SELF-ORGANIZED MINERAL TEXTURES OF IGNEOUS ROCKS - THE FRACTAL APPROACH

Many of the irregular patterns and textures that have been the subject of much recent scientific research are formed far from equilibrium, and are fractal in nature. Fractal structures are scale-invariant or self-similar. They appear the same, in a statistical sense, over large changes in scale. Silicate mineral crystals grown under conditions of disequilibrium frequently have a morphology composed of a hierarchy of similar branching parts. They are fractal objects and are self-organized on a macroscopic scale. The slopes of density-density correlation function plots are a measure of the fractal dimension. The plots show that some disequilibrium crystals exhibit a change from fractal to constant-density morphology. The growth of disequilibrium textures can be described in terms of the diffusion limited aggregation (DLA) algorithm. This is a stochastic model that mimics the Brownian motion of diffusing particles in the silicate liquid. It is an appropriate model as the disequilibrium crystals are known to have grown well below the liquidus under conditions of reduced atomic mobility. The simulations greatly resemble, and are quantitatively similar to naturally grown crystals. The branch growth is feedback-rich because the diffusing particles are not likely to cause growth anywhere, but near the branch tips. © 1990.