# Fractals and Numeration » Home

Welcome to the home page of the Fractals and Numeration (FAN) Project, funded by ANR and FWF.

## Topics

• Arithmetics, dynamics and expansions
• Normal numbers, algebraic numbers and fractals
• Natural extensions of $$\alpha$$-continued fraction transformations and $$\beta$$-transformations
• Diophantine equations, units and fractals
• Minimal weight expansions, redundancy and applications to cryptography
• Topological properties of fractals
• Topological properties of self-affine sets
• Topological properties of generalized Sierpinski carpets
• Rauzy fractals and substitutions
• Pisot substitutive dynamical systems
• S-adic expansions and Rauzy fractals
• Rauzy fractals and free group morphisms
• Fractals with a view towards applications
• Intersection of fractals with lines and its applications in science and medicine
• Automatic fractal sets and entropy
• Fractal transformations and their applications to image processing
• Pseudo-randomness

## Formal details

ANR Programme Blanc Inter II-SIMI 1 — ANR-12-IS01-0002.
FWF International Programs — I1136.

Duration: 48 months, from 2013-03-01 to 2017-02-28.