofE and the geometry of the complementary sets (C_n) . If they satisfy suitable regularity conditions, then the Bouligand dimension ofE is equal to the exponent of convergence of the series ∑(diam (C_n) ) ^α . We give here general conditions to obtain this equality, together with numerous examples and possible ways of developing this theory.