209 citations · 418 across the 14 of their papers we have counts for
18 papers
Dynamics and topology of the Hat family of tilings
Michael Baake, Franz Gähler, Lorenzo Sadun
The recently discovered Hat tiling admits a 4-dimensional family of shape deformations, including the 1-parameter family already known to yield alternate monotiles. The continuous…
Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples
Michael Baake, Franz Gaehler
This article presents, in an illustrative fashion, a first step towards an extension of the spectral theory of constant length substitutions. Our starting point is the general obse…
Substitution Rules for Higher-Dimensional Paperfolding Structures
Franz Gähler, Johan Nilsson
We present a general scheme how to construct a substitution rule for generating -dimensional analogues of the paperfolding structures. This substitution is proven to be primitiv…
A computer search for planar substitution tilings with n-fold rotational symmetry
Franz Gähler, Eugene E. Kwan, Gregory R. Maloney
We describe a computer algorithm that searches for substitution rules on a set of triangles, the angles of which are all integer multiples of π/n. We find new substitution rules ad…
Quotient cohomology of certain 1- and 2-dimensional substitution tiling spaces
Enrico Paolo Bugarin, Franz Gähler
The quotient cohomology of tiling spaces is a topological invariant that relates a tiling space to one of its factors, viewed as topological dynamical systems. In particular, it is…
Topology of the Random Fibonacci Tiling Space
Franz Gähler, Eden Provido
We look at the topology of the tiling space of locally random Fibonacci substitution, which is defined as a-->ba with probability p, a-->ab with probability 1-p and b-->a for 0<p<1…