The Wandering Circles: A Flicker Rate and Contour-Dependent Motion Illusion

Christopher D Blair; Gennady Erlikhman; Gideon P Caplovitz

doi:10.1177/2041669519875156

. 2019 Sep 25;10(5):2041669519875156. doi: 10.1177/2041669519875156

The Wandering Circles: A Flicker Rate and Contour-Dependent Motion Illusion

Christopher D Blair ^1,^✉, Gennady Erlikhman ², Gideon P Caplovitz ³

PMCID: PMC6790949 PMID: 31656578

Short abstract

Understanding of the visual system can be informed by examining errors in perception. We present a novel illusion—Wandering Circles—in which stationary circles undergoing contrast-polarity reversals (i.e., flicker), when viewed peripherally, appear to move about in a random fashion. In two psychophysical experiments, participants rated the strength of perceived illusory motion under varying stimulus conditions. The illusory motion percept was strongest when the circle’s edge was defined by a light/dark alternation and when the edge faded smoothly to the background gray (i.e., a circular arrangement of the Craik-O’Brien-Cornsweet illusion). In addition, the percept of illusory motion is flicker rate dependent, appearing strongest when the circles reversed polarity 9.44 times per second and weakest at 1.98 times per second. The Wandering Circles differ from many other classic motion illusions as the light/dark alternation is perfectly balanced in time and position around the edges of the circle, and thus, there is no net directional local or global motion energy in the stimulus. The perceived motion may instead rely on factors internal to the viewer such as top-down influences, asymmetries in luminance and motion perception across the retina, adaptation combined with positional uncertainty due to peripheral viewing, eye movements, or low contrast edges.

Keywords: motion, perception, visual illusion, flicker

The ability to accurately see the motion of objects around us is an essential component of visual perception. Here, we introduce a novel visual illusion that we call the Wandering Circles. The Wandering Circles is a dynamic illusion in which stationary objects appear to move. The illusion manifests when simple objects (i.e., circles) undergo contrast-polarity reversals and are viewed peripherally. While we would like to be able to state that we discovered this illusion through theoretically driven stimulus design, we first noticed the illusion quite by accident while developing stimuli for another completely unrelated project. In the configuration highlighted in Figure 1 and viewable in Demonstration Video 1, the circles are defined by contours that induce the Craik-O’Brian-Cornsweet Illusion (Cornsweet circles). In the video, the contrast polarity of these contours reverses ∼10 times a second (e.g., roughly 100 ms passed before each polarity change). When an observer maintains fixation near the center of this display, after a brief period of time, the circles will appear to randomly move around (i.e., wander). Viewers differ in their perceived strength of the illusion, as well as in how long it takes for the illusion to manifest. We have found that the illusion is strongest if stimuli are viewed peripherally, with the gaze held in a relaxed fashion. Also, the illusion often emerges over time, and the viewer should give themselves a few seconds of relaxed peripheral viewing before the illusion may manifest. At times, these illusory motions can be quite striking, with the circles appearing to follow remarkably long trajectories. Sometimes the circles will appear to follow the same trajectory, all moving together as a single group. At other times, each circle can appear to follow its own meandering path. This latter observation of independent motion trajectories demonstrates that the phenomenon is not solely caused by motion signals across the retina generated by the movements of the eyes. Because eye movements are almost exclusively translational in nature (Schütz, Braun, & Gegenfurtner, 2011), such eye movement-related motion signals would not be expected to generate percepts of independent motion for each of the circles.

Figure 1. — Stimuli used in Experiments 1 and 2. (a) Cornsweet circles: nonflickering Cornsweet circles; (b) flickering Cornsweet circles: Cornsweet circles reversing polarity over time; (c) unipolar Gaussians: circles with only a light or a dark edge fading to the color of the background that change between light and dark gray over time; and (d) solid lines: circles with a light and dark gray line at their edge that exchange positions over time.

Video 1.

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DOI: 10.1177/2041669519875156.M1

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Demonstration of the typical Wandering Circles illusion with circles reversing polarity at a rate of 9.44 times per second.

The Wandering Circles join a class of illusions in which motion is either seen when none is present, or when the perceived motion is different than that physically present in the image. The Wandering Circles illusion appears to share many features with previously examined motion illusions such as ambiguity in the perceived motion (Anstis & Ramachandran, 1986), as well as the necessity of flicker (Anstis & Rogers, 1975, 1986; Mather, 2017), peripheral viewing (De Valois & De Valois, 1991; Ramachandran & Anstis, 1990), and destabilized eye movements (Beer, Heckel, & Greenlee, 2008). However, as will be discussed further in the general discussion, in spite of these similarities, the specific combination of features and resulting percept of the Wandering Circles is unique when compared with other motion illusions such as apparent motion, reversed-phi motion, and drifting-Gabors (Anstis & Ramachandran, 1986; Anstis & Rogers, 1975, 1986; De Valois & De Valois, 1991; Mather, 2017).

Before attempting to assess what the Wandering Circles may clarify about the functioning of motion perception, it is necessary to first determine the stimulus conditions under which the Wandering Circles are most readily observed. Here, we describe the results of two experiments that probe two such factors: flicker rate and type of circle-defining contour that, in our initial observations, appear to be critically important for the manifestation of the illusion. Using a magnitude-estimation paradigm, we find that both flicker rate and contour-type modulate the strength of the illusion.

Experiment 1

Methods

Participants

Note that participant demographics apply to participants from both Experiments 1 and 2. Participants consisted of undergraduate student volunteers from the University of Nevada, Reno and an associate professor at the University of Nevada, Reno. There were a total of 24 participants with 10 of those participating in both Experiments 1 and 2. Of those 24, 17 participants reported demographic information. Of these, 10 identified as female, 6 as male, and 1 as other. The mean reported age was 24.4 years (SD = 6.8). Participants in Experiment 1 (n = 17) were naïve to the specific aims of the study before completing the experiment. All reported having normal or corrected-to-normal vision.

Presentation

Stimuli were presented on a Mitsubishi DiamondPro 2070 SB monitor (22-in., 1,024 × 768 pixel resolution) with an 85-Hz refresh rate. The stimulus computer was a 2.5-GHz Mac Mini with an Intel HD Graphics 4000 768 MB graphics processor (16 GB of DDR3 SDRAM). Stimuli were created and presented with the Psychophysics Toolbox (Brainard, 1997; Pelli, 1997) for MATLAB (version 2017b; Mathworks Inc., Natick, MA). Participants viewed the stimuli binocularly from a distance of 57 cm with their chin positioned in a chin rest. Eye movements were not monitored.

Stimuli

Two of the most readily apparent physical aspects of the Cornsweet circles stimulus in which we first observed the illusion are the abutting lighter and darker areas, as well as the Gaussian fading of the stimulus into the background. Thus, we developed three distinct stimuli for this experiment, each distinguished by the way their contours were defined. Cornsweet circles, as shown in Figure 1(a) and 1(b), had contours defined by a light gray (41 cd/m²) and dark gray (16 cd/m²) edge smoothly changing to the background gray (27 cd/m²) in an exponential fashion. Gaussian circles, as shown in Figure 1(c), had contours that were either light gray or dark gray and faded to the background gray both inward and outward in an exponential fashion. Finally, we examined solid-line circles that had contours defined by abutting light and dark gray lines, as shown in Figure 1(d). Each circle had a radius of 2° as measured from the center of the circle to the center of its contour.

Procedure

Passive example viewing

Before beginning the actual experiment, participants first viewed three examples of how three different levels of real motion might relate to a 1 to 9 Likert scale. They first viewed a nonflickering stationary Cornsweet circle at the center of the screen for 5,000 ms, while the label Motion Level 1 was displayed below it. Participants then viewed a Cornsweet circle that moved in a random direction up to 0.15°, roughly 10 times a second (9.44 times), thus corresponding to a speed of up to 1.5°/second within a constraint of 1° vertically or horizontally from the center of the screen, while the label Motion Level 5 was displayed below it. Finally, participants viewed a Cornsweet circle that moved in a random direction up to 0.3°, 10 times a second, thus corresponding to a speed of up to 3°/second. The label Motion Level 9 was displayed below it. Circles would start their motion in a randomly chosen direction and reverse their vertical or horizontal direction whenever they reached the limits of their motion constraint.

Active practice

After viewing the three examples, participants were then presented with seven practice trials. On each of these practice trials, as illustrated in Figure 2, four Cornsweet circles were presented in a roughly square shaped pattern (10° by 10°) centered on the screen center. The starting location for each circle could vary by up to 1° vertically or horizontally from the respective corner of the square pattern. As in the Passive example trials, the four Circles would start their motion in a randomly chosen direction and reverse their vertical or horizontal direction whenever they reached the limits of their 1° motion constraint. A different level of motion was shown on each 5,000 ms trial: up to a displacement of 0°, 0.03°, 0.09°, 0.15°, 0.21°, 0.27°, 0.3° per step, at a rate of 9.44 steps per second (see Demonstration Video 2). After the circles disappeared, participants were instructed to indicate, on a 1 to 9 Likert scale, how much motion they perceived.

Figure 2. — Stimulus arrangement. On each trial, four stimulus circles were displayed in a roughly square arrangement, each with a starting position no further than 1° from the corner of a 10° square. On trials in which there was real motion, stimuli moved no further than 1° from their original starting location before changing direction.

Video 2.

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DOI: 10.1177/2041669519875156.M2

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Demonstration of real motion condition in which circles change physical position at a rate of 9.44 times per second.

Experimental trials

The experimental procedure was identical to that used during the active practice, with the exception that participants completed 168 trials, which included 42 trials in which stimuli were Cornsweet circles moving at one of the previously listed speeds (6 trials at each speed), 42 trials in which stimuli were stationary Cornsweet circles reversing polarity 9.44 times a second (see Demonstration Video 1), 42 trials in which stimuli were stationary unipolar Gaussian circles reversing polarity 9.44 times a second (see Demonstration Video 3), and 42 trials in which stimuli were stationary solid-line circles reversing polarity 9.44 times a second (see Demonstration Video 4).

Video 3.

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DOI: 10.1177/2041669519875156.M3

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Demonstration of the unipolar Gaussian condition used in Experiment 1 with circles reversing polarity at a rate of 9.44 times per second.

Video 4.

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DOI: 10.1177/2041669519875156.M4

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Demonstration of the solid-line condition used in Experiment 1 with circles reversing polarity at a rate of 9.44 times per second.

Analysis

Likert ratings of real motion stimuli served two purposes in this study to contextualize the Likert scale ratings given by participants for the flickering, physically nonmoving stimuli (e.g., how do ratings for illusory motion compare with ratings for real motion; Figure 3). A relationship was modeled with a logarithmic function (y = a × ln(x) + b) correlating the real motion and Likert scale ratings for each participant (see Figure 3). A log fit was chosen as it was shown to have a closer fit than a linear fit, as measured by R² values, for the majority of the participants’ data. Thus, for each subject, we were able to obtain both a raw Likert rating and a value corresponding to the estimated strength of the illusion in terms of real motion for each of the three flickering stationary stimulus conditions. At the group level, we ran a Friedman test, as well as Wilcoxon Signed-rank tests to evaluate the statistical significance of any differences in perceived illusion strength between the three flickering stationary stimulus conditions. Nonparametric statistical methods were employed to account for potential violations of the necessary assumptions due to the use of Likert scale ratings as the primary measure. That being said, patterns of significant and nonsignificant results were identical when parametric equivalents were used to analyze the data.

Figure 3. — Estimating illusion magnitude. Representative data from one participant. Likert ratings in response to real motion (diamonds) were modeled using logarithmic regression (dashed line). This model was then used to estimate the physical equivalents of the perceived motion in the 9.44 reversals per second flickering stimuli for the Cornsweet (circle), solid-line (triangle), and Gaussian (square) conditions. For this typical participant, there is a strong positive relationship between the physical motion and reported motion. Although they were not physically moving, the participant rated the 9.44 reversals per second flickering Cornsweet circle, on average, at 4.6 on the Likert scale, which according to the logarithmic model, corresponds to a physical displacement of ∼0.12° per step or 1.2°/second. In contrast, for this participant, the solid lines exhibited less illusory motion and the Gaussians even less.

Results

Using average Likert scale ratings, we performed a Friedman test to determine if there were significant differences in the perceived motion for each stimulus type overall, as well as Wilcoxon Signed-rank tests to determine whether there was a significant difference in the illusion strength created by each flickering stimulus. The results of the Friedman test were compared against an alpha level of .05. As shown in Figure 4(a), there were significant differences in the strengths of the illusion perceived across stimulus types, χ²(2) = 24.471, p < .001. As demonstrated in post hoc comparisons (Bonferroni-adjusted critical p = .016), the Cornsweet circles produced an illusion strength that was significantly greater than that for both the unipolar Gaussians (Z = 3.621, p < .001, r = .878) and the solid lines (Z = 3.574, p < .001, r = .867). However, there was no significant difference in the illusion strength between the unipolar Gaussians and solid lines (Z = 1.942, p = .052, r = .471; Figure 4(a)). Further, we show that when real motion equivalents are calculated for each condition use the log fits, a similar pattern is observed across the Cornsweet circles (M = 0.202°, SD = 0.157°), unipolar Gaussians (M = 0.095°, SD = 0.145°), and solid lines (M = 0.104°, SD = 0.104°) conditions (Figure 5(b)).

Figure 4. — Experiment 1 results: (a) mean Likert ratings for amount of motion observed for 9.44 reversals per second flickering Cornsweet, unipolar Gaussian, and solid-line circles. At the group level, Cornsweet circles were perceived to have a greater illusion strength than either other stimulus type. It should be further noted that in spite of the lack of a significant difference in the perceived illusion strengths for the Gaussian and solid-line conditions, of the individual participants, only four produced an average illusion strength score that was higher for Gaussian circles than the solid-line stimuli. (b) Mean amount of motion observed in each condition in terms of real motion calculated using the log fit of real motion and Likert ratings for nonflickering Cornsweet circles. Error bars represent standard error.

Figure 5. — Experiment 2 results: (a) mean Likert ratings for amount of motion observed for 1.98, 9.44, and 28.33 reversals per second flickering Cornsweet circles; 9.44 and 28.33 reversals per second flickering circles both produced motion percepts greater than 1.98 reversals per second flickering circles, and the 9.44 reversals per second flickering circles also produced an illusion strength greater than that produced by the 28.33 reversals per second flickering circles. (b) Mean amount of motion observed in each condition in terms of real motion calculated using the log fit of real motion and Likert ratings for nonflickering Cornsweet circles. Error bars represent standard error.