Fractal Hypersurfaces, Wavelet Sets and Affine Weyl Groups

TL;DR

This paper explores the relationships between fractal hypersurfaces, wavelet sets, and affine Weyl groups, highlighting their interconnected roles in the theory of iterated function systems and fractal functions.

Contribution

It introduces new connections between fractal hypersurfaces, wavelet sets, and affine Weyl groups within the context of iterated function systems and fractal functions.

Findings

Establishes links between fractal hypersurfaces and wavelet sets.

Shows how affine Weyl groups relate to fractal attractors.

Provides a framework connecting fractal functions with wavelet theory.

Abstract

In these lecture notes we present connections between the theory of iterated function systems, in particular those attractors that are graphs of multivariate real-valued fractal functions, foldable figures and affine Weyl groups, and wavelet sets.