Chaim Goodman-Strauss
Discovered Tilings
Part of an infinite series, where most tilings in this series are not flc, this one is the exception.
The reason is that the inflation factor is a - real - PV number.
By an argument in [PR] this forces flc.
Interestingly, the shape of the tiles can vary.
That is, there is one free parameter $l$ , …
Finite Rotations Euclidean Windowed Tiling Polytopal Tiles Self Similar Substitution
One possible version of a substitution rule with a free parameter: The upper tip of the three triangles can be shifted arbitrarily in horizontal direction, the result is always a self-similar substitution.
The inflation multiplier is the smallest PV number, the Plastic Number which is a root of the polynomial $x^3 - x - 1 = 0$.
Self Similar Substitution Polytopal Tiles Plastic Number
Whereas it is simple to generate rhomb tilings with n-fold symmetry by the cut and project method, it can be hard to find a substitution rule for such tilings. Here we see a rule for n=7. This one was later generalized by E. Harriss to arbitrary n.
Finite Rotations Canonical Substitution Tiling Polytopal Tiles Parallelogram Tiles Rhomb Tiles Harrisss Rhomb
A simple non-periodic substitution tiling with just one decorated prototile mentioned in the extended version of [Goo98] .
Find here the vector graphic.