Ammann A1 tilings

The prototiles are squares with indentations and protrusions on the sides and corners that force the tiling to form a pattern of a perfect binary tree that is continued indefinitely.

The markings on the tiles in the pictures emphasize this hierarchical structure, however, they have only illustrative character and do not represent additional matching rules as this is already taken care of by the indentations and protrusions.

However, the tiling produced in this way is not unique, not even up to isometries of the Euclidean group, e.g. translations and rotations.

In the picture to the left, the initial patch in the left upper corner highlighted in blue can be prolonged by either a green or a red tile, which are mirror images of each other and instances of the prototile labeled b.

If one would deviate from the pattern for this next generation, one would run into configurations that will not match up globally at least at some later stage.