Ammann-Beenker tiling

We subsequently consider the problem of SAW in restricted geometries, confined to a wedge, a strip, a slab, a square or a cube. We then discuss SAW on non-regular lattices, such as the Penrose and Ammann-Beenker tilings. 

Figure 6. Examples of W°. .. W for a particular walk on the Ammann-Beenker tiling.

The total number of n-step SAWs for the Ammann-Beenker tiling and the rhombic Penrose tiling. 

The mean number of n-step SAPs and the total number of SAPs for the Ammann-Beenker tiling (first two columns) and for the rhombic Penrose tiling (last two columns), where A = 1 + /2 and r = (1 + y/E)/2. 

The above analysis has also been applied to the rhombic Penrose tiling data. That data displays qualitatively the same finite size behaviour as the Ammann-Beenker tiling data. In Table 7 estimates of Xc and 7 obtained by analysing first order differential approximants are given. 

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