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

Nick Petford, Dave Bryon, Michael P. Atherton, Robert H. Hunter

Research output: Contribution to JournalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)593-598
Number of pages6
JournalEuropean Journal of Mineralogy
Issue number3
Publication statusPublished - 7 Jun 1993


  • fractals
  • grain shape
  • texture
  • porosity
  • granodiorite


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