The size-weight illusion in 2-D nonlinear psychophysics

Gregson, Robert A. M.; Britton, Lesley

doi:10.3758/bf03206685

Cited by 7 publications

(3 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The r recursion (Campbell & Gregson, 1990;Gregson, 1988Gregson, , 1989aGregson, , 1989bGregson & Britton, 1989;Price & Gregson, 1988) in two-variable form is…”

Section: Attractor Propertiesmentioning

confidence: 99%

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

Gregson

Harvey

1992

Perception & Psychophysics

Self Cite

View full text Add to dashboard Cite

The production ofsequences ofsounds 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 degress of discriminability; they can be expresssed in an analog ofthe 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.A dynamic process is by definition something that evolves through time, and its mathematical representation is characterized both by the variables that themselves evolve, creating a time series of realizations of the process (either continuously or in discrete steps), and by parameters that determine the form of the evolution. The values of these parameters are critical, because in a nonlinear process, very small changes in the parameters can induce vast changes in the evolutionary dynamics. There is no necessary proportionality between changes in the values of the parameters governing the evolution of the process in time and the changes in the evolutionary path itself. This evolution of the process is sometimes called the trajectory of the variables.In some circumstances, which can be specified completely by the parameter values and the starting values of the process variables, the trajectory locks into a stable pattern, which is called an attractor. An attractor can be a single point, a cycle of fixed periodicity in the time units of the trajectory, or can take one of various more complicated forms, some of which are called chaotic. Chaotic behavior resembles random behavior but is completely deterministic. It is not locally predictable beyond a very short time ahead, and the degree of its unpredictability is quantifiable from properties of its algebra. The Lyapunov exponents are the most usual way to define the dynamics in this sense.The Lyapunov exponents measure the rate at which nearby trajectories diverge; "nearby" implies that t...

show abstract

“…The r recursion (Campbell & Gregson, 1990;Gregson, 1988Gregson, , 1989aGregson, , 1989bGregson & Britton, 1989;Price & Gregson, 1988) in two-variable form is…”

Section: Attractor Propertiesmentioning

confidence: 99%

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

Gregson

Harvey

1992

Perception & Psychophysics

Self Cite

View full text Add to dashboard Cite

show abstract

“…These regions are of potential interest because they may be interpreted as evidence of system dynamics where there is sensory overload and a predictable breakdown of normal functioning. They are of mathematical interest, in comparison with results in other simpler or better known recursions (Livi et al, 1988;Gumowski and Mira, 1980) which have been mapped. We report here an exploratory analysis of some Julia sets and Mandelbrot-type sets; computational problems are noted.…”

Section: Introductionmentioning

confidence: 99%

“…Its properties within a stable region have been shown to reproduce a diversity of empirical phenomena which are of interest to experimental psychologists (Gregson, 1989a, b;Gregson and Britton, 1989). The ranges of parameter values in the model which are appropriate for the simulation of psychophysical data have been illustrated for several examples in the references given.…”

Section: Introductionmentioning

confidence: 99%