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For any kite and dart tiling and any point that
is not on an edge of the tiling, we define the index sequence (a0 , a1
, a2 , ...) as follows:
Start with a tiling T. Make the triangulated tiling, T', and then compose
repeatedly to get T'', T''', etc. Now given a point, let ai
= 1 if the point is in a smaller triangle, and let ai = 0
if the point is in a larger triangle. This construction is due to
Robinson.
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The larger triangle can be either type. Below, the larger is always on the left. An animation
Note that the effect of the composition is to eliminate the smaller type triangle in moving from one step to the next. The consequence is that no index sequence contains the string 11.
