On wiki page about [Ammann–Beenker tiling](https://en.wikipedia.org/wiki/Ammann%E2%80%93Beenker_tiling#cite_note-7) is described the [substitution scheme](https://en.wikipedia.org/wiki/Ammann%E2%80%93Beenker_tiling#Pell_and_silver_ratio_features) $R → R r R ; r → R$ that introduces the ratio as a scaling factor: its matrix is the [Pell](https://en.wikipedia.org/wiki/Pell_number) substitution matrix, and the series of words produced by the substitution have the property that the number of $r$s and $R$s are equal to successive Pell numbers.

Q: the order of the $r$s and $R$s in the assignation $R → R r R ; r → R$ I don't understand. applying recursive definition of Pell numbers we see that in every recursion step if we associate $R\_{old}:= P\_n, r\_{old}:=P\_{n-1}$ then recursively we step forward by $R\_{new}:=P\_{n+1} = 2R\_{old} +r\_{old}$ and $r\_{new}=R\_{old}$. what I don't understand is the *order* of $R$ and $r$ in the assignation $R → R r R$.