Number systems with rational basis and fractal sets (CONTRIBUTED TALK)
speaker: Lucia Rossi (Montanuniversität Leoben)abstract: Number systems are a way to represent elements of a space using a base and a set of digits. We consider the case where the base is a rational number, or more generally an algebraic number.Many number systems are related to self-affine sets with a fractal structure,one famous example being Knuth’s Twin Dragon. We define a family of (non- Euclidean) fractal sets that are solutions of iterated function systems. For their construction, we need to introduce spaces that generalize p-adic numbers. These fractal sets can be interpreted in terms of a type of dynamical sys- tems, called shift-radix systems. These dynamical systems offer computational advantages that allowed us to come up with a physical model of tilings given by their ”slices”. They were obtained by laser cutting wood, and they take the form of puzzles. If possible, the puzzles can be presented in the talk.
timetable:
Mon 20 May, 11:30 - 12:00, Aula Dini
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