The aim of this survey is to discuss multidimensional continued fraction and Euclidean
algorithms from the viewpoint of numeration systems, substitutions, and the symbolic …

The aim of this paper is to discuss from an arithmetic and combinatorial viewpoint a simple
algorithmic method of generation of discrete segments in the three-dimensional space. We …

We show that the plane-probing algorithms introduced in Lachaud et al.(J. Math. Imaging
Vis., 59, 1, 23–39, 2017), which compute the normal vector of a digital plane from a starting …

We introduce a multi-dimensional generalization of the Euclidean algorithm and show how it
is related to digital geometry and particularly to the generation and recognition of digital …

Rauzy fractals are compact sets with fractal boundary that can be associated with any
unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff …

We consider S-adic expansions associated with continued fraction algorithms, where an S-
adic expansion corresponds to an infinite composition of substitutions. Recall that a …

We consider S‐adic expansions associated with continued fraction algorithms, where an S‐
adic ex‐pansion corresponds to an infinite composition of substitutions. Recall that a …