title: Symmetries in geology and geophysics.
abstract: Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth's topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters.
authors.affiliation: Department of Geological Sciences, Cornell University, Ithaca, NY 14853, USA.
authors.forename: D L
authors.initials: DL
authors.lastname: Turcotte
authors.forename: W I
authors.initials: WI
authors.lastname: Newman