Posts tagged: de Bruijn A Penrose tiling can be constructed
using just two different tiles in the shape of a thick and thin
rhombus: Here, the angles are multiples of ø = π/5. The edges of
these tiles are marked with two different kinds of arrows. This
is done to enforce a specific matching rule that ensures that
the tiling is non-periodic, which is one of the defining
features of Penrose tilings. Different tiles can only be placed
next to each other if the touching edges have the same type of
arrow and point in the same direction. If these matching
conditions were not in place, then it would be possible to
construct tilings which are periodic as shown in the following
image. There are translational symmetries present in 8 different
directions here: The image at the top shows a part of a Penrose
tiling obeying the matching conditions with the arrows
displayed. The numbers are just there to index some other
property of directionality not discussed here. If these matching
conditions are satisfied for a complete