International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 4.6, p. 595   | 1 | 2 |

Table 4.6.2.1 

W. Steurera* and T. Haibacha

aLaboratory of Crystallography, Department of Materials, ETH Hönggerberg, HCI G 511, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich, Switzerland
Correspondence e-mail:  walter.steurer@mat.ethz.ch

Table 4.6.2.1| top | pdf |
Expansion of the Fibonacci sequence [B_{n} = \sigma^{n}(\hbox{L})] by repeated action of the substitution rule σ: [\hbox{S} \rightarrow \hbox{L}], [\hbox{L} \rightarrow \hbox{LS}]

[\nu_{\rm L}], [\nu_{\rm S}] are the frequencies of the letters L and S in word [B_{n}].

[B_{n}][\nu_{\rm L}][\nu_{\rm S}]n
L 1 0 0
LS 1 1 1
LSL 2 1 2
LSLLS 3 2 3
LSLLSLSL 5 3 4
LSLLSLSLLSLLS 8 5 5
LSLLSLSLLSLLSLSLLSLSL 13 8 6
  [\vdots] [\vdots] [\vdots]
  [F_{n + 1}] [F_{n}] n