A review of the footsteps illusion
(movies and figures)

Akiyoshi Kitaoka
College of Comprehensive Psychology, Ritsumeikan University, Ibaraki, Osaka, Japan

Stuart Anstis
Department of Psychology, University of California, San Diego, CA, USA

<You can download the file by clicking on the image.>

since May 6, 2020


Movie 1. A demonstration of the footsteps illusion. Blue or yellow rectangles (20 pixels wide) move horizontally back and forth at a constant speed (1 pixel per each 30 ms) across a vertical grating made up of black and white stripes (10 pixels wide for each stripe), but they appear to move fast or slow like a footsteps motion.


Movie 2. A demonstration of the achromatic version of the footsteps illusion. Dark-gray (R: 77,G: 77, B: 77) or light-gray (R: 230, G: 230, B: 230) rectangles (20 pixels wide) move horizontally back and forth at a constant speed (1 pixel per each 30 ms) across a vertical grating of black and white stripes (10 pixels wide for each stripe), but they appear to move fast or slow like a footsteps motion.


Movie 3. A demonstration of the achromatic version of the footsteps illusion. black and white rectangles (20 pixels wide) move horizontally back and forth at a constant speed (1 pixel per each 30 ms) across a vertical grating of dark-gray (R: 77,G: 77, B: 77) or light-gray (R: 230, G: 230, B: 230) stripes (10 pixels wide for each stripe), but they appear to move fast or slow like a footsteps motion.


Movie 4. A demonstration of the inchworm illusion. Blue or yellow rectangles (30 pixels wide) move horizontally back and forth at a constant speed (1 pixel / 30 ms) in front of a vertical grating of black and white stripes (10 pixels wide for each stripe), but they appear to expand and contract as they move.


Movie 5. A demonstration of the inverted foostep illusion proposed by Howe et al. (2006). Blue or yellow rectangles (20 pixels wide) are stationary and a grating of black and white stripes (10 pixels wide for each stripe) moves rightward at a constant speed (1 pixel / 30 ms) behind the rectangles. Even if observers fixate at the stationary cross, a footsteps-like motion that resembles the footsteps illusion is observed.


Movie 6. A demonstration of the footsteps illusion based upon the difference in edge contrast. Blue or yellow rectangles (20 pixels wide) move horizontally back and forth at a constant speed (1 pixel / 30 ms) across a grating of black and white stripes (90 pixels wide). Black and white stripes are flipped over Every 300 ms. At that moment, their position moves by 10 pixels so that each rectangle moves in the middle of a stripe and the edges of a rectangle do not touch or step over borders of stripes. A weak footsteps motion is observed.


Movie 7. A demonstration of the footsteps illusion at a low speed. Blue or yellow rectangles move at a constant speed (1 pixel / 300 ms). When moving edges are of low contrast, the motion appears to be slow down or to be captured by the stationary stripes (position capture).


Movie 8. A demonstration of the inverted footsteps illusion at a low speed. The grating moves rightward at a constant speed (1 pixel / 300 ms). When the edges of a rectangle are of low contrast, the rectangle appears to be captured by the moving grating and appears to move with it (motion capture).


Movie 9. A demonstration of the belly dancer illusion. Columns of blue or yellow squares (20 pixels wide) that are aligned straightforwardly move horizontally back and forth at a constant speed (1 pixel / 30 ms) across a grating of black and white stripes (10 pixels wide for each stripe). Each column appears to undulate as it traverses the striped background.


Movie 10. A demonstration of the special case of the footsteps illusion. Black or white rectangles (20 pixels wide) move horizontally back and forth at a constant speed (1 pixel / 30 ms) in front of a grating of black and white stripes (10 pixels wide for each stripe). They appear to move fast or slow like a footsteps motion. Besides the involvement of the geometrical illusion, this perception is explained with position capture due to the lack of motion signals where ‘moving’ edges do not exist physically.


Movie 11. A demonstration of the inverted variant of the special case of the footsteps illusion. Black or white rectangles are stationary and the grating moves rightward at a constant speed (1 pixel / 30 ms) behind the rectangles. Even if observers fixate on the stationary cross, a footsteps motion is observed. Besides the involvement of the geometrical illusion, this perception is explained with motion capture due to the lack of motion signals where ‘stationary’ edges of rectangles do not exist physically.


Movie 12. A demonstration of another footsteps illusion presented by Howe et al. (2006). Blue or yellow rectangles (10 pixels height and 30 pixels wide) move horizontally back and forth at a constant speed (1 pixel / 30 ms) on black or white stripes. These stripes are flipped over every 300 ms. The rectangles appear to move fast or slow like a footsteps motion synchronously with the change of stripes.


Movie 13. A demonstration of the enhanced version of the horizontally elongated variant. Blocks of blue or yellow rectangles (5 pixels height and 60 pixels wide for each rectangle) move horizontally back and forth at a constant speed (3 pixels / 30 ms) across a checkerboard pattern or along rows of black or white rectangles (5 pixels height and 30 pixels wide for each rectangle). When moving edges are of low contrast (blue vs. black or yellow vs. white), they appear to move behind those of high contrast or to be captured there (position capture).


Movie 14. A demonstration of the inverted variant of the enhanced version of the horizontally elongated footsteps illusion. Blocks of blue or yellow rectangles (5 pixels height and 60 pixels wide for each rectangle) are stationary and the checkerboard pattern of black or white rectangles (5 pixels height and 30 pixels wide for each rectangle) move rightward at a constant speed (3 pixels / 30 ms). When the lateral edges of rectangles are of low contrast (blue vs. black or yellow vs. white), they appear to move slowly or to be captured by the moving checkerboard and move with it (motion capture).


Movie 15. A demonstration of the enhanced version of the horizontally elongated variant at a low speed (3 pixels / 300 ms). Position capture is clearly observed.


Movie 16. A demonstration of the inverted variant of the enhanced version of the horizontally elongated footsteps illusion at a low speed (3 pixels / 300 ms). Motion capture is observed.


Movie 17. A demonstration of the rail-track variant of the footsteps illusion. Each of blue or yellow rectangles (60 pixels high x 20 pixels wide) moves laterally back and forth at a constant speed (1 pixel / 30 ms) across a grating of black and white rectangles (60 pixels high x 10 pixels wide for each rectangle). The top and bottom of the moving rectangles are aligned with those of the grating. A strong footsteps motion comparable to the original footsteps illusion is observed.


Movie 18. A demonstration of the clearing-in-a-forest variant. Each of blue or yellow rectangles (60 pixels high x 20 pixels wide) moves horizontally back and forth at a constant speed (1 pixel / 30 ms) across a white or black gap between gratings of black and white rectangles (60 pixels high x 10 pixels wide for each rectangle). Little or no footsteps illusion is observed.


Movie 19. A demonstration of the color-based footsteps illusion. Magenta (R: 245, G: 0, B: 255) or cyan (R: 0, G: 150, B: 255) rectangles (20 pixels wide) move horizontally back and forth at a constant speed (1 pixel / 30 ms) across a grating made up of red (R: 255, G: 0, B: 0) and green (R: 0, G: 170, B: 0) stripes (10 pixels wide for each). The rectangles appear to move fast or slow like a footsteps motion.


Movie 20. A demonstration of the inverted variant of the color-based footsteps illusion. Magenta or cyan rectangles are stationary and a grating of red and green stripes moves rightward at a constant speed (1 pixel / 30 ms) behind the rectangles. Even if observers fixate on the stationary cross, a footsteps-like appearance is observed.


Movie 21. A demonstration of the contrast-modulated footsteps illusion. The pattern of random dots (1 x 1 pixel for each dot) is stationary all over the period, while luminance contrast is modulated. The background grating consists of high-contrast and low-contrast stripes (30 pixels wide for each stripe). Moving objects are high-contrast or low-contrast squares (60 x 60 pixels). The contrast of the high-contrast stripes (0 vs. 255 in a 256-level grayscale) is higher than that of the high-contrast squares (63 vs. 249), whereas the contrast of the low-contrast stripes (179 vs. 196) is lower than that of the low-contrast squares (160 vs. 211). Squares move horizontally back and forth at a constant speed (3 pixel / 60 ms) across the stripes. Squares appear to move fast or slow like a footsteps motion. Note that the difference in contrast between the high-contrast stripes and the high-contrast squares are so small that some displays cannot properly demonstrate this illusion because of clipping.


Movie 22. A demonstration of the inverted variant of the contrast-modulated footsteps illusion. The contrast-defined squares and the pattern of random dots are stationary and the contrast-defined stripes move rightward at a constant speed (3 pixel / 60 ms) behind the squares. Squares do not appear to show a footsteps motion or appear to display a weak one at best.


Movie 23. A demonstration of the offset-based footsteps illusion. Rectangular blocks made up of four thin line segments (1 pixel high x 60 pixels wide for each line segment; 20 pixels apart) move horizontally back and forth at a constant speed (3 pixels / 60 ms) in front of abutting gratings (30 pixels wide). The lateral edges of the blocks are subjective contours with a large offset or a small one. The blocks appear to move fast or slow like a footsteps motion.


Movie 24. A demonstration of the inverted variant of the offset-based footsteps illusion. Blocks are stationary and abutting gratings move rightward at a constant speed (3 pixels / 60 ms) behind the blocks. Even if observers fixate at the stationary cross, a footsteps-like appearance is observed.


Movie 25. A demonstration of the kickback illusion. Blue or yellow rectangles (20 pixels wide) move horizontally back and forth at a constant speed (1 pixel / 30 ms) in front of a grating made up of white or black pinstripes (2 pixels wide for each pinstripe; inter-pinstripe spacing: 20 pixels) on black or white backgrounds, respectively. Rectangles appear to jump backward when their edges pass over pinstripes.


Movie 26. A demonstration of the kickback illusion to show that this illusion independently occurs at both the leading and trailing edges. Blue or yellow rectangles (30 pixels wide) move horizontally back and forth at a constant speed (1 pixel / 100 ms) in front of a grating made up of white or black pinstripes (2 pixels wide for each pinstripe; inter-pinstripe spacing: 20 pixels) on black or white backgrounds, respectively. The leading/trailing edge of a rectangle appears to jump backward when it covers/uncovers a pinstripe.


Movie 27. A demonstration of the kickback illusion at a low speed. Blue or yellow rectangles move horizontally at a constant speed (1 pixel / 100 ms) in front of a grating of pinstripes. Rectangles appear to jump backward when their edges pass over pinstripes.


Movie 28. A demonstration of the kick-forward illusion. Black or white rectangles (20 pixels wide) move horizontally back and forth at a constant speed (1 pixel / 30 ms) in front of a grating made up of white or black pinstripes (2 pixels wide for each pinstripe; inter-pinstripe spacing: 20 pixels) on blue or yellow backgrounds, respectively. The rectangles appear to speed up when their edges pass over pinstripes.


Movie 29. A demonstration of the kick-forward illusion at a low speed. Blue or yellow rectangles move horizontally at a constant speed (1 pixel / 100 ms) in front of a grating of pinstripes. The rectangles appear to speed up when their edges pass over pinstripes.


Movie 30. A demonstration of the inverted variant of the kickback illusion. Blue or yellow rectangles (20 pixels wide) are stationary and a grating made up of white or black pinstripes (2 pixels wide for each pinstripe; inter-pinstripe spacing: 20 pixels) on black or white backgrounds, respectively, move rightward at a constant speed (1 pixel / 30 ms). The rectangles appear to jump in the same direction as the moving grating.


Movie 31. A demonstration of the inverted variant of the kick-forward illusion. Black or white rectangles (20 pixels wide) are stationary and a grating made up of white or black pinstripes (2 pixels wide for each pinstripe; inter-pinstripe spacing: 20 pixels) on blue or yellow backgrounds, respectively, moves rightward at a constant speed (1 pixel / 30 ms) behind the rectangles. The rectangles appear to jump in the opposite direction from the moving grating.


Movie 32. A demonstration of the luminance-change-dependent motion illusion underlying the ‘kick’ part of the kickback illusion, the kick-forward one, and their inverted variants. Circles appear to expand or contract when their circumference contours appear or disappear, though each circle does not change in size.


Movie 33. A demonstration of the driving-on-a-bumpy-road illusion. Blue or yellow rectangles (20 pixels wide) move horizontally back and forth at a constant speed (1 pixel / 60 ms) in front of a grating made up of black or white pinstripes (2 pixels wide for each pinstripe; inter-pinstripe spacing: 20 pixels) on white or black backgrounds, respectively. Rectangles appear to slow down when their edges pass over them.


Movie 34. A demonstration of the inverted variant of the driving-on-a-bumpy-road illusion. Blue or yellow rectangles (20 pixels wide) are stationary and a grating made up of black or white pinstripes (2 pixels wide for each pinstripe; inter-pinstripe spacing: 20 pixels) on white or black backgrounds, respectively, move rightward at a constant speed (1 pixel / 50 ms) behind the rectangles. The rectangles appear to be captured by the moving grating and move with it when pinstripes pass under their edges.


Movie 35. Another demonstration of the driving-on-a-bumpy-road illusion. Black or white rectangles (20 pixels wide) move horizontally back and forth at a constant speed (1 pixel / 60 ms) in front of a grating made up of blue or yellow pinstripes (2 pixels wide for each pinstripe; inter-pinstripe spacing: 20 pixels) on white or black backgrounds, respectively. Rectangles appear to slow down when their edges pass over them.


Movie 36. Another demonstration of the inverted variant of the driving-on-a-bumpy-road illusion. Black or white rectangles (20 pixels wide) are stationary and a grating made up of blue and yellow pinstripes (2 pixels wide for each pinstripe; inter-pinstripe spacing: 20 pixels) on white or black backgrounds, respectively, move rightward at a constant speed (1 pixel / 50 ms) behind the rectangles. The rectangles appear to be captured by the moving grating and move with it when pinstripes pass under their edges.


Movie 37. A demonstration of the pausing-and-sticking illusion. Moving dots appear to pause when they cross each other. Note that this effect is observed when moving dots appear to stream.


Movie 38. A demonstration of the footsteps illusion based upon reversed phi motion. Flickering rectangles (20 pixels wide) whose color alternates between black and white move horizontally back and forth at a constant speed (2 pixel / 140 ms on average) in front of a homogeneously gray background. They appear to speed up when they are in phi motion while they appear to slow down when they are in reversed phi motion. In this movie, two of the rectangles started with the phase of phi motion (see Figure 14), and 1400 milliseconds later they switch to the phase of reverse phi motion. Conversely, the other two rectangles started with the phase of reverse phi motion, and 1400 milliseconds later they switch to the phase of phi motion.




Figure 1. A demonstration of the Wenceslas illusion. In each color column, blue or yellow squares are aligned straightforward, but each column appears to undulate as if it were an instance of the Zöllner illusion (Thompson and Anstis, 2005).


Figure 2. The geometrical illusion observed in the footsteps illusion. For each image, upper and lower rectangles are aligned vertically. (a) The left edges of the left two rectangles are connected to the right edge of a black stripe, while the right edges of them are connected to the left edge of a white stripe. The opposite is true for the right two rectangles. In this condition, the spacing between the upper two rectangles appear to be larger than the spacing between the lower two. (b) The connections are inverted. The spacing between the upper two rectangles appears to be smaller than the spacing between the lower two.


Figure 3. A size illusion shown in the inchworm illusion. The upper-right blue rectangle and the lower-left yellow one appear to be wider than the upper-left and lower-right ones, though they are the same size.


Figure 4. An explanation of the footsteps illusion with the geometrical illusion and position capture. The stimulus is a periodic change, each cycle consisting of four phases depending on where the edges of rectangles lie. (a) In the condition that the edges of the rectangles touch the edges of stripes like Figure 2b, the spacing between the upper two rectangles appear to be smaller than the spacing between the lower two, though they are the same distance. (b) When these rectangles move rightward, their edges lie within stripes. In this phase, the upper-left rectangle appears to move slowly or stand still while the upper-right one appears to move as it does. Thus, the upper spacing appears to increase. On the contrary, the lower-left rectangle appears to move as it does while the lower-right one appears to move slowly or stand still. Thus, the lower spacing appears to decrease. (c) In the condition that the edges of the rectangles touch the edges of stripes like Figure 2a, the upper spacing appears to be larger than the lower one. (d) When these rectangles move rightward, their edges lie within stripes. In this phase, the upper-left rectangle appears to move as it does while the upper-right one appears to move slowly or stand still. Thus, the upper spacing appears to decrease. On the contrary, the lower-left rectangle appears to move slowly or stand still while the lower-right one appears to move as it does. Thus, the lower spacing appears to decrease.


Figure 5. An explanation of the inverted footsteps illusion with the geometrical illusion and motion capture. The stimulus is a periodic change, each cycle consisting of four phases depending on where the edges of rectangles lie. (a) In the condition that the edges of the rectangles touch the edges of stripes like Figure 2b, the spacing between the upper two rectangles appear to be smaller than the spacing between the lower two, though they are the same distance. (b) When the grating moves rightward, the edges of the rectangles lie within each stripe. In this phase, the upper-left rectangle appears to be stationary as it is while the upper-right one appears to be captured by the moving grating and to move rightward. Thus, the upper spacing appears to increase. On the contrary, the lower-left rectangle appears to be captured by the moving grating and to move rightward while the lower-right one appears to be stationary as it is. Thus, the lower spacing appears to decrease. (c) In the condition that the edges of the rectangles touch the edges of stripes like Figure 2a, the upper spacing appears to be larger than the lower one. (d) When the grating further moves rightward, the edges of the rectangles lie within each stripe. In this phase, the upper-left rectangle appears to be captured by the moving grating and to move rightward while the upper-right one appears to be stationary as it is. Thus, the upper spacing appears to decrease. On the contrary, the lower-left rectangle appears to be stationary as it is while the lower-right one appears to be captured by the moving grating and to move rightward. Thus, the lower spacing appears to decrease.


Figure 6. An extinction effect of edges of low contrast. (a) A grating condition. The upper-right blue thin line segment embedded in a black stripe and the lower-left yellow line segment embedded in a white stripe, i.e. edges of low contrast, appear to extinguish rapidly when observers fixate at the cross. The other two line segments of high contrast hardly appear to extinguish. (b) A homogeneous-background condition. Although the upper-right and lower-left ones are of low contrast, they do not appear to extinguish rapidly.


Figure 7. A demonstration of the extinction effect on edges of low contrast due to nearby edges of high contrast or components of high spatial frequency. An illustrated girl’s face of low contrast is embedded in a fine grating of high contrast, the face is hard to see when the high-contrast edges are clearly seen. When the image is blurred or is seen from a distance, or if the page is rapidly jiggled, the face is more discernible. This extinction effect is closely related to ‘hidden images’ (Wade, 1990). Both share the effect that “high-contrast, high spatial frequency contours can suppress the visibility of low-contrast, low spatial frequency components within them” (Wade, 2017).


Figure 8. One of the frames of Movie 10. The upper-right blue rectangle and the lower-left yellow one appear to be indistinct or sometimes appear to extinguish, while the other two are perceived clearly.


Figure 9. Frames of the enhanced version of the horizontally elongated variant. There is little or no positional illusion in the enhanced version of the horizontally elongated variant. Panel (a) shows the condition where the lateral edges of blue or yellow rectangles are aligned with vertical, phase-flipping borders of the checkerboard pattern. Panel (b) shows the other condition.


Figure 10. A footsteps-like positional illusion observed in the color-based footsteps illusion. For each image, upper and lower rectangles are aligned vertically. (a) The left edges of the upper-left magenta rectangle and the lower-left cyan one are connected to the right edge of a red stripe, and the right edges of them are connected to the left edge of a green stripe. The opposite is true for the right two rectangles. The spacing between the upper two rectangles appears to be larger than that between the lower two. (b) The connections are inverted. The spacing between the upper two rectangles appears to be shorter than that between the lower two.


Figure 11. The geometrical illusions observed in the contrast-modulated footsteps illusion. (a) The spacing of the upper two squares appear to be larger than that of the lower two, though they are aligned vertically. (b) The lower spacing appears to be larger than the upper one. For some observers, the geometrical illusions may be hard to see because the lower squares are hard to see.


Figure 12. The geometrical illusions observed in the offset-based footsteps illusion. (a) The spacing of the upper two blocks appear to be larger than that of the lower two, though they are aligned vertically. (b) The lower spacing appears to be larger than the upper one.


Figure 13. There are little or no footsteps-like positional illusion in the kickback illusion. Panel (a) shows the condition that the right edge of the upper-right blue rectangle and the right edge of the lower-left yellow rectangle touch white and black stripes, respectively. Panel (b) shows the condition that both edges of the upper-right blue rectangle and both edges of the lower-left yellow rectangle touch white and black stripes, respectively.


Figure 14. The phase of phi motion and that of reverse phi motion installed in Movie 38. One phase consists of a repetition of four frames (70 ms for each). Rectangles move 1 pixel from the first frame to the second one. They stay there from the second to the third. They move 1 pixel from the third to the fourth. They stay there from the fourth frame back to the first one of the next phase. For phi motion, contrast polarity does not change when rectangles move, whereas it changes while they stay there. Inversely, for reverse phi motion, contrast polarity changes when rectangles move, whereas it does not change while they stay there. The phase of phi motion is repeated five times (1400 ms), followed by the phase of reverse phi motion that is repeated five times, and vice versa.


Table 1. A list of the twenty-seven movies that were rated for the degree of footsteps appearance. Movie 1 that shows an instance of the standard footsteps illusion served as the reference rated ‘10’. A rating of ‘0’ was given to the perception of coherent motion as it is. The results are put in parentheses.

Movie Variants (mean ratings)
1 Footsteps illusion (10)
2 Achromatic footsteps illusion (dark-gray or light-gray rectangles) (10.7)
3 Achromatic footsteps illusion (black or white rectangles) (7.1)
5 Inverted variant of the footsteps illusion (Movie 1) (6.7)
6 Footsteps illusion without fine stripes (1.2)
10 Achromatic footsteps illusion (black or white rectangles and stripes) (11.9)
11 Inverted variant of the achromatic footsteps illusion (Movie 10) (9.0)
12 Horizontally elongated variant (2.2)
13 Enhanced version of the horizontally elongated variant (10.7)
14 Inverted variant of the enhanced version of the horizontally elongated variant (Movie 13) (5.9)
17 Rail-track variant (8.6)
18 Clearing-in-a-forest variant (0.1)
19 Color-based variant (3.6)
20 Inverted variant of the color-based variant (Movie 19) (3.2)
21 Contrast-modulated variant (7.4)
22 Inverted variant of the contrast-modulated variant (Movie 21) (0.6)
23 Offset-based variant (8.1)
24 Inverted variant of the offset-based variant (Movie 23) (5.5)
25 Kickback illusion (11.0)
28 Kick-forward illusion (7.4)
30 Inverted variant of the kickback illusion (Movie 25) (8.8)
31 Inverted variant of the kick-forward illusion (Movie 28) (7.5)
33 Driving-on-a-bumpy-road illusion (3.1)
34 Inverted variant of Movie 33 (2.6)
35 Another demonstration of the driving-on-a-bumpy-road illusion (1.5)
36 Inverted variant of Movie 35 (1.2)
38 Footsteps illusion based upon the reversed phi motion (9.6)



Figure 15. Mean rating scores and errors (SD) of the degree of footsteps appearance in the twenty-seven movies.


Figure 16. The geometrical illusions, in which the spacing of the upper two rectangles appears to be larger than that of the lower two for panels (a), (c) – (g), though they are aligned vertically. For panel (b), the reversal is true. (a) - (c) The static displacement illusion proposed by Gregory & Heard (1983). (d) A variant of the static displacement illusion corresponding to the geometrical illusion observed in the footsteps illusion. (e) A variant corresponding to the geometrical illusion observed in the color-based footsteps illusion. (f) A variant corresponding to the geometrical illusion observed in the contrast-modulated footsteps illusion. (g) A variant corresponding to the geometrical illusion observed in the offset-based footsteps illusion.


Figure 17. A tree diagram of a classification of the illusions reviewed in this paper. Movie numbers and ratings scores are put in parentheses.


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