fractal dimension, \(d\)

Also contains definitions of: Hausdorff dimension, mass fractal dimension
https://doi.org/10.1351/goldbook.FT07550
Parameter that provides a mathematical description of the fractal structure of a @P04742@, an aggregated @PT07510@, 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]