Fractal analysis in granitoid petrology: a means of quantifying irregular grain morphologies
Petford, Nick; Bryon, Dave; Atherton, Michael P.; Hunter, Robert H.
European Journal of Mineralogy Volume 5 Number 3 (1993), p. 593 - 598
published: Jun 14, 1993
manuscript accepted: Nov 23, 1992
manuscript received: Jan 15, 1992
ArtNo. ESP147050503009, Price: 29.00 €
Abstract Digitised outlines of a serially sectioned K-feldspar grain from a Cordilleran granitoid have been analysed for their fractal dimension. Although the grain boundary outlines are not truly fractal in the sense of Mandlebrot (1982), they do show a self-similarity over a statistically definable range, and can thus be assigned a dimensional value between 1 and 2. Each grain section has fractal dimension (D) > 1, ranging from 1.21-1.30. Scatter within the data sets have been used to define separate (pseudo)fractal elements that further characterise each grain outline. The development of fractal geometries within a particular granitoid can be broadly related to crystallisation within Ab-An-Or-Qz space. For example, Cordilleran T-type granitoids that crystallise from An-rich liquids may be expected to show both Euclidean and fractal geometries, while minimum melts and 'S'-type granites that crystallise in broadly eutectic proportions will have textures dominated by (pseudo)fractal grain outlines. The non-integer values that describe grain shape may also be useful in estimating the total grain (porosity) volume within the rock.