Perception, 1992, volume 21, pages 195-199
Anomalous spiral aftereffects: a new twist to the perception of rotating spirals Jack Broerse Department of Psychology, University of Queensland, St Lucia, Queensland 4072, Australia Peter Dodwell Department of Psychology, Queen's University at Kingston, Kingston, Ontario K7L 3N6, Canada Boris Crassini Department of Psychology, Deakin University, Victoria 3217, Australia Received 22 April 1991
Abstract. Stationary spirals viewed after inspecting rotating sectored disks appear to rotate and to expand or contract radially, even though the rotating disks contain no perceptible components of radial motion. Moreover, the relative directions of illusory rotation and radial motion observed in these instances are 'impossible' under the stimulus constraints normally imposed by the geometry of a spiral under rotation: the stationary spirals appeared to expand/contract in directions opposite to those normally observed under conditions of actual spiral rotation, and under conditions of illusory spiral rotation in classical spiral aftereffects. 1 Introduction T h e cubes illustrated in figure l a form an impossible triangle because they represent a 'structure' which cannot exist in three-dimensional (3-D) space. T h e component corners of this structure (figures l b , l c , and Id) each represent one of three different pairs of orthogonal directions in 3-D space, yet the 'triangle' formed by joining allthree corner components can in reality accommodate only two of these three orthogonal directions (cf figure le). In this paper we report a misperception of motion that
Figure 1. An 'impossible' 3-D representation of a triangle (a). The arms of each corner (b, c, and d) represent three different pairs of orthogonal directions in 3-D space which cannot all be joined end to end in a 'closed' 3-D configuration (e). Despite this, the 'impossible relationship' in (a) only become apparent on closer scrutiny.
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exhibits perceptual characteristics similar to those experienced when viewing an impossible figure. It occurs as a curious anomaly in the illusory motion that results when a stationary spiral is viewed immediately after inspection of a rotating sectored disk. The relationships between the directions of radial and rotational motion observed in these circumstances are 'impossible' in the sense that they do not, and indeed cannot, occur in a spiral of fixed geometry under particular directions of actual rotation. We term these misperceptions of motion anomalous spiral aftereffects. To appreciate the nature of the impossible relationships between radial and rotational motion in anomalous spiral aftereffects, it is necessary to consider the nature of the motion commonly experienced when rotating spirals are observed. The spiral patterns shown in figure 2, for example, will be seen to expand if the patterns are rotated in one direction, and to contract if rotated in the opposite direction/1) The perceived motion of these rotating spirals is thus described in terms of its direction along two orthogonal components: a rotational component which describes the clockwise or counterclockwise motion of the spiral, and a radial component which describes its apparent expansion or contraction (Scott and Noland 1965). For any particular spiral the rate and direction of perceived motion along these components depends on both the geometry (or form) of the spiral and its rate and direction of rotation (Hildreth 1990, pages 153-154). A left-throw spiral (figure 2a) will be seen to expand if it rotates in a clockwise direction, and to contract if it rotates in a counterclockwise direction. The converse relationships between direction of rotation and perceived expansion/contraction occur with a right-throw spiral (figure 2b). If an observer looks at a rotating spiral for a period of time and then looks at a stationary version of the same spiral, an illusion of movement in the tradition of negative motion aftereffects (MAEs) is seen (Wohlgemuth 1911). The stationary spiral appears to rotate in the opposite direction to the actual rotation initially observed, and also to expand or contract in the opposite direction to the radial motion initially observed. This is the classical spiral aftereffect (SAE) which since Plateau's experimental observations in the nineteenth century has been described as providing illusory experiences of radial and rotational motion similar to those experienced while observing spirals actually rotate (Holland 1965). That is, the expansion or contraction
Figure 2. Left-throw spirals (a) normally appear to expand under clockwise rotation, and to contract under counterclockwise rotation. Right-throw spirals (b) appear to contract under clockwise rotation, and to expand under counterclockwise rotation. Similar relationships between illusory radial and rotational motion are observed on stationary test spirals in conventional spiral aftereffects induced by prior inspection of a rotating spiral. Inverse relationships between illusory rotation and radial motion are observed on stationary test spirals in anomalous spiral aftereffects induced by prior inspection of a rotating sectored disk (c). (1)
Expanding spirals are also commonly reported to approach in depth, and contracting spirals to recede in depth. The motion-in-depth component of spiral aftereffects has been investigated byHershenson(1982,1987).
Anomalous spiral aftereffects
observed in SAEs is consistent with the expansion and contraction observed in a rotating spiral, the latter being constrained by the geometry of the spiral and its direction of rotation. However, our observations of SAEs induced by a pattern that merely rotates, and does not appear to expand or contract, indicate that this is not always the case. After inspecting a rotating sectored disk (figure 2c), the relationships between the directions of rotational and radial MAEs observed with stationary test spirals were the inverse of the relationships between the radial and rotational motion components observed during actual spiral rotation (and conventional SAEs). These are anomalous SAEs in the sense that the spiral appears to expand or contract in the 'wrong' direction relative to the direction of apparent rotation. 2 Methods and procedures Anomalous SAEs were originally observed by one of the authors (JB) during pilot tests for an experiment on motion perception. Since this initial observation, these phenomena have been confirmed by many observers both in individual and group testing contexts. Observers have included students (undergraduates and postgraduates) and academic staff, some of whom were naive with respect to MAEs (and misperceptions in general), and others familiar with such effects. In this study observers inspected a sectored disk (18 cycles, 50% duty cycle, figure 2c) rotating at approximately 18 rev min - 1 (5.4 cycles s - 1 ) in a clockwise or counterclockwise direction. The disk (165 mm diameter) was viewed from approximately 1.5 m (6.3 deg arc) and was rotated by a variable speed dc motor. Test figures consisted of stationary, five-throw (left and right) logarithmic spirals (105 mm diameter) mounted on cardboard and viewed from the same distance as the rotating disks (approximately 4 deg visual arc; figures 2a and 2b). After inspecting the rotating sectored disk for approximately 2 - 3 min, observers were asked to fixate the centre of one of the test spirals, which was presented at about 40 cm to the side of the induction pattern. They were asked to report whether the spiral appeared to rotate in a clockwise or counterclockwise direction, and also to report whether it appeared to expand or contract. If observers found it difficult to report the direction of radial motion in the test spiral, they were shown the induction figure for an additional 2 - 3 min and asked to try again. This 'top-up' procedure was necessary on only a few occasions. 3 Results and discussion It has been our experience that almost all observers subjected to the induction conditions described above report anomalous SAEs: left-throw spirals are seen to contract under induced clockwise rotation, and to expand under induced counterclockwise rotation; right-throw spirals are seen to expand under induced clockwise rotation, and to contract under induced counterclockwise rotation. In all cases the direction of radial motion perceived in relation to a particular direction of apparent rotation is in the opposite direction to that normally observed during actual spiral rotation. Although judged by experienced observers to be somewhat weaker than conventional SAEs (and MAEs in general), anomalous SAEs are robust phenomena and are easily demonstrated. Moreover, when observers were given the opportunity to compare their observations of radial motion (ie expansion or contraction) during illusory rotation of a spiral, with their observations of radial motion during actual spiral rotation (or during illusory rotation induced by inspection of a rotating spiral), they were surprised to see that the relationship between the rotational and radial motion components was reversed in these two cases. This surprise was particularly evident for observers familiar with MAE phenomena, and was described by some as resembling the surprise experienced when impossible figures such as the triangle in
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figure la are inspected. As indicated above, the impossibility of the global structure represented in this figure becomes apparent only when the separate components are explicitly attended to and compared. Explanations of classic MAEs induced with linear motion (eg the waterfall illusion; Addams 1834) have been proposed in terms of the selective adaptation of neural mechanisms sensitive to particular directions of motion (eg Barlow and Hill 1963; Sutherland 1961). Because of the adaptation effects produced in mechanisms during inspection of, say, a pattern moving downward, there is a decrease in the extent to which these mechanisms can respond in the presence of a stationary test pattern. There is no such decrease in the response rate of unadapted mechanisms (eg those sensitive to upward directions of motion), and the 'imbalance' in the relative rates of activity of adapted and unadapted mechanisms results in an illusory upward motion of the stationary test pattern (Hammond et al 1985; Mather and Moulden 1980; Over et al 1973; Wenderoth et al 1988). The global perceptions of movement generated by a rotating spiral is clearly more complex than simple linear motion in that it involves composite rotational, radial, and/or motion-in-depth dimensions. Neural substrates determining the perception of such complex motion have been presumed to involve either (a) linear motion-detecting mechanisms stimulated by the direction and orientation of contour, or (b) higher-order mechanisms that respond to global rotation, or to radial expansion/contraction and/or to motion in depth (Cavanagh and Favreau 1980; Hershenson 1982; Milligan and Scott 1971). In both cases, SAEs are attributed to adaptation effects in these mechanisms: the illusory rotation of the stationary spiral results from (and is proportional to) the rotational components) of the induction spiral, and illusory expansion/contraction results from (and is proportional to) the radial component(s) of the induction spiral (Hershenson 1987; Milligan and Scott 1971). In these terms, inspection of a rotating sectored disk, which has no radial motion component, should induce MAEs that exhibit only rotation. Thus a stationary disk of randomly textured elements will appear to rotate, but not to expand or contract. When a stationary spiral is used as a test figure, however, one of two outcomes might be expected. If the MAE depends exclusively on the adaptation of global mechanisms responding to pattern rotation, then the test spiral might appear to rotate without at the same time appearing to expand or contract. Alternatively, if the MAE involves the adaptation of local directionally-selective mechanisms, then MAE components might be expected to generalize from the contours of the induction disk to the contours of the test spiral, depending on the local orientation relationships between these contours (Over et al 1973). The stationary spiral might thus appear to rotate and to expand or contract in directions consistent with conventional SAEs.(2) Our observations of anomalous SAEs indicate that neither of these experiences occur. The stationary test spiral appeared to rotate and to expand or contract, but in directions that are impossible for a rotating spiral of a particular fixed geometry. Pending further investigations we reserve judgement as to why anomalous SAEs might occur. One avenue currently being investigated is based on Riggs and Day's (1980) observations that stationary patterns of dots or orthogonal contours appear to move in the direction of the resultant of two separate MAES, each induced by a pattern of dots or contours moving in an orthogonal direction to the other. That is, the stationary test-patterns appeared to move in the opposite direction to a component that was not actually present during induction. Furthermore, when the orthogonal MAE components were unequal, the perceived direction of stationary dot-patterns