Apparent Reversal Frequencies in Squares and Trapezia: The Effect of Invariant and Variant Information

Abstract

Three studies of apparent reversals (ARs) in rotating rectangular and trapezoid arrays are reported, together with a mathematical analysis. Study 1 explores the effect of different degrees of outline suppression on the frequency and distribution of ARs in squares and trapezia. Study 2 examines how modifications in both types of array reduce AR frequency, demonstrates a manipulation whereby ARs in rotating squares are eliminated, and suggests that ARs in squares and trapezia are of different origins. In the mathematical analysis, an invariant characteristic of the transformations of rotating rectangles is reported, and from this a numerical index is developed that expresses the extent to which a rotating trapezium may appear to pause just before each point of oscillation. In study 3 it is shown that this measure is a better predictor of AR frequencies than the heuristic proposed by Braunstein.