The fractal shape of sutured quartz grain boundaries: application as a geothermometer

Along grain boundaries of quartz from metamorphic and igneous rocks complex interfingering (sutures) may occur. Under the light microscope the lengths of the sutures range from approximately 10–1000 m. The sutured grain boundaries are statistically self-similar over one to two orders of magnitude. They represent fractals. Their mathematical counterpart are Koch curves which are developed after two to four iterations. The fractal (Hausdorff-Besicovitch) dimensions D of sutured quartz grain boundaries from different grades of metamorphism are between ca. 1.05 and 1.30. The D-value decreases with increasing temperature during formation of the sutures. On a statistical basis, D can be used as a measure of this temperature and, therefore, as a deformation-related thermometer.