Fractal analysis in granitoid petrology: a means of quantifying irregular grain morphologies

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 'I'-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.