5 citations · 6 across the 5 of their papers we have counts for
8 papers
The multifractal nature of a parametrized family of von Koch functions
Zoltán Buczolich, Yann Demichel, Stéphane Seuret
In a famous paper published in 1904, Helge von Koch introduced the curve that still serves nowadays as an iconic representation of fractal shapes. In fact, von Koch's main goal was…
Fractal random sets associated with multitype Galton-Watson trees
Pierre Calka, Yann Demichel
In this paper, we consider a regular tessellation of the Euclidean plane and the sequence of its geometric scalings by negative powers of a fixed integer. We generate iteratively r…
Who invented von Koch's Snowflake Curve?
Yann Demichel
A strange title, might you say: Answer is in the question! However, contrary to popular belief and numerous citations in the literature, the image of the snowflake curve is not pre…
Elongated Poisson-Voronoi cells in an empty half-plane
Pierre Calka, Yann Demichel, Nathanaël Enriquez
The Voronoi tessellation of a homogeneous Poisson point process in the lower half-plane gives rise to a family of vertical elongated cells in the upper half-plane. The set of edges…
Renormalization of the Hutchinson Operator
Yann Demichel
One of the easiest and common ways of generating fractal sets in is as attractors of affine iterated function systems (IFS). The classic theory of IFS's requires th…
The Poisson-Voronoi cell around an isolated nucleus
Pierre Calka, Yann Demichel, Nathanaël Enriquez
Consider a planar random point process made of the union of a point (the origin) and of a Poisson point process with a uniform intensity outside a deterministic set surrounding the…
The diameter of a random elliptical cloud
Yann Demichel, Ana Karina Fermin, Philippe Soulier
We study the asymptotic behavior of the diameter or maximum interpoint distance of a cloud of i.i.d. -dimensional random vectors when the number of points in the cloud tends to…
Fractal random series generated by Poisson-Voronoi tessellations
Pierre Calka, Yann Demichel
In this paper, we construct a new family of random series defined on , indexed by one scaling parameter and two Hurst-like exponents. The model is close to Takagi-Knopp funct…