  We consider dense random packing of disks with a power-law distribution of
radii and investigate their correlation properties. We study the corresponding
structure factor, mass-radius relation and pair distribution function of the
disk centers. A toy model of dense segments in one dimension (1d) is solved
exactly. It is shown theoretically in 1d and numerically in 1d and 2d that such
packing exhibits fractal properties. It is found that the exponent of the
power-law distribution and the fractal dimension coincide. An approximate
relation for the structure factor in arbitrary dimension is derived, which can
be used as a fitting formula in small-angle scattering. The findings can be
useful for understanding microstructural properties of various systems like
ultra-high performance concrete, high-internal-phase ratio emulsions or
biological systems.
