{"term":{"id":"07550","title":"fractal dimension","longtitle":"IUPAC Gold Book - fractal dimension","doi":"10.1351\/goldbook.FT07550","code":"FT07550","status":"current","also defines":"<em>also defines<\/em>: surface fractal dimension","synonym":"<em>synonyms<\/em>: Hausdorff dimension, mass fractal dimension","definitions":[{"id":1,"text":"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 \\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":"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."},"links":[{"term":"particulate sol","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/PT07510"},{"term":"polymer network","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/P04742"}],"sources":["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 (https:\/\/doi.org\/10.1351\/pac200779101801)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/FT07550\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/FT07550\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/FT07550\/plain"},"citation":"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. 10.1351\/goldbook.FT07550","license":"The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/) for individual terms.","collection":"If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .","disclaimer":"The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.","accessed":"2026-04-24T22:21:59+00:00"}}