{"term":{"id":"07550","doi":"10.1351\/goldbook.FT07550","code":"FT07550","status":"current","longtitle":"IUPAC Gold Book - fractal dimension","title":"fractal dimension","contains":"Hausdorff dimension, mass fractal dimension, surface fractal dimension","version":"2.3.3","lastupdated":"2014-02-24","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 ∝ 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 ∝ 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":[{"title":"polymer network","type":"goldify","url":"https:\/\/goldbook.iupac.org\/terms\/view\/P04742"},{"title":"particulate sol","type":"goldify","url":"https:\/\/goldbook.iupac.org\/terms\/view\/PT07510"}],"math":[{"alttext":"m ∝ r d","latex":"m \\propto r^{d}"},{"alttext":"m","latex":"m"},{"alttext":"r","latex":"r"},{"alttext":"d = 3","latex":"d = 3"},{"alttext":"d< 3","latex":"d<3"},{"alttext":"s ∝ r d '","latex":"s \\propto r^{d'}"},{"alttext":"s","latex":"s"},{"alttext":"r","latex":"r"},{"alttext":"d'","latex":"d'"}],"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)"]}],"referencedin":[{"title":"Wikipedia - Dimensione frattale (it)","url":"https:\/\/it.wikipedia.org\/wiki\/Dimensione_frattale"}],"links":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/FT07550\/html","json":"https:\/\/goldbook.iupac.org\/terms\/view\/FT07550\/json","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/FT07550\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/FT07550\/plain","pdf":"https:\/\/goldbook.iupac.org\/terms\/view\/FT07550\/pdf"},"citeas":"IUPAC. Compendium of Chemical Terminology, 2nd ed. (the \"Gold Book\"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. ISBN 0-9678550-9-8. https:\/\/doi.org\/10.1351\/goldbook.","license":"Licensed under Creative Commons Attribution-NoDerivatives (CC BY-NC-ND) 4.0 International (https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/)","collection_reuse":"For parties interested in reusing the entire IUPAC Gold Book please contact IUPAC here https:\/\/www.cognitoforms.com\/IUPAC1\/ContactInformationForm","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":"2023-03-29T13:21:24+00:00"}}