Edmund Harriss
Discovered Tilings
One of the rare examples of a tiling where the prototiles occur in infinitely many orientations. Apart from the pinwheel tiling and its generalizations [Sad98] there are only a few examples known which show infinite rotations.
The inflation factor of this one is a complex algebraic PV number of …
Infinite Rotations Infinite Local Complexity Polytopal Tiles Self Similar Substitution
A companion to infinite component Rauzy fractal. As mentioned for that rule, it was hoped that the result for two symbol substitution rules that the window is connected if and only if the rule is invertible. This substitution rules is not invertible and yet the Rauzy fractal is connected:
Euclidean Windowed Tiling One Dimensional Polytopal Tiles Self Simmilar Substitution
Finite Rotations Euclidean Windowed Tiling Polytopal Windowed Tiling Canonical Substitution Tiling Polytopal Tiles Parallelogram Tiles
Finite Rotations Polytopal Tiles Parallelogram Tiles Rhomb Tiles Harrisss Rhomb
In his PhD thesis, E. Harriss classified all substitution tilings which are canonical projection tilings.
Here one example is shown, derived from the cut and project scheme of the Ammann-Beenker tilings.
Finite Rotations Euclidean Windowed Tiling Polytopal Windowed Tiling Canonical Substitution Tiling Polytopal Tiles Parallelogram Tiles
In his PhD thesis, E. Harriss classified all substitution tilings which are canonical projection tilings.
Here one example is shown, derived from the cut and project scheme of the Ammann-Beenker tilings.
Finite Rotations Euclidean Windowed Tiling Polytopal Windowed Tiling Canonical Substitution Tiling Polytopal Tiles Parallelogram Tiles Rhomb Tiles
In his PhD thesis, E. Harriss classified all substitution tilings which are canonical projection tilings.
Here one example is shown, derived from the cut and project scheme of the Ammann-Beenker tilings.
Finite Rotations Euclidean Windowed Tiling Polytopal Windowed Tiling Canonical Substitution Tiling Polytopal Tiles Parallelogram Tiles
In his PhD thesis, E. Harriss classified all substitution tilings which are canonical projection tilings.
Here one example is shown, derived from the cut and project scheme of the Ammann-Beenker tilings.
Finite Rotations Euclidean Windowed Tiling Polytopal Windowed Tiling Canonical Substitution Tiling Polytopal Tiles Parallelogram Tiles
A pinwheel substitution rule with cubic scaling. As the scaling and the rotations for the tiles are all given by algebraic units, every vertex of the tiling lies within a finitely generated Z-module.
Infinite Rotations Infinite Local Complexity Polytopal Tiles Self Similar Substitution
The substitution rule a1->a1 b1, a2->b2 a2, b1->a2, b2->a1. The tilings generated become Fibonacci tilings under the projection a1,a2->a and b1,b2->b. Alternatively one can simply remove the colour labels on the tiles. The name comes from the projection structure of the tiling. The expansion …
Euclidean Windowed Tiling Polytopal Windowed Tiling Canonical Substitution Tiling One Dimensional Polytopal Tiles Parallelogram Tiles Self Similar Substitution Mld Class Fibonacci
An invertible substitution rule with a disconnected Rauzy Fractal. For two letter substitution rules the Rauzy fractal is connected if and only if the substitution is invertible. In fact as the window is one dimensional for these tilings it is an interval. It was hoped that the connectedness …
One Dimensional Euclidean Windowed Tiling Self Similar Substitution Polytopal Tiles
A one dimensional substitution rule with a two component Rauzy Fractal. For a second example and more details see infinite component Rauzy fractal.
One Dimensional Euclidean Windowed Tiling Self Similar Substitution
A volume hierarchic version of Conch.
Finite Rotations Euclidean Windowed Tiling Self Similar Substitution
This tiling and Nautilus are dual tilings generated by non-PV morphisms. As such they are the first step in a generalisation of the work of G. Rauzy, P. Arnoux, S. Ito and others for PV substitution rules. The work that developed out of G. Rauzy’s seminal paper [Rau82] .
The inflation factor for …
Finite Rotations Euclidean Windowed Tiling
A volume hierarchic version of Nautilus
Finite Rotations Euclidean Windowed Tiling Self Similar Substitution