Fractals and Numeration » Home

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


  • 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.