Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups (Q5902933)

This paper explores the geometry of the limit set of a special group of transformations of the hyperbolic plane based upon inversions. This limit set, a fractal curve in the author's terminology, was among those illustrated in the classical treatise by R. Fricke and \textit{F. Klein} [Lectures on the theory of automorphic functions. I (German), Teubner, Leipzig, 1897]. By using careful computer graphics, the author corrects errors in the old diagrams, and reveals new properties of these limit sets. The article is well illustrated with the old and new diagrams.