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 polymer network, an aggregated particulate sol, or of the particles that comprise them.
Notes:
  1. m∝rd 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∝rd′ 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]
Citation: 'fractal dimension' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.FT07550 RIS BibTex EndNote
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Last revised: February 24, 2014