Similarities of low-dimensional chaotic auditory attractor sequences to quasirandom noise

The production of sequences of sounds of various pitch levels from the algebra of chaotic attractors' trajectories is relatively straightforward. Meyer-Kress (cited in Kaneko, 1986) suggested that such sequences would be distinguishable from random independent identically distributed sequences. In psychophysical terms, this is a pattern-discrimination or pattern-similarity perception task, but these two tasks are not exactly the same thing. Nine attractors from the algebras of Henon, Zaslavskii (1978), Kaplan and Yorke (1979), Lorenz, and Gregson, and the logistic and Baker transformations, were paired with 10 realizations of a random series. The identification of the random member in each pair, the confidence of identification, and the perceived pairwise similarity were recorded by 65 subjects without initial feedback and by 76 subjects with initial feedback on five trials only, for each of 20 such pairs. The results indicate varying degrees of discriminability; they can be expressed in an analog of the receiver-operating characteristics of the attractors. There is no evidence of any homogeneous basis for the discrimination, and subjects who perform better are apparently not using the same bases as those who perform poorly. The fractal dimensionality of attractors may furnish a basis for their recognition, or the consequent autoregressive spectra induced in finite (short) samples, but recent work suggests the latter spectra can be insensitive to low-dimensional attractor dynamics.