Strange Attractors in Plagioclase Oscillatory Zoning: Petrological Implications

Oscillatory zoning in plagioclase crystals from different mixed lava flows cropping out on the Island of Capraia (Italy) has been investigated. An-calibrated profiles from back-scattered-electron images are used as compositional time series of oscillatory zoning. They are analyzed by a qualitative visual method that allows to appreciate at first sight the global structure of the time series and by a quantitative method to reconstruct the attractors associated to the oscillatory patterns, and to calculate the fractal dimension of attractors. Results show that attractors have fractional dimensions, indicating that series are chaotic. In addition, it is evidenced that there is a wide variation in oscillatory zoning in crystals from the same lava flow and that plagioclase populations from the different lava flows differ in the shape of frequency histograms of attractor dimension. The development of oscillatory zoning is simulated by considering a chemically inhomogeneous magmatic mass governed by chaotic flow fields, coupled with chemical diffusion, in which plagioclase crystals grow according to the availability of nutrients in their neighborhoods. Results show that in such a dynamical system plagioclase crystals develop chaotic zoning patterns analogous to those observed in natural plagioclases. This approach allows us to explain the differences observed in plagioclase crystals from the same lava flow and the differences in the shape of frequency histograms of attractor dimensions in the four lava flows.