Figure 1: Three periods of a Fibonacci approximant {f3, f4} in the hyperspace d = 2 (sawtooth cut ES). . . . +−, + − +− . . . are irrational segments parallel to E||, slope −1, linked by the ’phason’ shifts . . . −+, −+, − + . . . perpendicular to E||; . . . A, B,C . . . are vertices of the lattice. AB = BC = . . . = {f4, f3}. The approximant generated by the sequence of irrational cuts is the same as the approximant generated by E (dashed rational line), slope f3/f4 = 2/3.

Figure 1: Three periods of a Fibonacci approximant {f3, f4} in the hyperspace d = 2 (sawtooth
cut ES). . . . +−, +
−
+− . . . are irrational segments parallel to E||, slope −1, linked by
the ’phason’ shifts . . . −+, −+,
−
+ . . . perpendicular to E||; . . . A, B,C . . . are vertices of
the lattice. AB = BC = . . . = {f4, f3}. The approximant generated by the sequence of irrational
cuts is the same as the approximant generated by E (dashed rational line), slope f3/f4 = 2/3.