## Wikipedia - Dimensione frattale (it) fractal dimension, $$d$$

Also contains definitions of: Hausdorff dimension, mass fractal dimension, surface fractal dimension
https://doi.org/10.1351/goldbook.FT07550
Parameter that provides a mathematical description of the fractal structure of a @[email protected], an aggregated @[email protected], or of the particles that comprise them.
Notes:
1. $$m \propto r^{d}$$ in which $$m$$ is the mass contained within a radius, $$r$$, measured from any site or bond within a fractal structure.
2. For a Euclidean object of constant density, $$d = 3$$, but for a fractal object, $$d<3$$, such that its density decreases as the object gets larger.
3. For the surface area of a fractal object, $$s \propto r^{d'}$$ in which $$s$$ is the surface area contained within a radius, $$r$$, measured from any site or bond and $$d'$$ is termed the surface fractal dimension.
Source:
PAC, 2007, 79, 1801. (Definitions of terms relating to the structure and processing of sols, gels, networks, and inorganic-organic hybrid materials (IUPAC Recommendations 2007)) on page 1811 [Terms] [Paper]