The Fibonacci Tiling The Fibonacci Tiling The Fibonacci Tiling

LetPR be the set of patches of radius R, modulo translation. The tiling has finite local complexity (FLC), if and only if PR is a finite set for all R. In particular R→PR is locally constant and non-decreasing. Thus there is a sequence R0 = 0 < R1 < · · · < Rn < · · · with Rn→ ∞ such thatPR =Pn for Rn ≤ R < Rn+1. Inverse Limit There is a restriction map pi:Pn+1→Pn. Then the transversal is defined by the inverse limit Ξ = lim←piP