In some substitution tilings it is possible to decorate the prototiles with line segments such that they produce a grid of straight lines extending over the whole tiling. Here is an example for the case of the Penrose Rhomb tiling.
These decorations are called Ammann bars, because R.Ammann discovered the appropriate decorations for the Penrose rhomb tilings, as well as for some others. In some cases, they can be used to express matching rules by requiring, that tiles have to meet in a way such that the line segments continue as straight lines across the edges of the tiling. For more details, see [GS87].
Tilings and Patterns
W.H. Freeman, 1987, , MR0857454
Ammann lines, Ammann grid