Scintillating Starbursts: Concentric Star Polygons Induce Illusory Ray Patterns

Abstract

Here, we introduce and explore Scintillating Starbursts, a stimulus type made up of concentric star polygons that induce illusory scintillating rays or beams. We test experimentally which factors, such as contrast and number of vertices, modulate how observers experience this stimulus class. We explain how the illusion arises from the interplay of known visual processes, specifically central versus peripheral vision, and interpret the phenomenology evoked by these patterns. We discuss how Starbursts differ from similar and related visual illusions such as illusory contours, grid illusions such as the pincushion grid illusion as well as moiré patterns.

Keywords: Gestalt; illusion; illusory contours; moiré pattern; pincushion grid illusion; scintillating grid; unconscious inference.

Figure 1.

The Scintillating Starburst stimulus. This stimulus is made up of several star polygons with faces that bisect each other (see the Method section for details). Most observers perceive fleeting rays, beams, or lines emanating from the center that appear to be brighter than the background.

Figure 2.

Starbursts and their FT. A: {10/2} Scintillating Starburst. The 10 perceptual rays match the components of the FT in B. C: {12/2} Scintillating Starburst. The 12 perceptual rays match the components of the FT in D. E: {14/2} Scintillating Starburst. The 14 perceptual rays match the components of the FT in F. G: {16/2} Scintillating Starburst. The 16 perceptual rays match the components of the FT in H. {p/q} denotes Schläfli notation, where p is the number of vertices and q is the turning number (Coxeter, 1974, p. 14).

Figure 3.

FT of Starbursts and seemingly similar phenomena. A: A Scintillating Starburst stimulus with associated FT in B. C: Phantom bands of a Motokawa grid with associated FT in D. E: The Pincushion grid illusion with associated FT in F. G: The Hermann grid with associated FT in H. I: A scintillating grid with associated FT in J. K: A radial scintillating grid with associate FT in L.

Figure 4.

An illustration of how the Scintillating Starburst stimulus was constructed. Top row: nonbisecting stimuli, bottom row: bisecting stimuli. A: A single polygon—here, a heptagon, which we call a strand. B: Two heptagons with faces that bisect each other to form a {14/2} star polygon known as a tetradecagram, which we call a braid. C: Two concentric nonbisecting strands. D: Two braids scaled so they just touch, making up one wreath. E: Two concentric nonbisecting pairs of strands. F: Two concentric wreaths. G: Three concentric nonbisecting pairs of strands. H: Three concentric wreaths. This stimulus corresponds to the Scintillating Starburst stimulus shown in Figure 1, but on a white background and smaller.

Figure 5.

A representative sample of 20 out of the 162 stimuli used in this study. Pictograms of the stimuli are arranged in increasing order of average ray strength reported by our sample of observers. Top rows: weak ray strengths. These rows are predominantly made up of triangular polygons, low-contrast stimuli, and nonbisecting stimuli. Second to last row: stimuli with moderate experienced ray strength—predominantly bisecting pentagons. Bottom row: These five stimuli evoked the strongest ray experiences. These stimuli consist of high-contrast bisecting heptagons with several wreaths. This stimulus is made up of several interlocking polygons that bisect each other’s faces (see the Method section for details). Most observers perceive fleeting rays, beams, or lines emanating from the center that appear to be brighter than the background. The label above each icon indicates the level of the independent variable, in order (number of vertices per polygon, contrast, line width, number of wreaths, and whether the polygon faces bisect each other). The RS value below each icon denotes the average experienced ray strength.

Figure 6.

Means plot of main effects of the repeated measures ANOVA from Table 1. Each panel corresponds to a different independent variable (levels are on the x axis), whereas the y axis represents the average experienced ray strength (RS) reported by our observers.

Figure 7.

Two-way interaction plots between all independent variables used in the repeated measures ANOVA. Each panel corresponds to a different independent variable (levels are on the x axis), whereas the y axis represents the average experienced ray strength (RS) reported by our observers. Each line corresponds to a different level of the second independent variable, as detailed in the legends.

Figure 8.

Ray strength responses evoked by all 162 stimuli in our set, arranged by increasing average ray strengths. The label above each histogram denotes the combination of independent variable levels that corresponds to the stimulus, as in Figure 3. The bars represent the response histogram evoked by each stimulus. The modal response is colored in terms of the following color code: blue: no rays, green: maybe rays, yellow: subtle rays, orange: clear rays, red: striking rays.

Figure 9.

The suggested mechanism underlying the Scintillating Starburst effect. A: A Starburst made up of four concentric wreaths at high contrast. B: A low-passed version of this stimulus. As you can see, there are islands of relative brightness where the faces bisect. C: A version of the stimulus in A where the braids are made up of polygons at half-contrast. Only the bisection spots—where the polygons sum—are at full contrast. D: A low-pass filtered version of the stimulus in C. Note that there are no net bright spots in this blurry version, as the full contrast bisections blend in with the rest of the stimulus. E: This is the stimulus in C subtracted from the stimulus in A, akin to Movshon et al. (2003). As you can see, bright features emerge in this subtractive version. This stimulus appears to have even stronger rays, likely because the aligned bisection points are luminance-defined and objectively brighter than their surroundings, much like in a moiré pattern.