Fractal Mineral

IGNEOUS rocks formed from lava flows of the Archaean era (>2,700 million years ago) are often found to contain disequilibrium-textured crystals characterized by spherulitic, branching or dendritic morphologies that occur in layers near the flow surface. Well-known examples are the plagioclase spherulites of basalts and the platy and branching spinnifex-textured olivines and pyroxenes of komatiites. Here we present evidence that, over a finite range of length scales, some disequilibrium textures are scale invariant. This observation implies that over this range of length scales their random patterns can be quantitatively characterized by a unique number, the fractal dimension3. We also demonstrate that some textures have a crossover from fractal to non-fractal behaviour. It is known that most disequilibrium crystals arise in part from rapid cooling and represent the case where the growth rates of the crystals are large compare to the diffusion rates in the silicate melt. We therefore formulate a quantitative model for the growth that is based on a variant of diffusion-limited aggregation (DLA).

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