5 citations · 11 across the 10 of their papers we have counts for
11 papers
Neighbors of self-affine tiles and Rauzy Fractals
Benoît Loridant, Jörg M. Thuswaldner, Shu-Qin Zhang
Although the theory of self-affine tiles and the theory of Rauzy fractals are quite different from each other, they have some common features. Both, self-affine tiles and Rauzy fra…
Intersection the twin dragon with rational lines
Shigeki Akiyama, Paul Grosskopf, Benoît Loridant +1
The Knuth Twin Dragon is a compact subset of the plane with fractal boundary of Hausdorff dimension , . Although the intersection with…
Topology of planar self-affine tiles with collinear digit set
Shigeki Akiyama, Benoît Loridant, Jörg Thuswaldner
We consider the self-affine tiles with collinear digit set defined as follows. Let satisfy and be an integral matri…
A Core Decomposition of Compact Sets in the Plane
Benoit Loridant, Jun Luo, Yi Yang
A Peano continuum means a locally connected continuum. A compact metric space is called a \emph{Peano compactum} if all its components are Peano continua and if for any constant $C…
Fibers and local connectedness of planar continua
Benoît Loridant, Jun Luo
We describe non-locally connected planar continua via the concepts of fiber and numerical scale. Given a continuum and , we show that the set o…
Geometrical models for a class of reducible Pisot substitutions
Benoit Loridant, Milton Minervino
We set up a geometrical theory for the study of the dynamics of reducible Pisot substitutions. It is based on certain Rauzy fractals generated by duals of higher dimensional extens…