Introduction

The watercolor illusion (WCI) is a color-spreading illusion that occurs when a shape has an inner and outer border contrasting in luminance and hue. This border generates a perceptual filling-in of the center of the shape with a hue similar to the inner border, often referred to as the “fringe” (Pinna et al., 2001). Both borders are necessary to induce the illusion, as can be seen in Fig. 1. When viewed together, the combination of outer border and inner fringe generates a perception of color spreading away from the fringe in a hue similar to the fringe. The aim of this study was to investigate the impact of local (i.e., inside the color-spreading region) and global (i.e., stimulus parts exterior to the color-spreading region) context on the spatial expanse of WCI color spreading. By manipulating local and global contexts we were able to test a simple question: Does color always spread outward from unenclosed WCI stimuli?

Fig. 1
figure 1

Example watercolor illusion (WCI) stimuli with the majority of the fringe facing out (A) versus in (B). Notice how the color spreads outward into space away from the fringe in both examples. If the contrasting border is removed (C) or the fringe is removed (D), no color spreading is perceived

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Many factors have already been shown to impact the spatial expanse and illusion magnitude of the WCI. For instance, the WCI dissipates substantially beyond 45° of visual angle, suggesting there is a maximum range across which the color can spread (Pinna et al., 2001). Additionally, illusion magnitude decreases as the border contour thickness increases with an optimal contour thickness of 6′ of visual angle. The borders of WCI stimuli are often wavy or scalloped. This shortens the distance between certain points along the inside of the shape, which helps to strengthen the illusion. Pinna and colleagues (Pinna et al., 2001) note “…the strength of color spreading increases monotonically with increasing spatial frequency of the sinusoidal modulation” (p. 2671) even though stimuli with straight borders produced substantial (albeit weaker) illusion magnitudes. The colors and relative luminance of the inner and outer borders are also relevant to the strength of the illusion. While most combinations of colors and contrasts produce at least a modest spreading effect, the greatest illusion magnitudes are reported for stimuli with high contrast between the inner and outer border in regard to both color and luminance (Devinck et al., 2005). Stimuli with a blue or purple outer border and a yellow or orange inner border elicit the most vibrant spreading. A similar watercolor effect has even been observed achromatically, suggesting color is not required for a similar perceptual-spreading phenomenon to occur (Cao et al., 2011; Pinna, 2006).

A number of local stimulus parameters can influence illusion magnitude. For example, dotted and solid contours can produce equal illusion magnitude (Broerse & O'Shea, 1994; Pinna et al., 2001; Pinna & Grossberg, 2005), but increasing lateral spacing of the dots in dotted contours decreases illusion magnitude. The spacing between inner and outer contours is also relevant. When an interspace exists between the inner and outer contours, illusion magnitude decreases at a rate dependent on the size of the interspace (Devinck & Spillmann, 2009). These findings highlight the necessity of certain local factors within the stimulus in generating a more global surface color spreading. The WCI is strongest when the inner and outer contours are spatially contiguous and continuous. The perceived colored surface spreads from these local features, remaining constant across the entirety of the WCI region (Pinna et al., 2001). For example, an orange opaque surface perceived to extend from one inner contour across space to an adjacent inner contour appears phenomenally to be constant. The luminance contrast between the inner and outer contours can directly affect illusion magnitude (Devinck et al., 2005), indicating long-range color spreading is mediated at least in part by luminance-dependent mechanisms.

The WCI has also been shown to be connected to perceptual organization. The illusion shows a unique figure-ground effect somewhat similar to Gestalt cues of figure-ground organization (Pinna, 2005; Pinna et al., 2003; Pinna & Reeves, 2006; von der Heydt & Pierson, 2006). An enclosed WCI region tends to be perceptually organized as a figure; however, this cue is often stronger than many figure-ground cues including grouping, proximity, symmetry, convexity, surroundedness, parallelism, closure, similarity (Pinna, 2005; Pinna et al., 2001; Pinna et al., 2003), good continuation, convexity, amodal completion, and past experience (Pinna et al., 2003). These findings suggest the WCI may manifest differently in different contexts based on the perceptual organization cues presenst in or around the color-spreading region.

Previous research on the WCI has largely focused on how certain stimulus parameters affect illusion magnitude and what mechanisms likely generate the illusion. Research, however, has rarely investigated how more complex stimulus configurations may influence the spatial expanse of WCI color spreading. One such level of complexity that could be studied is dimensionality. We could investigate the impact of more complex stimulus configurations consisting of two- versus three-dimensional-appearing shapes. These stimuli would be more representative of the normal human visual environment and could therefore start an exploration of how the WCI relates to everyday perceptual processes. This is one factor we investigate in the following two experiments.

Another factor that could be studied is enclosedness. Previous research has demonstrated that an unenclosed WCI stimulus will spread color beyond the borders of the stimulus itself until it reaches another border – even if that border is the edge of the page or screen on which the stimulus is being viewed (Pinna, 2005; Pinna et al., 2001). This configuration is not optimal in terms of stimulus strength for the WCI. This results in a weakened color across the entire spreading region – not just the area outside of the stimulus borders. The uniformity of this illusory degradation demonstrates how local stimulus changes (i.e., an unenclosed region) can affect global processing.

We know with an unenclosed WCI stimulus the perception of color will spread relatively far beyond its border. However, a real surface does not “leak” its color into space – regardless of the filling-in mechanism implemented by the visual system to perceive the surface’s color. The FAÇADE model attributes this to the Boundary Contour System (BCS), which is responsible for creating “end-cuts” at the ends of lines (“boundaries”) that stop color from leaking (Grossberg, 2014). Theoretically, if these end-cuts were not created, color would leak into space even in real-world viewing conditions.

Previous research has also demonstrated how global stimulus configuration can influence color spreading in unenclosed stimuli (Hale, 2018; Hale & Brown, 2018). Enclosed WCI stimuli were physically divided and separated into parts, thereby creating unenclosed stimuli. Participants reported similar illusion magnitudes in the enclosed and unenclosed stimuli. However, color did not spread into the empty space between stimulus parts. Perceptual organization cues were reported, including occlusion and illusory color contours that resulted in immediate cessation of color spreading past the fringe end-points. This implies a border may in fact be necessary to stop color spreading, but an illusory border can suffice within the context of global figure-ground organization. The influence of enclosedness is further investigated here.

The following experiments sought to explore how these two factors, dimensionality and enclosedness, impact the spatial expanse of the WCI. Illusion magnitude ratings and pencil shading of stimulus parts were used to determine our participants’ perceptions. Local changes (within the color-spreading region) and global changes (stimulus parts outside the color-spreading region) between various conditions allowed for a systematic exploration of these factors (e.g., dimensionality and enclosedness). Stimuli consisted of images of two- (e.g., square) and three-dimensional (e.g., cube) shapes with the WCI-inducing fringe on one surface. Regardless of dimensionality or the extent of fringe within it, this surface was fully enclosed in some conditions and unenclosed in others.

The purpose of using three-dimensional-appearing configurations was to investigate how color would spread if depth implied a change from one surface to another. If one were observing a real cube-shaped object (e.g., a cardboard box), it would consist of multiple visible surfaces with slight changes in hue and luminance based on a variety of factors including physical color, illumination, and viewpoint. We are arguing that color-spreading illusions like the WCI may be caused (at least in part) by some form of surface completion mechanism. When a color spreading surface is configured to imply color should spread outward freely (e.g., Fig. 1), it does so. When a color-spreading surface is fully enclosed, color spreading is contained inside the physical borders. What happens if we remove a physical border in a three-dimensional configuration? Will the color spread “around the corner”? There are three options. Option 1: the color spreads around corner. This would suggest the depth cue provided by the global (outside the color-spreading region) stimulus contours surrounding the fringe contours does not constrain color spreading from the unenclosed color-spreading surface. This would also suggest local (within the color-spreading region) lower-level perceptual organization processes are not enough to limit color spreading. Option 2: the color does not spread around the corner. This could be due to the depth cue signaling the color-spreading surface ends precisely where the adjoining surface without fringe extends back into space, resulting in immediate cessation of color spreading. Option 3: the color does not spread around the corner; however, instead of global depth cues ceasing the color spreading, it could be due to local factors related to perceptual organization of the color-spreading surface itself. This could be caused by “end-cuts”, as described by Grossberg (2014).

The WCI illusion is phenomenological. It is perceived quickly, consistently, and ubiquitously. As you will see, and as we discuss in detail, the stimuli clearly rule out Option 1. The color does not spread “around the corner” in our three-dimensional-appearing stimuli. Then, how can we determine if Option 2 or Option 3 is correct? We must compare a similar local area (i.e., the unenclosed color-spreading region and the adjoining region with no fringe) without the surrounding global information that implies depth. If the color spreads into the adjoining region with no fringe in this condition, then Option 2 is likely to be correct. However, if it still does not spread into the adjoining region with no fringe, even when the dimensionality cues have been removed, then Option 3 is the best explanation.

Experiment 1

To begin our exploration of how context, namely dimensionality and enclosedness, impact the spatial expanse of the WCI, we created images producing four stimulus conditions: (1) two-dimensional, enclosed; (2) two-dimensional, unenclosed; (3) three-dimensional, enclosed; (4) three-dimensional, unenclosed.

Condition 1 consisted of three basic shapes: a square, a pentagon, and a hexagon. Each shape had a purple outer border and orange inner fringe, thereby turning the shapes into WCI stimuli (see Fig. 2). While a wavy/scalloped fringe would have produced a stronger illusion magnitude, for simplicity of construction and because illusion magnitude per se was not of central concern, we used a straight-edged fringe. For this completely enclosed condition, we expected the color to spread fully inside the shapes with no color leaking outside of them. We also expected this condition to have a reasonably strong illusion magnitude due to its simplicity and similarity to traditional WCI stimuli.

Fig. 2
figure 2

Stimulus versions from all four conditions of Experiment 1. Conditions 2 and 4 had two parts participants were asked to rate (i.e., Region 1 and Region 2). These parts are numbered here for clarity

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Condition 2 stimuli were identical to those in Condition 1, except an adjacent stimulus part was added to one side, thereby creating a new two-dimensional configuration. The new stimulus part had a purple outer border but no orange fringe. The border at which the original shape and this new stimulus part join was removed, resulting in an unenclosed color-spreading region (see Fig. 2). Previous research suggests color spreading continues beyond an unenclosed color-spreading region (Devinck et al., 2005; Pinna, 2011; Pinna et al., 2001; Pinna & Grossberg, 2005; Pinna & Reeves, 2006; Pinna & Reeves, 2015). As such, we might expect color to spread into the new region in Condition 2 (i.e., from the region with fringe (“Region 1”) to the region without fringe (“Region 2”); see Fig. 2) since no physical border exists between these regions. To determine whether participants actually saw stimuli in Condition 2 as two-dimensional, we conducted a pilot study to assess stimulus dimensionality (see Table 1). Using a Likert-type scale ranging from 1 to 7, where “1” was two-dimensional/flat and “7” was three-dimensional/depthful, the average rating for all stimuli was 1.71. This confirmed participants largely saw the stimuli as two-dimensional.

Table 1 Two-dimensional versus three-dimensional rating pilot data for Experiment 1 and 2 stimuli
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Contrary to the assumption that color would spread into Region 2, our phenomenological impression was of strong color spreading in Region 1 and a conspicuous lack of color spreading in Region 2. This could potentially be explained via viewpoint-invariant models of object recognition like the Recognition-By-Components model (Biederman, 1987, 2001). This model suggests object recognition occurs due to the relative configuration of an object’s parts. In Condition 2, an illusory color contour appeared to be present between Region 1 and Region 2. This contour seemed to “belong” to the color-spreading surface and define the separation between the regions. This would suggest the two regions are being perceived as completely separate surfaces. Therefore, the spatial expanse of the color spreading ceases at the border (physical, illusory, or implied) separating the two surfaces. To further test this theory, three-dimensional versions of these two conditions were created.

Condition 3 consisted of three-dimensional versions of the shapes from Condition 1, resulting in a cube, a pentagonal prism, and a hexagonal prism. The fringe was only in the original color-spreading surface, not in any of the new surfaces (see Fig. 2). This is the first study to examine the WCI within the context of stimuli depicting three-dimensional shapes. As with Condition 1, the color-spreading region is completely enclosed. Therefore, we expect the color to spread fully inside this surface with no color leaking outside of it.

Condition 4 merged the three-dimensional shapes used in Condition 3 with the missing border in Condition 2 (see Fig. 2), resulting in unenclosed stimulus configurations of stimuli depicting three-dimensional shapes. In Condition 2, the two adjoining regions were perceived as flat. In the three-dimensional shapes used in Conditions 3 and 4, the adjoining regions have an implied depth. Therefore, it is easier to perceptually organize the regions into separate surfaces. In Condition 3, a physical border separated the color-spreading region from all adjoining regions. In Condition 4, no physical border exists between Region 1 and Region 2. Does color spread into the adjoining region with no fringe? As with Condition 2, our immediate impression was that color does not spread beyond this implied boundary. Instead, an illusory contour seems to separate robust color spreading in Region 1 from a conspicuous absence of color in Region 2. Our phenomenological experiences with these stimuli were striking and consistent. Nevertheless, we needed to confirm these findings in a larger participant sample.

General method

Participants

Thirty participants (i.e., 15 each for Experiments 1 and 2) from the University of Georgia research participant (RP) pool were recruited for this study. All participants had normal or corrected-to-normal vision as verified by acuity and phoria testing, normal color vision as verified by pseudoisochromatic plates, and no history of an attention-deficit disorder. Participants were at least 18 years old at the time of the experiment. All research was conducted in accordance with the Declaration of Helsinki and under the approval of the University of Georgia Institutional Review Board (IRB) ethical guidelines for research involving human participants. All participants received partial course credit as compensation for their participation.

Stimuli and apparatus

Images were presented on a cathode ray tube (CRT) monitor operating at an 85-Hz refresh rate using E-Prime v3 software. Participants viewed the monitor from 172.4 cm creating a visual angle of 8.6° (height) × 12.1° (width) in a room with low illumination from an 11 W “natural daylight” bulb. Responses were recorded using the computer keyboard. A chin-and-forehead rest was used to minimize head movements and fix gaze distance. Images were created using Adobe Photoshop. All stimuli were contained within 6′ of visual angle, and the WCI region (i.e., Region 1; the “front surface” region from Condition 1) subtended an area of 2.40′ of visual angle. Similar to Pinna et al. (2001) and Pinna and Reeves (2006), the outer contour was dark purple (RGB: 165, 80, 226; CIE-L*ab: 50.953, 59.644, -60.371; 25.02 cd/m2) and the inner contour was light orange (RGB: 255, 207, 37; CIE-L*ab: 85.008, 2.615, 80.643; 54.09 cd/m2) to optimize a strong color illusion. All stimuli consisted of a central object or objects on a white (RGB: 255, 255, 255; CIE-L*ab: 100.000, 0.000, -0.000; 59.08 cd/m2) background. A comparison stimulus was used during instructions and prior to each trial (see Fig. 3). The comparison stimulus consisted of two adjoining purple squares located in the center of the screen with fringe inside the square on the right and no fringe inside the square on the left. The numbers “1” and “7” were written under each square, respectively.

Fig. 3
figure 3

Example of a trial sequence. Each trial starts with a blank screen (500 ms) followed by a comparison stimulus (2,000 ms), another blank screen (500 ms), and then the test stimulus, which remained on-screen until a response was entered. This example is from Experiment 1

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Design and procedure

For both experiments participants adapted to the low room lighting for 5 min before beginning the experiment. In this time, the experimenter explained the procedure and asked if the participant had any questions. To determine the perceived spatial extent of color spreading, participants provided feedback through two dependent measures. The first was an illusion magnitude estimation. This measure used a Likert-type scale ranging from 1 to 7 where a response of “1” indicated no color spreading is present, “4” indicated a moderate illusion magnitude, and “7” indicated maximum illusion magnitude. A comparison stimulus was shown at the start of each trial providing an example of a “1” and a “7” on this scale before participants saw a test stimulus and made a response. See Fig. 3 for an example of a trial sequence. Ratings were made using a computer number pad and the “Enter” key to record their response. For conditions with only one rating, pressing “Enter” automatically started the next trial. For conditions with two ratings (e.g., Experiment 1 Condition 4), participants pressed “Enter” to submit their first rating and then pressed “Enter” again to submit their second rating and advance to the next trial. All responses were also visible on the screen (i.e., the first response displayed in red, the second response (if any) displayed in purple). Participants completed three magnitude estimation trials for each stimulus type. The first trial of any stimulus type per condition was treated as a practice trial and removed prior to analyses. Therefore, there were 24 experimental trials in Experiment 1 (i.e., 36 total minus 12 practice) and 42 experimental trials in Experiment 2 (i.e., 63 total minus 21 practice).

The second dependent measure was a handwritten shading task. Following magnitude estimation ratings for each condition, participants were given a printed stimulus card containing a black outline of a single stimulus from that condition (e.g., Condition 1 Version 2). The WCI stimulus was shown on-screen for the duration of the shading task. Participants were told to observe the on-screen stimulus. Then they used a pencil to fill in the stimulus card anywhere they perceived color spreading. This shading process was repeated for all stimulus versions for a given condition. Then the next condition began (i.e., magnitude estimation first followed by the shading task). The purpose of the handwritten shading data was to confirm the perceived spatial expanse of color spreading. In combination with the magnitude estimation data (i.e., the degree to which they saw any WCI), we obtained a clear understanding of where color tended to spread and where it did not. Once all conditions were completed for any given experiment, the experimenter debriefed the participants and answered any questions.

Condition order

For Experiment 1, all participants completed magnitude estimations for Condition 1 first, followed by Conditions 2–4 in a counterbalanced order. Condition 1 was shown first to establish a baseline while participants remained naïve to the existence of three-dimensional conditions or unenclosed conditions. The remaining conditions were counterbalanced to avoid confounding order effects. For Experiment 2, all participants completed magnitude estimations for Condition 1A and 1B first, followed by Conditions 2–6 in a counterbalanced order. Conditions 1A and 1B were shown first to establish a baseline while participants remained naïve to the existence of three-dimensional conditions or unenclosed conditions. The remaining conditions were counterbalanced to avoid confounding order effects. In both experiments, the handwritten shading task was completed following magnitude estimations for a given condition. Stimulus cards for all stimulus versions were given to participants one at a time in a counterbalanced order.

Analyses

Homogeneity of variance was confirmed for magnitude estimation data for all participant groups; Levene’s test of equality of error variances was not violated for any statistical test in either Experiment 1 or Experiment 2, p < 0.005. All pairwise comparisons were collapsed across Version in both experiments. The handwritten shading data from Experiments 1 and 2 were coded to determine the percentage of participants who perceived color spreading across the stimulus. See Figs. 5 and 9 for these data displayed in “heat maps” for Experiments 1 and 2, respectively. Heat maps were created using a conditional formatting grid in Microsoft Excel for the purpose of compiled data visualization.

Experiment 1: Method

Stimuli

Four sets of three stimuli were created for each condition resulting in a total of 12 stimuli for Experiment 1. Condition 1 consisted of pictures of one of three centrally located two-dimensional shapes: a square, a pentagon, and a hexagon. Condition 2 consisted of shapes similar to Condition 1; however, one border from Condition 1 was removed and an adjacent stimulus part was added without fringe. Condition 3 consisted of pictures of three-dimensional versions of the shapes in Condition 1: a cube, a pentagonal prism, and a hexagonal prism. Stimuli for Condition 4 were identical to Condition 3 except one side (including the outer contour and inner fringe) of the surface containing the WCI fringe was removed (similar to Condition 2).

Design and procedure

For all conditions participants reported the illusion magnitude of the interior of the two-dimensional shape or foremost surface of the three-dimensional shape (i.e., Region 1). Conditions 2 and 4 required participants to also report the illusion magnitude in the adjoining region (i.e., Region 2). Brief instructions were provided prior to each condition to ensure the participants understood to which region or regions they were responding. Participants completed the handwritten measures as detailed in the General methods.

Experiment 1: Results and discussion

A 4 (Condition) × 3 (Version) repeated-measures ANOVA was conducted using the Region 1 magnitude estimation data. The purpose of having three different versions was to ensure that our findings were not due to the specific configuration of any one of the shapes. Therefore, we did not expect to find a main effect of Version; however, a main effect of Condition is likely to exist due to the unenclosed conditions (i.e., Conditions 2 and 4) since a border was removed resulting in less illusion-inducing fringe. We found a significant main effect of Condition, F(3,168) = 3.961, p = 0.009, no main effect of Version, F(2,168) = 0.517, p = 0.597, and no significant interaction, F(6,168) = 0.146, p = 0.990 (see Fig. 4). Further analyses were collapsed across version after determining no significant differences exist between versions.

Fig. 4
figure 4

Illusion magnitude data collapsed across Version for Experiment 1 Conditions 1–4. Example stimuli from Version 3 are shown beneath each Condition. Conditions 2 and 4 had two ratings (i.e., Region 1 and Region 2). These parts are numbered here for clarity

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There are two distinct variables that could contribute to our main effect of Condition in the above analyses: Dimensionality (i.e., two- vs. three-dimensional-appearing stimuli) and Enclosedness (i.e., fringe-enclosed color-spreading region vs. unenclosed color-spreading region). A 2 (Dimensionality) × 2 (Enclosedness) repeated-measures factorial ANOVA was conducted to systematically investigate these factors. For Dimensionality, Conditions 1 and 2 were considered two-dimensional, while Conditions 3 and 4 were considered three-dimensional. For Enclosedness, Conditions 1 and 3 were enclosed while Conditions 2 and 4 were unenclosed. We found a significant main effect of Dimensionality, F(1,14) = 6.199, p = 0.026, a nearly significant main effect of Enclosedness, F(1,14) = 4.057, p = 0.064, and a significant interaction between Dimensionality and Enclosedness, F(1,14) = 5.736, p = 0.031. This interaction implies only stimuli that were two-dimensional and enclosed had a significantly higher illusion magnitude. This could be due to dimensionality (i.e., “Option 2” discussed previously), some kind of visual interference caused by additional adjacent spaces (“Option 3”), an anchoring effect due to condition order (see Experiment 1B), or some combination of these factors.

Additional planned pairwise comparisons were computed between conditions. Condition 1 was the two-dimensional baseline for Condition 3 used to determine what impact three-dimensionality had on illusion magnitude. These were both enclosed conditions, but Condition 3 contained additional adjacent spaces to create the three-dimensional shape. Condition 3 illusion magnitude ratings were significantly lower than those for Condition 1, p = 0.004. To interpret this finding, it is important to note that there are two important differences between Condition 1 and 3. As described above, Condition 1 is two-dimensional whereas Condition 3 is three-dimensional. This is one potential cause for the drop in illusion magnitude. The other difference between these conditions, and therefore a potential alternate explanation for the difference in illusion magnitude, is the existence of additional adjacent spaces. The addition of these surrounding contours may impact illusion magnitude due to a perceptual process completely independent of dimensionality. However, as we will see in this experiment and in the following experiment, dimensionality seems unlikely to be the driving factor controlling the spatial expanse of the WCI in our stimuli. Our main focus was to determine where color spreads in a variety of contexts. Perceptual organization factors other than perceived depth seem more likely to impact the spatial expanse of WCI color spreading.

Pairwise comparisons involving our unenclosed conditions found Condition 2 ratings, p = 0.011, and 4, p = 0.004, were statistically lower than Condition 1. Removing this border reduces the amount of illusion inducing fringe, and in these cases, seems to necessitate the perceptual synthesis of an illusory color contour to enclose these color-spreading regions. Similar to Conditions 1 and 3, Conditions 2 and 4 are identical except for the addition of adjacent spaces that change the perception of the stimulus from two-dimensional (Condition 2) to three-dimensional (Condition 4). Condition 2 was not significantly different from Condition 4, p = 0.712, suggesting the addition of adjacent spaces in order to create an impression of three-dimensionality does not impact watercolor illusion magnitude. Finally, Condition 3 was not significantly different from Condition 4. These conditions were identical except for the removal of the border; however, this physical difference between conditions did not generate any significant difference in illusion magnitude between the two conditions, p = 0.977, indicating the removal of some of the inducing fringe does not necessarily reduce illusion magnitude.

To investigate the spatial expanse of color spreading in the WCI in the unenclosed conditions, we needed to look at whether any illusion was reported in Region 2 for both of our unenclosed conditions (i.e., Conditions 2 and 4). If color spreads into the adjoining region, similar illusion magnitude should potentially be reported for both Regions 1 and 2. If color fails to spread into the adjoining region, the illusion magnitude should be statistically different between these regions. A 2 (Condition) × 3 (Version) × 2 (Region) repeated-measures ANOVA found no main effect of Condition, F(1,168) = 0.088, p = 0.768, suggesting dimensionality and the addition of adjacent spaces did not impact the spatial expanse of the WCI in Regions 1 and 2. However, there was a significant main effect of Region, F(1,168) = 228.997, p < 0.001. This and the handwritten shading results indicate participants saw illusory color spreading in Region 1 but not in Region 2 for both conditions. As with previous analyses, no significant main effect of Version was found, and there were no significant interactions between these factors.

Experiment 1B

In Experiment 1, the WCI only spread within Region 1 for all conditions, regardless of dimensionality or enclosedness. This suggests local (inside the color-spreading region) rather than global (stimulus pieces exterior to the color-spreading region) stimulus factors influenced the spatial expanse of WCI color spreading. Illusion magnitude data and handwritten shading data (see Fig. 5) support this conclusion. However, illusion magnitude seemed relatively stable in Region 1 for all conditions except Condition 1, where the illusion was reported to be strongest. It is possible that, because participants all rated Condition 1 first before moving on to future conditions, they were anchored to this condition as a kind of benchmark for future stimuli. To test this possibility, we needed to collect magnitude estimation data for these four conditions in a fully counterbalanced order.

Fig. 5
figure 5

Participants shaded line drawings of each of the stimuli viewed per condition. These data were averaged across individuals for each stimulus, and a conditional formatting grid was used to create these heat maps as an approximated visual display of these data. As indicated by the scale below the heat maps, a darker, more saturated orange correlates with a higher percentage of individuals shading this area. These heat maps are not representative of how hard or light someone shaded, but rather the percentage of individuals who shaded a particular area

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Method

Seventeen participants from the University of North Georgia research participant pool were recruited. Participants had normal or corrected-to-normal visual acuity and normal color vision. Participants were at least 18 years old at the time of the experiment. All research was conducted under the approval of University of North Georgia IRB ethical guidelines for research involving human participants. All participants received partial course credit as compensation for their participation.

Images were presented on a liquid-crystal display (LCD) monitor operating at an 80-Hz refresh rate using E-Prime v3 software. Stimuli and presentation were identical to Experiment 1.

For all conditions, participants reported the illusion magnitude of Region 1. Conditions 2 and 4 required participants to also report the illusion magnitude of Region 2. Conditions 1–4 were presented in a counterbalanced order.

Experiment 1B: Results and discussion

The purpose of this experiment was to determine if the difference in illusion magnitude between Conditions 1 and 3 in Experiment 1 were caused by Condition 1 always being shown first. By counterbalancing all four conditions in Experiment 1B, illusion magnitudes cannot be anchored to Condition 1. A one-way ANOVA comparing Region 1 from all four conditions (collapsed across versions) found no significant difference between our conditions, F(3,16) = 0.974, p = 0.413. Pairwise comparisons between all pairings confirmed these findings, p ≥ 0.152. This suggests illusion magnitude ratings for Experiment 1 were likely higher for Condition 1 than Condition 3 due to condition presentation order.

However, this new counterbalance order did not change the perceived spatial expanse of color spreading in our unenclosed conditions. As with Experiment 1, participants reported significantly higher illusion magnitudes in Region 1 than in Region 2 for Condition 2, t(15) = 13.236, p < 0.001, and Condition 4, t(15) = 14.337, p < 0.001 (see Fig. 6). Together, these findings improve our understanding of the magnitude estimations in this study, and importantly they highlight that condition order does not impact the spatial expanse of the WCI. Our main focus in these experiments was to determine where color spreads in a variety of contexts. Experiment 1B supports Experiment 1’s findings related to the spatial expanse of color spreading.

Fig. 6
figure 6

Illusion magnitude data collapsed across Version for Experiment 1B Conditions 1–4. Example stimuli from Version 3 are shown beneath each Condition. Conditions 2 and 4 had two ratings (i.e., Region 1 and Region 2). These parts are numbered here for clarity

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Experiment 2

In Experiment 2, the impact of dimensionality and enclosedness on WCI color spreading were further explored using stimulus configurations that appeared transparent (rather than opaque as in Experiment 1). Unique local properties in these transparent stimuli created new conditions for probing the influence of enclosedness on the expanse of WCI color spreading. There were seven stimulus conditions. The first (1A) was identical to Experiment 1 Condition 1. The next four were wireframe analogs to the identically numbered conditions in Experiment 1: (1B) two-dimensional, enclosed; (2) two-dimensional, unenclosed; (3) three-dimensional, enclosed; and (4) three-dimensional, unenclosed. The last two were variants of Condition 3 with reduced fringe that stopped at intersecting lines (5) or an arbitrary point past intersecting lines (6).

Condition 1A was identical to Experiment 1 Condition 1 and consisted of three basic shapes: a square, a pentagon, and a hexagon. Each shape had a purple outer border and orange inner fringe, thereby turning the shapes into a WCI stimuli (see Fig. 7). As a fully enclosed condition, we expected the color to spread fully inside the shape with no color leaking outside of the shape. We also expected this condition to have a strong illusion magnitude due to its simplicity and similarity to traditional WCI stimuli.

Fig. 7
figure 7

Stimulus versions from all seven conditions of Experiment 2. Note stimulus names are based on similarity between experiments. Condition 1A is identical to Condition 1 in Experiment 1. Condition 1B is a baseline condition unique to Experiment 2. Conditions 2–4 in both experiments are analogous. Conditions 5 and 6 are unique to Experiment 2. Condition 5 has less fringe that stops at local contour intersections creating a smaller enclosed color-spreading space. Condition 6 extends this fringe past local contour intersections creating a more ambiguous organization. Conditions 2, 4, 5, and 6 had two parts participants were asked to rate (i.e., Region 1 and Region 2 in Conditions 2 and 4; Regions 1A and 1B in Conditions 5 and 6). Each part is numbered here for clarity

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Condition 1B was identical to Condition 1A except they were “transparent.” That is, the contours visible through Region 1 in three-dimensional conditions of this experiment (e.g., Condition 3) due to the wireframe nature of these stimuli are also present in this baseline configuration (see Fig. 7). To determine whether participants actually saw stimuli in Condition 1B as two-dimensional, we conducted a pilot study to assess stimulus dimensionality (see Table 1). Using a Likert-type scale ranging from 1 to 7 where “1” was two-dimensional/flat and “7” was three-dimensional/depthful, the average rating for all stimuli was 3.86. This confirmed participants largely saw the stimuli as more two-dimensional than the three-dimensional stimuli used in later conditions (e.g., Condition 3).

Condition 2 was the wireframe analog of Experiment 1 Condition 2. Stimuli were identical to those in Experiment 1 except the contours visible through Region 1 (and Region 2 when present) in three-dimensional conditions of this experiment (e.g., Condition 3) due to the wireframe nature of these stimuli were also present (see Fig. 7). Dimensionality pilot data for this condition found an average rating of 3.95 out of 7. This confirmed participants largely saw the stimuli as more two-dimensional than the three-dimensional stimuli used in later conditions.

As with Experiment 1, our phenomenological impression was of strong color spreading in Region 1 and a conspicuous lack of color spreading in Region 2. An illusory color contour appeared to be present between Regions 1 and 2 that belonged to the color-spreading surface. The two regions seem to be perceived as completely separate surfaces. For all conditions up to this point, the spatial expanse of the color spreading ceases at the border (physical, illusory, or implied) separating the two surfaces. As with Experiment 1, three-dimensional versions of these conditions were created to further this exploration.

Condition 3 consisted of three-dimensional versions of the shapes from Condition 1B, resulting in a wireframe cube, a pentagonal prism, and a hexagonal prism. This condition is the wireframe analog to Experiment 1 Condition 3. The fringe was only in the original color-spreading surface, not in any of the new surfaces (see Fig. 7). As with Condition 1B, the color-spreading region was fully enclosed.

Condition 4 merged the three-dimensional shapes used in Condition 3 with the missing border in Condition 2 (see Fig. 7) resulting in three-dimensional, unenclosed stimuli. This condition is the wireframe analog to Experiment 1 Condition 4. In Condition 2, the two adjoining regions were perceived as relatively flat. In the three-dimensional shapes used in Conditions 3 and 4, the adjoining regions have an implied depth. Therefore, it is easier to perceptually organize the regions into separate surfaces. In Condition 3, a physical border separated the color-spreading region from adjoining regions. In Condition 4, no physical border exists between Regions 1 and 2. As with Condition 2 (and the unenclosed conditions in Experiment 1), our immediate impression was that color does not spread beyond this implied boundary. Instead, an illusory contour seems to separate robust color spreading in Region 1 from a conspicuous absence of color in Region 2.

In all of the conditions up to this point, the illusory color was expected to traverse a plane in space perceived to be the foremost surface of an object. In other words, it is more likely that an observer may perceive the hexagonal prism (Version 3) from Condition 3 as a wireframe object with a transparent orange front surface than as a wireframe object with no front surface and four partial orange surfaces. Both of these organizations are possible. However, the first is more parsimonious. Therefore, the visual information is perceptually organized in this way. In fact, this perception is so preferable it is nearly impossible to perceive the stimulus as four orange regions all approaching intersecting contours instead of one continuous orange surface in front of these other contours. This is not to say that these objects themselves are not reversible. The wireframe cube (Condition 3, Version 1) is a bistable Necker cube with an orange front surface (Kornmeier & Bach, 2005). With minimal effort, this impression can be switched to an upward-facing Necker cube with an orange back surface. However the strong figurality commonly associated with the WCI is able to keep this reversibility to a minimum in favor of the WCI region in the foreground (e.g., Pinna, 2005).Footnote 1

Another factor contributing to an orange front surface being the preferred interpretation was the amount of orange fringe inside of Region 1. In Condition 5 we reduced the amount of orange fringe further from the unenclosed wireframe objects in Condition 4 so it stopped whenever it reached an intersecting contour. This divided Region 1 into Region 1A (i.e., the fringed region) and Region 1B (i.e., the non-fringed region; see Fig. 7). Based on past literature, this fringe reduction should reduce illusion magnitude across the entirety of Region 1 if participants continue to perceive this region as a colored transparent surface as in Condition 4. However, we noticed Region 1A appeared to fill with illusory color while the rest of Region 1 (i.e., 1B) remained a simple wireframe with no color spreading. This indicates a reduction or elimination of the illusion in 1B while still being visible in 1A. From the perspective of local processing, the color does not appear to spread past the contours that enclose Region 1A because the fringe does not extend past this region. This local processing may then affect the more global perception of the object described above.

More information was likely necessary for the color to spread beyond the enclosed 1A region. Condition 6 was identical to Condition 5, except we extended the fringe 0.5° of visual angle in both directions to an arbitrary stopping point inside Region 1 (see Fig. 7). Now that the fringe extends further into Region 1 beyond the intersecting contours, we expected color would spread into all of Region 1 resulting in color spreading similar to Conditions 3 and 4. However, this is not what happened. Instead, Region 1 appeared to divide into two parts separated by an illusory color contour exactly at the end-cuts where the fringe terminated.

Altogether, this experiment explored a more complex assortment of stimulus configurations with many variations in dimensionality and enclosedness. The wireframe configurations were compared to their opaque analogs from Experiment 1 to determine how this manipulation affected the spatial extent of WCI color spreading. As with Experiment 1, our phenomenological experiences with these stimuli were striking and consistent. Nevertheless, we needed to confirm these findings in a larger participant sample.

Experiment 2: Method

Stimuli

Seven sets of three stimuli were created for Conditions 1A, 1B, and 3–6. Stimuli for Condition 1A were identical to Experiment 1 Condition 1. Condition 1B consisted of the same pictures of two-dimensional shapes as Condition 1A with the addition of any contours present within these shapes (i.e., Region 1) in the three-dimensional wireframe versions (e.g., Condition 3). Condition 2 consisted of Regions 1 and 2 and the additional contours described in Condition 1B (i.e., those that were visible in the shape in the three-dimensional version). Condition 3 consisted of three-dimensional wireframe versions of the stimuli from Condition 1B with fringe in only the foremost surface (i.e., cube, pentagonal prism, hexagonal prism). Stimuli for Condition 4 were identical to Condition 3, except one side (including the outer contour and inner fringe) of the surface containing the WCI fringe was removed. Stimuli for Condition 5 were identical to Condition 3, except the fringe only extended to the points at which it crosses an intersecting contour now visible due to the wireframe configuration. Condition 6 was identical to Condition 5, except the fringe extended 0.50° of visual angle into Region 1B.

Design and procedure

The design and procedure were identical to Experiment 1. For Conditions 5 and 6, the two ratings recorded were for Regions 1A and 1B (rather than Regions 1 and 2).

Results and discussion

A 7 (Condition) × 3 (Version) repeated-measures ANOVA was conducted using the Region 1 magnitude estimation data only. As in Experiment 1, the purpose of having three different shapes was to ensure our findings were not due to the specific configuration of any one of them, and, so, a main effect of Version was not expected. A main effect of Condition was expected due to the anticipated weakening of the WCI in the unenclosed conditions (i.e., Conditions 2 and 4) and when a partial fringe exists (i.e., Conditions 5 and 6). Condition 1A should also be different than the remaining conditions since it was the only non-transparent condition. We found a significant main effect of Condition, F(6,294) = 4.909, p < 0.001, no main effect of Version, F(2,294) = 0.199, p = 0.820, and no significant interaction, F(12,168) = 0.523, p = 0.900 (see Fig. 8).

Fig. 8
figure 8

Illusion magnitude data collapsed across Version for Experiment 2. Conditions 2, 4, 5, and 6 had two ratings (i.e., Region 1 and Region 2 in Conditions 2 and 4; Regions 1A and 1B in Conditions 5 and 6). Example stimuli using Version 3 are shown beneath each Condition

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As with Experiment 1, there are two distinct variables that might contribute to our main effect of Condition in the above analyses: Dimensionality (i.e., two- vs. three-dimensional-appearing stimuli) and Enclosedness (i.e., fringe-enclosed color-spreading region vs. unenclosed color-spreading region). A 2 (Dimensionality) × 2 (Enclosedness) repeated-measures factorial ANOVA was conducted to systematically investigate these factors. For Dimensionality, Conditions 1B and 2 were considered two-dimensional while Conditions 3 and 4 were considered three-dimensional. For Enclosedness, Conditions 1B and 3 were enclosed while Conditions 2 and 4 were unenclosed. The illusion magnitude ratings were similar for conditions 1B–4. As such, no main effect of Dimensionality, F(1,14) = 0.503, p = 0.490, or Enclosedness, F(1,14) = 0.787, p = 0.390, was found. Additionally, there was not a significant interaction between Dimensionality and Enclosedness, F(1,14) = 0.513, p = 0.486.

There were additional planned pairwise comparisons between conditions. Condition 1B was not significantly different from Condition 3, p = 0.248. The surrounding three-dimensional structure did not alter the illusion magnitude. The same was also true for Condition 4 compared to its baseline condition (i.e., Condition 2), p = 0.869. Interestingly, there were no statistically different pairwise comparisons between any combination of Conditions 3–6, p ≥ 0.210, indicating no differences in color appearance existed between these conditions despite the removal of one border in Condition 4 or the reduction in fringe in Conditions 5 and 6.

The relative difference in illusion magnitude between Regions 1 and 2 in Conditions 2 and 4 is also informative in regard to how this illusion spreads in unenclosed spaces. Remember, how saturated the WCI color appeared (i.e., illusion magnitude) was not the main concern for this study, rather the presence of color or not was used to indicate, in conjunction with the heat maps, where color was perceived, indicating the extent of color spreading. Therefore, a 2 (Condition) × 3 (Version) × 2 (Region) repeated-measures ANOVA was conducted. A main effect of Condition was not found, F(1,168) = 0.032, p = 0.858, suggesting participants had a similar visual experience for two-dimensional (i.e., Condition 2) and three-dimensional (i.e., Condition 4) configurations for Regions 1 and 2. This is confirmed by the statistically significant main effect of Region, F(1,168) = 426.504, p < 0.001, and is consistent with our findings from Experiment 1. As predicted, there was not a significant main effect of Version, and there were no significant interactions between these three factors.

Additionally, a 2 (Condition) × 3 (Version) × 2 (Region) repeated-measures ANOVA was conducted to compare Regions 1A and 1B in Conditions 5 and 6. We found a significant main effect of Region, F(1,168) = 335.054, p = < 0.001, indicating that color failed to spread from Region 1A to Region 1B in either condition. There was no main effect of Version, and interactions were not significant.

Conditions 1/1A of Experiments 1 and 2 were identical in order to have a baseline comparison between these two groups of participants. Conditions 1–4 from Experiment 1 and Conditions 1B, 2, 3, and 4 from Experiment 2 were identical except for the perceived opaque versus wireframe configurations. Therefore a 2 (Experiment) × 4 (Condition) × 3 (Version) mixed-subjects ANOVA was conducted to analyze the differences between these two experiments. We hypothesized a main effect of Experiment due to the solid nature of the illusion in Experiment 1 compared to the veil-like color spreading with the wireframe versions in Experiment 2. As the Conditions and Versions are essentially the same for these experiments, we expected to find a main effect of Condition and no main effect of Version. Interestingly, despite the differences between these two experiments, no main effect of Experiment was found, F(1,336) = 2.241, p = 0.135. As predicted, there was a main effect of Condition, F(3,336) = 4.132, p = 0.007, and no main effect of Version, F(1,336) = 0.696, p = 0.499. There were no significant interactions between these factors. Independent-samples t-tests confirmed participants were not statistically different in their magnitude estimation ratings when comparing Conditions 1 and 1A between experiments, t(28) = 0.071, p = 0.262, Condition 2 between experiments, t(28) = 0.379, p = 0.708, Condition 3 between experiments, t(28) = -0.912, p = 0.377, or Condition 4 between experiments, t(28) = -0.459, p = 0.653. However, participants were statistically different in their magnitude estimation ratings when comparing Conditions 1A and 1B within Experiment 2, t(14) = 2.743, p = 0.016.

An exploration of the findings from Experiment 2 supports our hypothesis that additional parts/contours within (local) and around (global) the color-spreading region and perhaps implied three-dimensionality can negatively impact illusion magnitude. As with Experiment 1, color does not spread into a second region when there is a simple way to perceptually organize the surface into two distinct surfaces. This is most interesting in Condition 6. The fringe in this condition stops at an arbitrary end-cut along the inside of the front surface of each object. Nevertheless, color does not spread past the fringe. Most participants still reported a distinct stopping point for the observed color spreading between Regions 1A and 1B as can be seen in the shading heat maps (see Fig. 9). The fact that all of the stimuli used for Experiments 1 and 2 use straight contours and basic shapes may lend itself to easier perceptual dissection (i.e., perceptually organizing a surface into more than one distinct surface). A straight contour can be drawn between the end-cuts of the fringe in Condition 6 to create two parts that fit together side-by-side, thus creating a multipart front surface of each object. The two surfaces are on the same plane, but they were distinctly individual. Therefore, the color logically would not spread into the neighboring region. This seems to be true for all “unenclosed” conditions in these experiments, including those without a border (i.e., Conditions 2 and 4 in Experiments 1 and 2) and those with reduced fringe (i.e., Conditions 5 and 6 in Experiment 2). Participants primarily observed color spreading in the original color-spreading region only (see Figs. 5 and 9). This differs from an unenclosed serpentine WCI stimulus (e.g., Fig. 1) simply due to the configural nature of the stimuli. Therefore, these experiments support our hypothesis that context can impact the spatial expanse of WCI color spreading.

Fig. 9
figure 9

Participants shaded line drawings of each of the stimuli viewed per condition. These data were averaged across individuals for each stimulus, and a conditional formatting grid was used to create these heat maps as an approximated visual display of these data. As indicated by the scale below the heat maps, a darker, more saturated orange correlates with a higher percentage of individuals shading this area. These heat maps are not representative of how hard or light someone shaded, but rather the percentage of individuals who shaded a particular area

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General discussion

Experiments 1 and 2 explored how the factors of dimensionality and enclosedness impact the spatial expanse of the WCI. Local changes (within the color-spreading region) and global changes (stimulus parts outside the color-spreading region) between various conditions allowed for a systematic investigation of these factors. Stimuli consisted of images of two- (e.g., square) and three-dimensional shapes (e.g., cube) with the WCI on one surface. Regardless of dimensionality, this surface was fully enclosed in some conditions and unenclosed in others. By manipulating these local and global contexts we were able to test a simple question: does color always spread outward from unenclosed WCI stimuli? Based on the results of these two experiments, the answer is clearly no.

The purpose of using three-dimensional configurations was to investigate how color would spread if depth implied a change from one surface to another. If one were observing a cube-shaped object in the real world such as a cardboard box, it would consist of multiple visible surfaces with slight changes in hue and luminance based on a variety of factors including physical color, illumination, and viewpoint. We are arguing that color spreading illusions like the WCI may be caused (at least in part) by some form of surface completion mechanism. When a color spreading surface is configured to imply color should spread outward freely (e.g., Fig. 1), it does so. When a color-spreading surface is fully enclosed (e.g., Experiment 1 Conditions 1 and 3), color spreading is contained inside the physical borders. We explored what happens if a physical border in a three-dimensional configuration is removed, creating an unenclosed color spreading surface (e.g., Experiment 1 Condition 4). Would the color spread around the corner into adjoining regions as proposed in the first of three options we considered (detailed previously)? Based on phenomenological observation and the results of both experiments, the answer is no, ruling out Option 1. Finding color did not spread around a corner into adjoining regions it was possible the global depth cue signaling the surface ends precisely where the adjoining surface extends back into space was responsible (i.e., Option 2). Another possibility was that instead of global depth cues constraining the color spreading, it could be due to local (i.e., inside the color-spreading region) factors related to perceptual organization of a single surface (i.e., Option 3). This could be caused by “end-cuts” as described by Grossberg (2014) in conjunction with other low-level factors related to perceptual organization.

To determine which possibility (Option 2 vs. 3) was the best account for why color did not spread around the corner we compared a similar local area (i.e., the fringe-surrounding color-spreading region and the adjoining open region with no fringe) without the surrounding global information (i.e., Experiment 1 Condition 2). By removing the surrounding contours, the image loses its impression of depth (or it is greatly reduced; see Table 1). If this global depth information were constraining the spread of color around the corner, then when removed the color should spread freely, but this was not the case. As can be seen phenomenologically and echoed by our participants’ illusion magnitude and handwritten shading responses, the color does not spread around the corner in our three-dimensional unenclosed configurations. This suggests local factors related to perceptual organization involving the fringe “end-cuts” within the color-spreading region are causing the cessation of color spreading (i.e., Option 3 is correct).

Experiment 2 had three objectives. First was to test our conclusion stated above related to Option 3. We did this by providing additional depth cues by using wireframe versions with more contours contributing to the perception of depth relative to two-dimensional controls. Second, given these wireframe configurations, we wanted to know how color spreading might be affected when physical borders are seen within the color-spreading surface. Unlike the opaque-appearing stimuli of Experiment 1, transparent stimuli would require color to spread across local (i.e., internal) contours within the color-spreading surface while the perceived three-dimensionality of the stimuli indicated these contours did not belong to that surface. Finally, considering the evidence from Experiment 1 that local factors related to perceptual organization involving the fringe “end-cuts” within the color-spreading region can constrain color spreading, would color spread to the rest of the front surface if the fringe ended at another physical contour (Condition 5) or at an arbitrary point inside the front surface (Condition 6).

The results echoed those found in Experiment 1. Depthfulness does not seem to impact the spatial expanse of the WCI with these stimuli. From the final two conditions, we found that not only does color spreading limit itself to a smaller, but still enclosed, region (Condition 5), it also confines itself in an arbitrary configuration based only on the end-points of the fringe (Condition 6). It does this by creating an illusory color contour, similar to the contour formed in Experiment 1 Condition 4 (and other unenclosed conditions) when a single contour was removed. This suggests the WCI does require enclosure to stop color spreading, but that an illusory contour is sufficient as part of that enclosure (also see Hale, 2018; Hale & Brown, 2018).

Together, these findings help us better understand the nature of the WCI and how it interacts with a variety of local and global contextual factors. Local and global factors like dimensionality and enclosedness can impact the WCI magnitude. However, the spatial expanse of color spreading in the WCI is limited by local perceptual organization factors. These are some of the first experiments to explore the impact of changes to local and global context on the spatial expanse of the WCI.