Vision Research 177 (2020) 12–19

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Vision Research
journal homepage: www.elsevier.com/locate/visres

Spatial dynamics of the eggs illusion: Visual field anisotropy and peripheral
visionT

Kun Qiana, , Hiroyuki Mitsudob⁎abInstitute of Decision Science for a Sustainable Society, Kyushu University, Fukuoka, Japan
Faculty of Human-Environment Studies, Kyushu University, Fukuoka, Japan

ARTICLE INFOABSTRACT

Keywords:
Visual illusion
Shape perception
VisionPerception
Grid illusion
Peripheral vision

The eggs illusion is a visual phenomenon in which bright circular patches located at the midpoints between theintersections of a dark grid are perceived as being elongated along the direction orthogonal to the grid line. In
the four experiments we report here, we explored the spatial properties of the eggs illusion by manipulating
retinal eccentricity and the location of the stimulus in the visual field. In Experiment 1, we examined whether
central and peripheral configurations affected the illusory magnitude. In Experiment 2, we varied the spatial
location of grid patterns and found that the eggs illusion was intensified when the pattern was presented in thehorizontal, not vertical or diagonal position, relative to the fixation. In Experiment 3, we varied the retinal
eccentricity of the pattern along the horizontal meridian and found that the illusion was enhanced in the retinal
periphery. In Experiment 4, we manipulated the size of the stimulus and found that peripheral enhancement of
the eggs illusion was more apparent for a larger pattern. The visual field anisotropy and the peripheral enhancement of the eggs illusion are discussed in relation to mechanisms underlying grid-induced illusions.

1. Introduction
The eggs illusion is a recently discovered visual phenomenon inwhich bright circular patches located at midpoints between adjacentintersections in a dark grid with a black background are perceptually
deformed as elliptical (Qian & Mitsudo, 2016; Fig. 1). For example,
perfect circular patches appear elongated at right angles to their embedding grid contours (Qian & Mitsudo, 2016, 2019). The visual illusions generated by grid patterns, such as the Hermann grid illusion(Brewster, 1844; Hermann, 1870), Bergen’s illusion (Bergen, 1985), theblanking phenomenon (McAnany and Levine, 2004), and the scintillating grid illusion (Schrauf, Lingelbach, Lingelbach, & Wist, 1995;
Schrauf, Lingelbach, & Wist, 1997), are related to the perception ofbrightness. Conversely, the eggs illusion relates to the perception ofshape. Qian and Mitsudo (2016) first reported the eggs illusion anddemonstrated that the magnitude of the illusion was affected by thepatch size and grid luminance. A follow-up study explored the temporalfeatures of the eggs illusion and revealed the role of orientation processing in generating the illusion (Qian & Mitsudo, 2019). These twostudies suggested a remarkable similarity between the eggs illusion andthe scintillating grid illusion, with evidence that both illusions are affected by the stimulus size, luminance contrast, presentation duration,and orientation information. The function of these factors on⁎

scintillating grid illusion have been demonstrated by a series of previous studies (Schrauf et al., 1997; Schrauf, Wist, & Ehrenstein, 2000;
Qian, Yamada, Kawabe, & Miura, 2009; Qian, Kawabe, Yamada, &Miura, 2012). Based on these common features, Qian and Mitsudo(2016, 2019) proposed a tentative hypothesis that the eggs illusion
shares the same underlying mechanism as the scintillating grid illusionin that processing local and relative orientation plays a critical role ingenerating the illusion. In this hypothesis, shape distortion in the eggs
illusion appears to arise from a mechanism similar to orientation contrast (Suzuki & Cavanagh, 1998) from their embedding local grid
contours and can be enhanced by the global grid configurations.
Orientation processing is an important part of spatial vision (DeValois & De Valois, 1980). The relevance of orientation processing to
the eggs illusion implies the necessity of exploring the illusion further
and within the context of spatial vision. For the scintillating grid illusion, VanRullen and Dong (2003) revealed that the illusion wasstronger in peripheral vision than in foveal vision. Qian and Mitsudo(2016, 2019) noted the potential role of peripheral presentation in theeggs illusion based on informal observations, without support of experimental investigation. In the present study, we focused on the spatial
properties of the eggs illusion by manipulating the location and eccentricity of the stimulus in the visual field. Based on the findings on
the scintillating grid illusion and our informal observations of the eggs

Corresponding author.
E-mail addresses: qk@kyudai.jp (K. Qian), hmitsudo@lit.kyushu-u.ac.jp (H. Mitsudo).

https://doi.org/10.1016/j.visres.2020.08.008
Received 31 May 2020; Received in revised form 19 August 2020; Accepted 19 August 20200042-6989/ © 2020 Elsevier Ltd. All rights reserved.

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MB871J/A) and a CRT monitor (EIZO, FlexScan F931, 1152 × 870
pixels, 75 Hz), and it was generated by MATLAB R2017a using
Psychtoolbox (Brainard, 1997; Pelli, 1997). The viewing distance was
60 cm, and the observers’ heads were stabilized by a chin-and-foreheadrest.
The basic stimulus consisted of a black background, a gray grid, andan array of perfectly circular white patches, the same as what was usedin Qian and Mitsudo (2016). The luminance values of the black background, gray grid, and white patches were 1 cd/m2, 28 cd/m2, and94 cd/m2, respectively. The grid was composed of 11 horizontal and 11
vertical bars that were spaced equally. Each bar in the rows or columns
subtended 25° × 35.4′ and was placed 1.73° of visual angle apart fromits adjacent bars. Ten white circular patches with diameters of 39.8′
were placed on each bar. Each patch was positioned at the midpoints
between two adjacent intersections of the grid. All stimuli were drawn
using the anti-aliasing method. We modified this basic stimulus into
two experimental stimuli. For the central condition, we used the central
part of the basic stimulus, a 3 × 3 grid pattern (6.8° × 6.8°), and wetrimmed off all other elements. For the peripheral condition, the central
5 × 5 grid (11.4° × 11.4°) was erased from the basic stimulus. To
replicate the findings of Qian and Mitsudo (2019), in this experiment,
we set the presentation duration to 40, 67, 133, 213, 347, 493, 693, and1000 ms.
A 9-point scale was used in the response display, which accompanied a series of patches under the scale. Under the leftmost point of
the scale, two white circular patches with diameters of 44.4′ were
presented in a column. At the third, fifth, seventh, and ninth points
from the left, four sets of elliptic patches were presented. The two elliptic patches presented in each column had identical shapes and differed in their orientation. The major axis of the upper patch was vertical, and that of the lower patch was horizontal. All eight ellipticalpatches had the same minor-axis length of 44.4′. The major-axis lengthsof the ellipses under the third, fifth, seventh, and ninth points from theleft were 48.0′, 50.4′, 54.0′, and 57.6′, corresponding to aspect ratios of
1.08, 1.14, 1.22, and 1.30, respectively. Larger-sized patches were usedin the matching task for better visibility, to make it easier to compare
perceived shape (i.e., not presented in the matching display) with thepresented ellipses. Almost the exact same response display was used in
Qian and Mitsudo (2016, 2019).

Fig. 1. A demonstration of the eggs illusion. The bright circular patches locatedon the dark grid lines are perceived as ellipses elongated at right angles to theirembedding grid contours.

illusion, we hypothesized that the eggs illusion could also be
strengthened in peripheral vision. Exploring a potential impact of retinal stimulus position is essential to understand the mechanisms underlying the eggs illusion, because it is unclear what stimulus is optimalfor generating the eggs illusion. To examine this, we conducted four
psychophysical experiments. In Experiment 1, we investigated a central
and peripheral configuration of the eggs illusion. In Experiment 2, we
systematically controlled the position and eccentricity of the stimulus
display. The spatial properties of the eggs illusion discovered in Experiment 2 were investigated further in Experiments 3 and 4.
2. Experiment 1: Central/peripheral display of the eggs illusion

2.1.3. Procedure
Each observer binocularly viewed the monitor in a darkened room.
A black background was presented for 1000 ms at the beginning of eachtrial. After this, a red fixation cross (1.1° × 1.1° of visual angle) waspresented for 213 ms, which was followed by the presentation of thetest stimulus for one of the eight durations (40–1000 ms). The fixation
cross remained on the screen until the test stimulus disappeared.
Observers were required to view the fixation cross when it was displayed, regardless of whether the test stimulus was present or not. Afterthe test stimulus and fixation cross disappeared, a black-and-white,random-dot pattern was displayed as a mask for 493 ms. The response
scale was displayed after the mask disappeared. Observers were asked
to choose from the nine options (points on a scale) and select the onethat was most similar to the perceived shape of the white patches in thetest stimulus. Observers were instructed to choose the option closest to
the average shape if the patches were perceived in different shapes
across locations. There was no time limit for observers’ responses.
Sixteen experimental conditions (two display patterns × eight
presentation durations) were tested five times each. Consequently, 80
experimental trials in total were run in a randomized order. The observers were asked to complete approximately 10 practice trials in
advance to get accustomed to the task.

In this experiment, we exploratorily examined the effect of peripheral presentation on the eggs illusion. Fig. 2a shows our two stimulus configurations, in which the central part of the original pattern
was presented (central condition) and removed (peripheral condition).
We also varied the presentation duration because the illusion’s magnitude changes over time, as found in Qian and Mitsudo (2019). Basedon the informal observations stated above, we predicted that the illusion would not diminish, even at peripheral presentation.
2.1. Methods
2.1.1. Observers
Ten observers participated in Experiment 1 (five males and fivefemales; mean age = 30.3 years; SD = 6.7 years). Every observer had
normal or corrected-to-normal visual acuity and was naïve to the purpose of the experiment. Participants were recruited from the students,
faculty members, and administrative staffs at Kyushu University. All thefour experiments were approved by the Ethics Committee for
Psychological Studies at the Institute of Decision Science for a
Sustainable Society, Kyushu University (No. 2017/2-3, No. 2019/1-8).
Written consent was obtained from each participant at the beginning of
the experiment.

2.2. Results and discussion

2.1.2. Apparatus and stimuli
The experiment was conducted using a computer (Apple, Mac Pro,

Fig. 2 shows the perceived aspect ratios as a function of the13Vision Research 177 (2020) 12–19

K. Qian and H. Mitsudo

Fig. 2. Stimuli and results for Experiment 1. (a) Schematic illustrations of the test stimuli used in the central and peripheral conditions. (b) Results of Experiment 1.
Mean perceived aspect ratios, averaged over the 10 observers, are shown as a function of presentation duration. Error bars denote standard errors of the mean.

presentation duration, which were averaged over the 10 observers inExperiment 1. A two-way within-participant analysis of variance(ANOVA) on the mean perceived aspect ratios, with factors of display
pattern and presentation duration, resulted in a significant main effectof presentation duration [F (7, 63) = 9.648, p < .001, η2p = .517].
However, neither the main effect of retinal position [F (1, 9) = 0.011,
p = .92, η2p = .001] nor the two-way interaction [F (7, 63) = 1.282,
p = .27, η2p = .125] was significant. Multiple comparisons revealed thatthe following pairs of presentation-duration combinations differedsignificantly: 40–213, 40–347, 40–493, 40–693, 40–1000, 67–213,
67–347, 67–493, 67–693, 67–1000, 133–347, and 133–493 ms (ps <.05).
In summary, the magnitude of the illusory deformation did not
differ, irrespective of whether the stimulus was presented centrally or
peripherally. In each configuration, the illusion increased up to aroundpresentation durations of 200–300 ms. This result replicates that of
Qian and Mitsudo (2019). In addition, based on informal interviews of
six naive participants after the experiment, all participants thought thatphysically elliptical patches with variable aspect ratios were presented
across trials. Therefore, we believe that the observers’ response reflects
their percept rather than response bias or expectations.
Why was no decrease or increase in the illusory magnitude foundeven in the peripheral presentation? One possibility is that the stimulus
differed considerably between the two conditions. For example, boththe size of the grid and the number of patches were greater in the
peripheral condition than in the central condition. To examine thisissue, we conducted Experiment 2.

Experiment 1), and it is expected to prevent saccades that reduce retinal
eccentricity. We predicted that the magnitude of the illusion would
alter depending on different positions.
3.1. Methods
The methods were identical to those used in Experiment 1, except
for those described below.
3.1.1. Observers
Twenty-five observers participated in Experiment 2 (nine males and
16 females; mean age = 20.8 years; SD = 2.8 years). One of them hadparticipated in Experiment 1.
3.1.2. Stimuli and procedure
A constant stimulus duration of 212 ms was used throughout theexperiment to avoid reflexive saccades to the test stimulus. There were
two experimental variables in Experiment 2. One was the visual field ofpresentation, in which the center of the stimulus pattern was presented
on one of four radial orientations: the horizontal axis (H), the verticalaxis (V), and along axes oriented at +45° (R-tilt) and −45° (L-tilt) fromthe vertical axis. Fig. 3 shows the centers of the 3 × 3 grid pattern,which was located upright at one of the five intersections on each lightgray scale. The two polar positions in the same radial direction weremerged in our data analysis (e.g., the upper and lower position on thevertical axis). The other variable was retinal eccentricity (i.e., the distance between the centers of the screen and the grid pattern), selectedfrom 4.8°, 6.1°, 7.4°, 8.7°, and 10° of visual angle. Four visual fields andfive levels of eccentricity constituted 20 conditions in this experiment.
Each condition was tested six times in a randomized order. In total, 120
trials were run in Experiment 2. The mask of a black-and-white,random-dot pattern was not used in Experiment 2.

3. Experiment 2: Manipulation of location and eccentricity in thevisual field
The purpose of Experiment 2 was to systematically examine whether the magnitude of the eggs illusion changed across different retinal
positions and eccentricities. We located the 3 × 3 grid pattern used in
the central condition of Experiment 1 at one of several positions aroundthe central fixation. To accurately control the stimulus position andeccentricity, we chose a stimulus duration of around 200 ms because
this length of time is sufficient to produce the eggs illusion (as found in

3.2. Results and discussion
Fig. 4 shows the results of Experiment 2. A two-way within-participant ANOVA was conducted on the mean perceived aspect ratios withfactors of visual field and eccentricity. The results of the ANOVA
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visual inspection of Fig. 4 suggests a decrease accompanied by increasing eccentricity in the vertical and two tilt positions, this tendency
was not statistically significant.
The lack of impact of peripheral presentation on the eggs illusion
might be due to a response bias possibly related to an anisotropy ofvisual acuity. For example, the observers might have chosen a more
elliptic patch because visual acuity in the peripheral field is relatively
higher along the horizontal meridian than along the vertical meridian(Kondo et al., 2008). To examine this issue, we conducted Experiment
3.
4. Experiment 3: Manipulation of eccentricity in the horizontal
visual field
In Experiment 3, we examined the peripheral eggs illusion found inExperiment 2 using physically elongated patches on the grid line. The
shape deformation in the eggs illusion occurs along the direction orthogonal to the grid line. We aimed to determine the degree to which
the eggs illusion depends on local grid orientation, by assessing theimpact of physical aspect ratio of the patches on the perceived patch
shape. Qian and Mitsudo (2016, 2019) employed the same procedureand found a clear slope of the selected ellipse around an aspect ratio of
1.0 when the illusion was evident. We also modified the method of
stimulus display because a one-sided presentation of the stimulus inExperiment 2 might have prevented observers from focusing their attention on the fixation cross.

Fig. 3. Stimulus configuration in Experiment 2. The intersections on each lightgray scale denote the positions where the center of the 3 × 3 grid pattern was
located. This panel is based on a screenshot of the vertical visual field at an
eccentricity of 4.8°. Light gray scales and all figure legends are included for
explanation and were not presented in the actual experimental display. In theactual experiment, the background was black, identical to that of the gray gridshown in this figure.

4.1. Methods
The methods were the same as those in Experiment 2, except for thefollowing.
4.1.1. Observers
Twenty-five observers participated in Experiment 3 (eight males
and 17 females; mean age = 20.4 years; SD = 2.7 years). Twenty-threeof them had participated in Experiment 2.
4.1.2. Stimuli and procedure
Two independent variables were used in this experiment. First, eccentricity was again manipulated in Experiment 3 with the same levels
as those used in Experiment 2 (4.8°, 6.1°, 7.4°, 8.7°, and 10° of visual
angle). Second, the shape of the white patches was varied at three levels. In addition to the perfect circle (circle condition), we employed
two different types of elliptical white patches. In the parallel condition,
the patches were elongated along the grid orientation (left panel inFig. 5). In the orthogonal condition, the patches were elongated along
the orientation orthogonal to the grid orientation. The lengths of thelonger and shorter axes were 40.8′ and 39.0′, respectively (aspectratio = 1.05). Based on Qian and Mitsudo (2016, 2019), it was expected that the illusion magnitude in the parallel condition would be
weaker due to the cancellation of illusory deformation along the orientation orthogonal to the grid line.
In an attempt to prevent potential reflexive saccades to the stimulus,
a grid without a patch (empty grid) was presented on the opposite sideof the test eggs pattern (right side in Fig. 5). The locations of the empty
and test grid patterns were counterbalanced. Sixty trials (5 eccentricities × 3 patch shapes × 4 repetitions with counterbalance) wereconducted in a randomized order.

Fig. 4. Results of Experiment 2. Mean perceived aspect ratios averaged over the
25 observers are shown as a function of visual field. Error bars denote standard
errors of the mean.

revealed significant main effects of visual field [F (3, 72) = 4.454,
p = .006, η2p = .157]. However, neither the main effect of eccentricity[F (4, 96) = 1.630, p = .173, η2p = .064] nor the interaction of the twovariables [F (12, 288) = 0.997, p = .452, η2p = .040] was significant.
Regarding the significant main effect of visual field, post-hoc tests in
Tukey’s method revealed significant differences between the H and Rtilt conditions (p = .028) and between the H and L-tilt conditions(p = .029). No other pairs were significant.
The prediction regarding the effect of stimulus position was supported by the results because we found a significant increase in theillusory magnitude when the grid was presented in the horizontal position as compared to the two oblique positions (R-tilt and L-tilt).
However, no peripheral enhancement was demonstrated. Although a

4.2. Results and discussion
Fig. 6 shows the perceived aspect ratios as a function of eccentricity.
The results of a two-way, within-participant ANOVA revealed significant main effects of eccentricity [F (4, 96) = 6.145, p < .001,
η2p= .204] and patch shape [F (2, 48) = 8.365, p < .001, η2p= .258]
and a significant interaction [F (8, 192) = 2.058, p = .042, η2p = .079].
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Fig. 5. Schematic illustration of stimuli used inExperiment 3. The intersections of each light grayscale denote the positions where the center of thegrid pattern was located. This figure is based on ascreen shot of the stimulus display with conditions of
4.8° as the eccentricity and parallel ellipse as thepatch shape. Light gray scales and the figure legend
are included for explanation and were not presented
in the actual experimental display.

Fig. 7. Averaged SD of selected aspect ratio shown as a function of eccentricity.
Fig. 6. Results of Experiment 3. Mean perceived aspect ratios, averaged over 25
observers, are shown as a function of eccentricity. Error bars denote standard
errors of the mean.

eccentricity increased.
An anonymous reviewer commented on possible changes in confidence when considering the effect of eccentricity. We conducted an
additional analysis of response variability in this experiment. We calculated the SD of selected ellipses in the response display for eachcondition. If the peripheral enhancement of the eggs illusion is entirely
based on a decrease of response confidence, the averaged SD of theselected ellipses would be expected to increase as a function of eccentricity. However, as shown in Fig. 7, there was no systematic change in
response variability. Therefore, we believe that confidence is unlikely
to play a critical role in the peripheral enhancement of the eggs illusion.

Post-hoc tests with Tukey’s method revealed significant differences
between the parallel and orthogonal conditions (p < .001) for the
shape patches, between 4.8° and 10° (p = .001), and between 6.1° and
10° (p < .001) for eccentricity. Tests of simple main effects showedthat the effect of eccentricity was significant for each patch shape[parallel: F (4, 288) = 2.785, p = .027; circle: F (4, 288) = 4.158,
p = .003; orthogonal: F (4, 288) = 3.780, p = .005]. The simple main
effect of patch shape was significant when the eccentricity was 4.8°,
7.4°, and 10° [4.8°: F (2, 240) = 7.262, p < .001; 6.1°: F (2,240) = 0.726, p = .485; 7.4°: F (2, 240) = 4.765, p = .009; 8.7°: F (2,240) = 2.250, p = .108; 10°: F (2, 240) = 3.095, p = .047]. Multiple
comparisons based on significant simple main effects showed a significant difference in the pair of 4.8°–10° for the condition of parallel
ellipse; in the pairs of 4.8°–8.7°, 6.1°–8.7°, 4.8°–10°, and 6.1°–10° for thecircle condition; and in pairs of 6.1°–10° and 8.7°–10° for the conditionof orthogonal ellipse (ps < .05). At eccentricities of 4.8° and 7.4°,
significant differences were found between the parallel and orthogonalconditions and between the circle and orthogonal ellipses; at an eccentricity of 10°, a significant difference was found between the paralleland orthogonal conditions (ps < .05).
The results of Experiment 3 replicated those of Qian and Mitsudo(2016, 2019) in that the eggs illusion could be systematically alteredusing patches deformed along the grid line. We found reliable andconsistent slopes at almost all eccentricities, which suggests that the
peripheral eggs illusion is not a response bias. Furthermore, we foundthat the eggs illusion could be rather enhanced as the stimulus

5. Experiment 4: Manipulation of eccentricity and stimulus size
The purpose of Experiment 4 was to further examine whether theeggs illusion could occur strongly in the peripheral visual field. One
technical problem contrary this purpose is that small patches in the eggs
pattern are almost invisible in peripheral vision, where visual acuity ismuch lower than in foveal vision (Mandelbaum & Sloan, 1947;
Anderson et al., 1991). Therefore, to increase the visibility of a pattern,enlarging the stimulus size is necessary (Anstis, 1974; Kondo et al.,2008). In the experiment, a magnified size of the eggs pattern wasadded to explore the interaction between stimulus size and eccentricity.
Qian and Mitsudo (2016) reported that when viewed at the perifovea,
larger patches on the grid produced a weaker eggs illusion. Therefore,
we predicted that a magnified eggs pattern would produce a weaker
illusion in central vision, but produce a stronger illusion in peripheral
vision.

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5.1. Methods

Similar to Experiment 3, an additional analysis of response variability was conducted. As shown in Fig. 7, there was no systematicchange in response variability in Experiment 4. Therefore, confidence isunlikely to play a critical role in the peripheral enhancement of the eggs
illusion.
The results of Experiment 4 revealed the influence of stimulus sizeon peripheral enhancement of the eggs illusion. Our prediction waspartially supported in that the illusion magnitude increased as a function of stimulus eccentricity only when the stimulus was magnified.
Although Fig. 8 shows that magnified stimulus seemed to produce aweaker illusion than the original one, the difference between magnified
and original conditions was not significant. We estimated the corticalrepresentation sizes of the stimuli at each eccentricity condition by
calculating the cortical magnification factor (M values), using the same
method as that in a previous study (Carrasco & Frieder, 1997). As
shown in Fig. 8, the cortical representation size of the original stimulus
at eccentricities of 4.8°-6.1° was approximately equal to that of themagnified stimulus at eccentricities of 8.7-10°, and the illusory deformation was similar in these conditions. Thus, we speculate that theeggs illusion may occur when the cortical representation size of thestimulus patch is smaller than a particular value.

The methods were identical to those in Experiment 3, except for thefollowing.
5.1.1. Observers
Twenty-five observers participated in Experiment 4 (10 males and
15 females; mean age = 20.5 years; SD = 2.7 years). Twenty-three ofthem had participated in Experiment 3.
5.1.2. Stimuli and procedure
The two independent variables were eccentricity and stimulus size.
Eccentricity was manipulated in the same way as in Experiments 2 and3. For the stimulus size, we prepared two levels: the original and themagnified patterns. The original pattern was identical to the 3 × 3 gridwith white patches used in Experiments 2 and 3. The magnified pattern
was overall one-and-a-half times as large as the original one. Different
from Experiment 3, we did not present an empty grid without patches.
The shapes of the white patches were always perfect circles. Five levelsof eccentricity and two levels of stimulus size yielded 10 experimental
conditions. Each condition was tested six times, including the counterbalance for the stimulus position (the right and left side of the
fixation). In total, 60 trials were conducted in a randomized order.

6. General discussion
The present study examined the spatial properties of the eggs illusion by manipulating the position of the stimulus in the visual field. In
Experiment 1, we replicated findings on the temporal properties of theeggs illusion (Qian & Mitsudo, 2019), in which the magnitude of theillusion reached the peak and showed no significant changes when thepresentation duration was longer than around 200 ms. In Experiment 2,
we controlled the position and eccentricity of the grid pattern in detailand found a visual field anisotropy of the eggs illusion, in which theillusion was strengthened in the horizontal visual field. However, themain effect of eccentricity was not significant. In Experiment 3, weconcentrated on the horizontal visual field, in which a stronger illusion
was generated, and found that the illusion was enhanced as eccentricity
increased. Lastly, in Experiment 4, we varied the stimulus size to accommodate a property of peripheral vision, i.e., lower spatial resolution
and visual acuity, and found that peripheral enhancement of the eggs
illusion occurred with a larger stimulus size. Taken together, we demonstrated that the eggs illusion is anisotropic across the visual fieldand can be enhanced in peripheral vision.
As noted in the introduction section, peripheral enhancement occurs
in the scintillating grid illusion (VanRullen & Dong, 2003). In thisstudy, we demonstrated a similar peripheral enhancement of the eggs
illusion only in the horizontal visual field, which provides partial support for the common features between the eggs illusion and the scintillating grid illusion. Referring to the discussion presented by
VanRullen and Dong (2003) regarding the scintillating grid illusion, we
consider that peripheral enhancement of the eggs illusion might also be
related to the spatial dynamics of visual attention between the central
and peripheral visual field (Posner, 1980; Carrasco, 2011).
Furthermore, the present study demonstrated visual field anisotropyof the eggs illusion, which has not been reported for the scintillating
grid illusion. Visual field anisotropy has been clarified in basic geomatical illusions on length perception (Bertulis & Bulatov, 2005;
Mikellidou & Thompson, 2013); the illusion of motion direction (Loffler& Orbach, 2001); illusory motion (Ehrenstein, 1997); and perceptual
filling-in (Sakaguchi, 2003). Bertulis and Bulatov (2005) demonstrated
the visual field anisotropy of length perception using the Müller-Lyer
pattern (Müller-Lyer, 1889) and the Oppel-Kundt pattern (Oppel, 1855;
Kundt, 1863), by controlling the relative angle between test and references parts of the stimuli. However, unlike Bertulis and Bulatov(2005) and Loffler and Orbach (2001), the present study manipulated
the presentation positions in the visual field but not the orientation of
stimuli. Sakaguchi (2003) found that perceptual filling-in required

5.2. Results and discussion
Fig. 8 shows the perceived aspect ratios as a function of eccentricity.
We ran a two-way, within-participant ANOVA with factors of eccentricity and stimulus size. The results of the ANOVA revealed a significant main effect of eccentricity [F (4, 96) = 3.009, p = .022,
η2p = .111] and a significant interaction between the two variables [F(4, 96) = 4.736, p = .002, η2p = .165]. The main effect of stimulus size
was not significant [F (1, 24) = 2.984, p = .097, η2p = .111]. Tests ofsimple main effects showed that the effect of eccentricity was significant for the magnified pattern [original: F (4, 192) = 0.728,
p = .574; magnified: F (4, 192) = 6.812, p < .001]. The simple main
effect of stimulus size was significant when the eccentricity was 4.8°
and 6.1° [4.8°: F (1, 120) = 6.276, p = .014; 6.1°: F (1, 120) = 8.016,
p = .005; 7.4°: F (1, 120) = 1.165, p = .283; 8.7°: F (1, 120) = 1.862,
p = .175; 10°: F (1, 120) = 0.631, p = .429]. Multiple comparisonsbased on significant simple main effects showed significant differences
for pairs of 4.8°–10°, 6.1°–8.7°, 6.1°–10°, and 7.4°–10° for the magnified
pattern (ps < .05).

Fig. 8. Results of Experiment 4. Mean perceived aspect ratios, averaged over 25
observers, are shown as a function of eccentricity. Error bars denote standard
errors of the mean. The cortical magnification factor for each experimental
condition is displayed in light gray color.
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more time in the horizontal position, which implies that illusory fillingin is more difficult in the horizontal visual field when compared withthe other visual fields. This tendency is contrary to the case of the eggs
illusion reported here. Thus, the anisotropy found in the eggs illusion is
likely to be different from that reported in the other illusions.
Experiment 2 found that the eggs illusion was stronger in the horizontal position than in the oblique positions. This is somewhat similar
to the oblique effect—a relative deficiency in visual perception of oblique lines when compared with that of the horizontal or vertical lines(Mach, 1861; Appelle, 1972). In addition, Hubel and Wiesel (1959)
provided neurophysiological evidence that the orientation-selective
neurons of V1 that respond to horizontally or vertically oriented bars
are much numerous than those that respond to oblique ones. However,
our results should be distinguished from the oblique effect, because theprevious studies are involved in the processing for oblique orientations,
not processing in oblique positions of the visual field.
Why did peripheral enhancement of the eggs illusion occur particularly in the horizontal visual field? Interestingly, a visual field anisotropy of peripheral sensitivity is also reported for moving patterns inwhich perceptual sensitivity is less impaired by eccentricity in thehorizontal visual field (Tynan & Sekuler, 1982). Although the eggs
pattern is essentially static, we speculate that the eggs illusion involves
transient visual processing that operates a large portion of the visual
field, because this illusion is likely to be enhanced by voluntary saccades (Qian & Mitsudo, 2016) and to occur at brief stimulus presentations (Qian & Mitsudo, 2019). According to this tentative interpretation, no peripheral enhancement in Experiment 1 may be due to visual
crowding (Whitney & Levi, 2011), in which simultaneously presented
flankers can reduce target visibility (i.e., white small patches in thisstudy).
There were several limitations in this study, which suggest directions for future studies on the eggs illusion. An anonymous reviewer
advised systematic manipulation of contrast and context. For contrast,
we have demonstrated how luminance of the grid, which eventually
altered both patch and grid contrasts, affected the eggs illusion (Qian &Mitsudo, 2016, 2019). However, we did not alter patch luminance andgrid luminance independently. For context, the effect of crowding anddensity, as well as the association with perceived deformation of textures (i.e. the honeycomb illusion, Bertamini, Herzog, & Bruno, 2016)
calls for further investigations in the future. One may think that theeggs illusion arises from lateral inhibition or orientation repulsion. As
to lateral inhibition, we believe that its contribution to the eggs illusion
is limited because lateral inhibition primarily involves brightness, notshape. Even for brightness (i.e., the Hermann grid and scintillating grid
illusions), psychophysical data do not necessarily support the theory oflateral inhibition (Schiller & Carvey, 2005; Qian et al., 2012). Furthermore, the tilt angle of orientation repulsion (Westheimer,
Shimamura, & McKee, 1976), i.e. 10°–20° was considerably different
from the orientation of deformation in the eggs illusion (orthogonal).
However, experimental investigations on lateral inhibition and orientation repulsion are necessary for future studies.
In conclusion, we experimentally demonstrated visual field anisotropy and peripheral enhancement of the eggs illusion. These characteristics may provide insights into the mechanisms underlying thefamily of grid-induced illusions, such as the Hermann and scintillating
grid illusions.

Acknowledgments
This study is supported in part by JSPS KAKENHI JP17H06342,
JP20K03479 and the Hirose Research Grant from the Hirose
International Scholarship Foundation to KQ, and by JSPS KAKENHI
JP18K03180 to HM.
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CRediT authorship contribution statement
Kun Qian: Conceptualization, Data curation, Formal analysis,
Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing - originaldraft, Writing - review & editing. Hiroyuki Mitsudo:
Conceptualization, Data curation, Formal analysis, Investigation,
Methodology, Resources, Supervision, Validation, Visualization,
Writing - review & editing.
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K. Qian and H. Mitsudo
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