I'm a physicist who specializes in studying the behavior of granular materials. Research has confirmed that certain distributions of granular sizes exhibit fractal characteristics. In simpler terms, the number of particles larger than a particular size 'd' follows a specific power-law relationship, with the exponent referred to as the fractal dimension.
I'm currently investigating a related aspect of these granular materials: the spaces between the particles, known as pores. As this space is the complementary space of the grains inside a constant volume, I'm curious to know if the size distribution of these pores also displays fractal properties similar to the distribution of the grain sizes. My question to the mathematicians is this: if a fraction of a fixed volume is a fractal, does the complementary space also exhibit fractal behavior ? If so, is the fractal dimension of the complementary space comparable to that of the initial space? I’m sorry if my question is not well formulated.