On a Conjecture about the Fractal Structure of Language

Two forms of Hrebicek's conjecture (formulated and explained in Hrebicek, 1992, 1994, 1997, 1998, 2002) about the fractal structure of language are clarified in terms of a precise mathematical formalism. This allows us, among other things, a more detailed understanding of Kohler's objections to the conjectures (Kohler, 1995, 1997). The approach using iterated function systems and the Moran-Hutchinson formula is newly applied to analyze and visualize linguistic structures. The role of a hyperspace is indicated in reply to questions posed in Leopold (2001). Some open problems are finally formulated in concluding remarks.