Self-Similar Nanostructures

Abstract

The geometric description of the world is at the root of Western thought: to the first (perhaps mythic) philosopher, Thales, we owe a theorem of plane geometry. The role of geometry in the construction of physical theories is equally important: on the cosmological scale, gravitation is explained in terms of space curvature; on the submicroscopic scale, quantum mechanics may be explained in terms of fluctuation of the metric tensor [303]. On the laboratory length scale, the most important geometric property of any thermodynamic system is most likely its shape. The general mathematical description of surfaces is a notoriously complicated affair – especially if one tries to describe real surfaces.