9 citations · 10 across the 10 of their papers we have counts for
10 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…
When the conformal dimension of a self-affine sponge of Lalley-Gatzouras type is zero
Yanfang Zhang, Shu-Qin Zhang
It is well known that if a metric space is uniformly disconnected, then its conformal dimension is zero. First, we characterize when a self-affine sponge of Lalley-Gatzouras type i…
Overlapping substitutions and tilings
Shigeki Akiyama, Yasushi Nagai, Shu-Qin Zhang
We generalize the notion of (geometric) substitution rule to obtain overlapping substitutions. Our motivating example is the substitution presented in Ziherl, Dotera and Bekku \cit…
On self-affine tiles that are homeomorphic to a ball
Jörg M. Thuswaldner, Shu-Qin Zhang
Let be a integer matrix which is expanding in the sense that each of its eigenvalues is greater than in modulus and let be a…
On self-affine tiles whose boundary is a sphere
Jörg Thuswaldner, Shu-qin Zhang
Let be a integer matrix each of whose eigenvalues is greater than in modulus and let be a set with , ca…
Optimal parametrizations of a class of self-affine sets
Shu-Qin Zhang
In this paper, we study optimal parametrizations of the invariant sets of a single matrix graph IFS which is a generalization of the result of Rao and Zhang (2016). We show that th…
Space-filling curves of self-similar sets (III): Skeletons
Hui Rao, Shu-Qin Zhang
Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. It is shown in [Dai, Rao and Zhang, Space-filling curves of self-similar sets (II): Ed…
Topology of a class of -crystallographic replication tiles
Benoît Loridant, Shu-qin Zhang
We study the topological properties of a class of planar crystallographic replication tiles. Let be an expanding matrix with characteristic polynomial $…
Space-filling curves of self-similar sets (II): Edge-to-trail substitution rule
Xi-rong Dai, Hui Rao, Shu-qin Zhang
It is well-known that the constructions of space-filling curves depend on certain substitution rules. For a given self-similar set, finding such rules is somehow mysterious, and it…
Space-filling curves of self-similar sets (I): Iterated function systems with order structure
Hui Rao, Shu-Qin Zhang
This paper is the first paper of three papers in a series, which intend to provide a systematic treatment for the space-filling curves of self-similar sets. In the present paper, w…