1. M. Griniasty and S. Fishman, Phys. Rev. Lett., 60, 1334 (1988).

3. Figure 3: (a) The distribution of χ 2, calculated for single sequence elements (k=1) from the sequence x n ={αn 2 } (histogram), compared with the corresponding theoretical distribution expected for a truly random sequence (smooth curve). (b) Absolute value of the area difference (A) between the histogram and the theoretical curve in figures similar to (a), as a function of r, for various sequences. N. Brenner and S. Fishman, Nonlinearity, 4, 211-235 (1992).

4. Figure 4: Same as in the previous figure but for the distribution of pairs of consecutive sequence elements (k=2). N. Brenner and S. Fishman, Nonlinearity, 4, 211-235 (1992).

5. Figure 5: Same as in the previous figures (here k=1) for x n ={αn 2.1 }, where α= 1/(2·3 1/2 ). N. Brenner and S. Fishman, Nonlinearity, 4, 211-235 (1992).

6. A Figure 6

7. Figure 7: Same as the previous figures for x n ={αn 3/2 }, α=π, single elements (k=1). N. Brenner and S. Fishman, Nonlinearity, 4, 211-235 (1992).

8. Figure 8: x n ={αn 3/2 }, distribution of pairs (k=2). The number of pairs N =10 4, and the number of realizations r =100: (a) the first N pairs; (b) N pairs starting from the vicinity of around 10 7. N. Brenner and S. Fishman, Nonlinearity, 4, 211-235 (1992).

9. Figure9: Results for the “folded Fibonacci sequence”: (a) as in Fig. 3 (k=1); (b) as in Fig. 4 (k=2); (c) inverse localization length in the nearest-neighbour model with E=0. N. Brenner and S. Fishman, Nonlinearity, 4, 211-235 (1992).