A Sturmian sequence is an infinite nonperiodic string over two letters with minimal subword
complexity. In two papers, the first written by Morse and Hedlund in 1940 and the second by …

The critical thickness of an arithmetical discrete plane refers to the infimum thickness that
preserves its 2-connectedness. This infimum thickness can be computed thanks to a …

A digital discrete hyperplane in ℤ d is defined by a normal vector v, a shift μ, and a thickness
θ. The set of thicknesses θ for which the hyperplane is connected is a right unbounded …

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 …

We investigate a construction scheme for digital planes that is guided by generalized
continued fractions algorithms. This process generalizes the recursive construction of digital …

We work on the Réveillès hyperplane P (v, 0, ω) with normal vector v∈ R d, shift μ= 0 and
thickness ω∈ R. Such a hyperplane is connected as soon as ω is greater than some value …

We work with attracting subshifts generated by substitutions which are also irreducible
parageometric automorphisms of free groups. For such a dynamical system, we construct a …