REVIEW REPORT

A review of the footsteps illusion
Akiyoshi Kitaoka1*
1
2

and Stuart Anstis2

College of Comprehensive Psychology, Ritsumeikan University, Ibaraki, Osaka, Japan;
Department of Psychology, University of California, San Diego, CA, USA

Abstract
Studies on the footsteps illusion proposed by Anstis (2001) and its variants are reviewed in thisarticle. The footsteps illusion has been explained as a difference in perceived speed depending
on edge contrast (Thompson, 1982). In addition to this explanation, it is suggested that thefootsteps illusion and its variants can also be attributed to the geometrical illusion presented
by Gregory and Heard (1983), to the extinction effect similar to hidden images by Wade (1990),
and to subsequent position or motion captures. Related illusions, for example, the kickback
illusion (Howe, Thompson, Anstis, Sagreiya, & Livingstone, 2006), the kick-forward illusion,
the driving-on-a-bumpy-road illusion, or the footsteps illusion based upon reverse phi motion,
are discussed in this article.
Keywords: footsteps illusion; motion perception; contrast; geometrical illusion; extinction effect; ­position
capture; motion c­ apture; reverse phi

Edited by
Yuki Yamada
Kyushu University, Japan
Reviewed by
Piers Howe
The University of Melbourne,
Australia
Hiroyuki Ito
Kyushu University, Japan

Received: 1 October 2020; Accepted: 28 January 2021; Published: 22 March 2021

M

otion perception is an intriguing subject thathas been fascinating vision researchers and artists. It is not simply the perception of a set ofdifferent still images that are arranged along a time axis.
For example, a motion aftereffect is observed when observers watch a stationary image after seeing a moving object(Anstis, Verstraten, & Mather, 1998). There are several
instances of motion illusion in a still image without prioradaptation to motion (Kitaoka, 2014, 2017; Kitaoka &Ashida, 2007; Pinna & Brelstaff, 2001; Spillmann, Saito, &Komatsu, 2016). A change in luminance alone can cause
motion perception (Anstis, 1970; Gregory & Heard, 1983;
Rogers, Anstis, Ashida, & Kitaoka, 2019).
Although there are a variety of topics in motion perception, the footsteps illusion (Anstis, 2001, 2003, 2004)
is particularly intriguing because the object’s motion
becomes dramatically faster or slower depending on the
background. The study of this illusion is expected tohelp to clarify the mechanism of motion perception. To
achieve this goal, we here review the footsteps illusion, its
abundant variants, and new related illusions.
The footsteps illusion
The footsteps illusion is a motion illusion in which
objects appear to move fast or slow even when they

move at a constant speed. For example, when blue
or yellow rectangles move horizontally at a constant
speed across a stationary grating of vertical black andwhite stripes, they appear to accelerate or decelerate
repeatedly (moving or pausing) like a footstep motion(Movie 1). Each rectangle has the same width as two
stripes, so that its leading and trailing edges always
lie on the same color (black or white). The rectangles
appear to slow down when their moving edges are oflower contrast (blue vs. black; yellow vs. white). Color
is not indispensable, and achromatic (dark-gray orlight-gray) rectangles instead of the chromatic ones
work (Movie 2). The footsteps illusion is also observed
when rectangles are black or white and the stripes aredark-gray or light-gray (Movie 3). It is therefore suggested that the essential factor is the luminance contrast of moving edges.
When the rectangles have the same width as three
stripes, so that their leading and trailing edges always lie
on the different color (black vs. white), the ‘inchworm’
variant of the footsteps illusion is observed (Anstis, 2001)(Movie 4). The rectangles appear to repeatedly expand
and contract horizontally. This illusion indicates that theleading and trailing edges independently contribute to thefootsteps illusion.

Correspondence: Akiyoshi Kitaoka. Email: akitaoka@lt.ritsumei.ac.jp
Journal of Illusion 2021. © 2021 Akiyoshi Kitaoka and Stuart Anstis. This is an Open Access article distributed under the terms of the Creative Commons CC-BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/), allowing third parties to copy and redistribute the material in any medium or format and to remix, transform, and build upon the material for any purpose,even commercially, provided the original work is properly cited and states its license.
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

1

Akiyoshi Kitaoka and Stuart Anstis

Movie 1. A demonstration of the footsteps illusion. Blue or
yellow rectangles (20 pixels wide) move horizontally backand forth at a constant speed (1 pixel per each 30 ms) acrossa 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 footstep motion.

Movie 2. A demonstration of the achromatic version of thefootsteps illusion. Dark-gray (R: 77,G: 77, B: 77) or lightgray (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 tomove fast or slow like a footstep motion.

The inverted footsteps illusion
Even when rectangles are stationary and the grating
moves, the former appear to move like the footsteps illusion (Movie 5). This illusion was presented by Howe etal. (2006) as their Stimulus 2d demo. Since the rectangles
are stationary, this footstep motion is an induced motion.
Hereafter, we call this phenomenon as the ‘inverted footsteps illusion’.

2

Movie 3. A demonstration of the achromatic version of thefootsteps 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 fastor slow like a footstep motion.

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

Anstis (2004) attributed the footsteps illusion to thedifference in perceived speed that depends on the difference in luminance contrast. This hypothesis is based upon
the observation that gratings of lower contrast appear
to move slower than those of higher contrast (Stone &Thompson, 1992; Thompson, 1982).

Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

A review of the footsteps illusion

This hypothesis was criticized by Howe et al. (2006),
who reported a much weaker footstep appearance when
the target moved on a homogeneous background alternating between black and white. This hypothesis cannot beapplied to the inverted footsteps illusion, either, because

the target is stationary. Yet, it should be stressed that thefootsteps illusion based upon the difference in apparent
speed depending on edge contrast is observed to someextent (Anstis, 2003) (Movie 6).
Involvement of position capture andmotion capture
Here we demonstrate that the footsteps illusion and theinverted one can be observed well even at a low speed.
Movie 7 shows the footsteps illusion at a low speed. When
moving edges are of low contrast, the motion appears toslow down or to be captured there. The latter is typicallyMovie 5. A demonstration of the inverted footsteps illusion
proposed by Howe et al. (2006). Blue or yellow rectangles (20pixels wide) are stationary, and a grating of black and white
stripes (10 pixels wide for each stripe) moves rightward at aconstant speed (1 pixel / 30 ms) behind the rectangles. Even if
observers fixate at the stationary cross, a footstep motion that
resembles the footsteps illusion 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 thestationary stripes (position capture).

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 ata 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 touchor step over borders of stripes. A weak footstep motion isobserved.

Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

Movie 8. A demonstration of the inverted footsteps illusion ata low speed. The grating moves rightward at a constant speed (1pixel / 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).

3

Akiyoshi Kitaoka and Stuart Anstis

referred to as ‘position capture’ (Murakami & Shimojo,1993), and the rectangles seem to lie alternately closer
together and further apart.
Movie 8 shows the inverted footsteps illusion at a low
speed. 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. This phenomenon is typicallyreferred to as ‘motion capture’, although this term usuallyindicates the phenomenon that a stationary object contoured by color edges (e.g. red vs. green) of low luminancecontrast appears to move, being induced by the surroundthat moves (Goda & Ejima, 1997; Ramachandran, 1987).
In addition, when the edges of a rectangle are of highcontrast in Movie 8, the rectangle seems to undergo
induced movement, seeming to move in a direction
opposite to the stripe. This may be a partial cause of theinverted footsteps illusion.

Fig. 1. A demonstration of the Wenceslas illusion. In eachcolor column, blue or yellow squares are aligned in straightlines, but each column appears to undulate as if it were an
instance of the Zöllner illusion (Thompson & Anstis, 2005).

Involvement of the geometrical illusion
Thompson and Anstis (2005) suggested a contributionof the geometrical illusion, presenting the Wenceslas­illusion. Figure 1 shows an instance, in which multiple
squares appear to be placed in an undulating manner
although they are aligned in a straight line. This geometrical illusion or position illusion corresponds to the ‘belly
dancer illusion’ that Howe et al. (2006) demonstrated as
its moving counterpart (Movie 9).
Subsequently, Sunaga, Sato, Arikado and Jomoto(2008) claimed that the footsteps illusion is an outcomeof a geometrical illusion. Figure 2 demonstrates illusory positional shifts of rectangles. In Fig. 2a, the spacing between the upper two blue rectangles appears to be

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

Fig. 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 appears 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.

4

Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

A review of the footsteps illusion

shorter than the spacing between the lower two yellow
rectangles, although they are the same distance apart. On
the other hand, in Fig. 2b, the reverse is observed. Whena dark object (blue rectangle) is connected to a thin dark
object (black stripe), the connected edge appears to shift
toward the latter. When a light object (yellow rectangle)
is connected to a thin light object (white stripe), the connected edge appears to shift toward the latter. This geometrical-illusion hypothesis can be applied to the inverted
footsteps illusion too.
We think that this geometrical illusion should be credited to Gregory and Heard (1983), although Thompson
and Anstis (2005) or Sunaga et al. (2008) did not mention

Fig. 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,
although they are of the same size.

it. This issue is described later. For the inchworm illusion(Movie 4), this positional illusion is converted to a size
illusion (Fig. 3).
Explanations that take into account the capture
phenomena and the geometrical illusion
Combining the geometrical illusion (Fig. 2) and the
motion phenomena (position capture: Movie 7; motion
capture: Movie 8), we explain the footsteps illusion andthe inverted one as follows. For the footsteps illusion,
let us start with a condition like Fig. 4a in which theedges of the rectangles touch those of the stripes. In thiscondition, the spacing between the upper two rectangles
appears to be smaller than that between the lower two
rectangles, although they are the same distance apart.
When the rectangles move rightward (Fig. 4b), the upperleft 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 standstill. Thus, the lower spacing appears to decrease. Whenedges of the rectangles touch those of stripes again(Fig. 4c), the upper spacing appears to be larger than thelower one. Finally, when the rectangles move rightward(Fig. 4d), 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 moveslowly or stand still, while the lower-right one appears
to move as it does. Thus, the lower spacing appears todecrease. This repetition makes the rectangles appear tomove like a footstep.

Fig. 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 Fig. 2b, the spacing between the upper two rectangles appears to be smaller than thespacing between the lower two rectangles, although they are the same distance apart. (b) When these rectangles move rightward,
their edges lie within each stripe. 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 tomove 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 Fig. 2a, the upper spacing appears to be larger thanthe lower one. (d) When these rectangles move rightward, their edges lie within each stripe. 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 todecrease. On the contrary, the lower-left rectangle appears to move slowly or stand still, while the lower-right one appears to moveas it does. Thus, the lower spacing appears to decrease.
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

5

Akiyoshi Kitaoka and Stuart Anstis

Fig. 5. An explanation of the inverted footsteps illusion with the geometrical illusion and motion capture. The stimulus is aperiodic change, each cycle consisting of four phases depending on where the edges of rectangles lie. (a) In the condition thatthe edges of the rectangles touch the edges of stripes like Fig. 2b, the spacing between the upper two rectangles appears to besmaller than the spacing between the lower two, although they are the same distance apart. (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 toincrease. On the contrary, the lower-left rectangle appears to be captured by the moving grating and to move rightward, while thelower-right one appears to be stationary as it is. Thus, the lower spacing appears to decrease. (c) In the condition that the edgesof the rectangles touch the edges of stripes like Fig. 2a, the upper spacing appears to be larger than the lower one. (d) When thegrating 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, theupper 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.

Fig. 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, that is, 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.

For the inverted footsteps illusion, let us start with a condition like Fig. 5a in which the edges of rectangles touch
those of the stripes. In this condition, the spacing between
the upper two rectangles appears to be smaller than thatbetween the lower two rectangles, although they are thesame distance apart. When the grating moves rightward
behind the rectangles (Fig. 5b), 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 moverightward. 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. When edges of therectangles touch those of stripes again (Fig. 5c), the upperspacing appears to be larger than the lower one. Finally,

6

when the grating moves rightward (Fig. 5d), the upper-leftrectangle appears to be captured by the moving grating andto move rightward while the upper-right one appears to
be stationary as it is. Thus, the upper spacing appears todecrease. 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 upper spacing appears to increase. This repetition
makes the rectangles appear to move like a footstep.
Involvement of the extinction effect
There is a possibility that the position capture phenomenon observed in the footsteps illusion (Movie 7) and the
motion capture phenomenon found in the inverted footsteps illusion (Movie 8) could be attributed to an extinction effect of edges of low contrast in a special condition.
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

A review of the footsteps illusion

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

Fig. 7. A demonstration of the extinction effect on edges oflow contrast due to nearby edges of high contrast or components of high spatial frequency. An illustrated girl’s face oflow 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, orif 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 6a demonstrates that thin line segments of low
contrast appear to extinguish rapidly when observers
fixate at the cross. When objects are placed on a homogeneous background, they do not appear to extinguishsoon (Fig. 6b). It is suggested that the essential factor be
a combination between edges of low contrast and edgesof high contrast close to the former (Fig. 7). In the chapter entitled ‘Hidden images’, Wade (2017) mentioned thathigh-contrast, high spatial frequency contours can suppress the visibility of low-contrast, low spatial frequency
components within them. This suggestion is consistent
with Zenger-Landolt and Koch (2001) who reported
that the apparent contrast of an edge is reduced by surrounding edges of high contrast. It is plausible that thisCitation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

extinction effect causes the position capture and motion
capture of edges of low contrast in the footsteps illusion
and the inverted footsteps illusion, respectively.
Moreover, the footsteps illusion and the inverted one areobserved even when blue and yellow rectangles are replacedwith black and white ones, respectively (Movies 10 and 11).
In this footsteps illusion, position capture occurs when
there are no physical motion signals, that is, when theedges of a black rectangle lie inside a black stripe or thoseof a white rectangle stay inside a white stripe. This variant was presented in Howe et al. (2006), who reported astrong illusion. In the inverted footsteps illusion, motion
capture occurs when there are no physical motion signals,
which would induce imaginary rectangles to move. It is suggested that the original footsteps illusion (Movie 1) and its
inverted one (Movie 5) be attributed to or be equivalent tothese variants through the process of the extinction effect.
Other variants of the footsteps illusion
The horizontally elongated variant
The extinction-effect hypothesis may help to explain
another footstep phenomenon presented by Howe et al.
(2006, their Stimulus 2e demo) (Movie 12). In their stimulus, both rectangles and stripes are elongated horizontally,
and the height of each rectangle is the same as that of each
stripe. The upper and lower sides of a rectangle touch thelower edge of the upper stripe and the upper edge of thelower stripe, respectively. When one horizontally moves

7

Akiyoshi Kitaoka and Stuart Anstis

Movie 11. A demonstration of the inverted variant of thespecial case of the footsteps illusion. Black or white rectangles are stationary, and the grating moves rightward at aconstant speed (1 pixel / 30 ms) behind the rectangles. Even
if observers fixate on the stationary cross, a footstep motion
is observed. Besides the involvement of the geometrical illusion, this perception is explained with motion capture due tothe 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 backand forth at a constant speed (1 pixel / 30 ms) on black orwhite stripes. These stripes alternate over every 300 ms. The
rectangles appear to move fast or slow like a footstep motion
synchronously with the alternation of stripes.

a blue rectangle that is placed on a black stripe and issandwiched by the upper and lower white stripes (e.g.
the upper-right rectangle of Fig. 8: #1), the blue rectangle appears to move behind a yellow rectangle that isplaced in the same condition (e.g., the lower-right rectangle of Fig. 8: #2). When one horizontally moves a yellow

8Fig. 8. One of the frames of Movie 12. The upper-right blue
and the lower-left yellow rectangles appear to be indistinct
or sometimes appear to extinguish, while the other two areperceived clearly.

rectangle that is placed on a white stripe and is flanked
by the upper and lower black stripes (e.g., the lower-leftrectangle of Fig. 8: #3), the yellow rectangle appears tomove behind a blue rectangle that is placed in the same
condition (e.g., the upper-left rectangle of Fig. 8: #4). The
extinction effect is observed for the rectangles #1 or #3,
which appear to be indistinct or sometimes disappear.
This horizontally elongated variant (Movie 12) is not
so strong as the original (Movie 1), as pointed out byHowe et al. (2006) who suggested the involvement of anadditional mechanism. This suggestion is discounted asfollows. One plausible reason is that this variant is notaccompanied by the geometrical illusion. Another one isthat there is no clue to position capture, although the rectangles #1 and #3 show the extinction effect. It is therefore
suggested that the weak footsteps illusion observed in thisvariant be equivalent to the footsteps illusion based solely
upon the difference in apparent speed depending on edge
contrast (Anstis, 2003) (Movie 6). Moreover, movies inwhich the stripes repetitively reverse their polarity overtime (such as Movie 12) give rather weak effects, which are
generally masked by a strong apparent motion in which
the blue and yellow bars appear to jump back and forth.
The enhanced version of the horizontally elongated variant
Movie 13 shows a new version of the horizontally elongated variant, which presents a much stronger footstep
motion comparable to the original footsteps illusion(Movie 1). Blocks of horizontally elongated rectangles
move horizontally across a stationary checkerboard pattern instead of the alternating stripes (Fig. 9). Moving
edges of low contrast (blue vs. black or yellow vs. white)
appear to move slower than those of high contrast or topause there (position capture).
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

A review of the footsteps illusion

Movie 14 shows its inverted one, in which rectangles
are stationary and the checkerboard pattern moves.
Stationary lateral edges of low contrast appear to be captured by the moving checkerboard pattern and to movewith it (motion capture), while those of high contrast
appear to be stationary as they are.
This footsteps illusion or the inverted one is observed
even if rectangles or the checkerboard move slowly(Movies 15 and 16). Moreover, the geometrical illusion
does not seem to be involved in these variants (Fig. 9).
These observations suggest that these horizontallyelongated variants chiefly depend on the extinction
effect and subsequent capture phenomena in addition

to the difference in apparent speed depending on edge
contrast.

Movie 13. A demonstration of the enhanced version of thehorizontally 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 (3pixels / 30 ms) across a checkerboard pattern or along rowsof 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 movebehind those of high contrast or to be captured there (position capture).

Movie 14. A demonstration of the inverted variant of theenhanced version of the horizontally elongated footsteps
illusion. Blocks of blue or yellow rectangles (5 pixels heightand 60 pixels wide for each rectangle) are stationary and thecheckerboard 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 edgesof rectangles are of low contrast (blue vs. black or yellow vs.
white), they appear to move slowly or to be captured by themoving checkerboard and move with it (motion capture).

The railroad-track variant
In the railroad-track variant of the footsteps illusion(Anstis, 2004), rectangles move across a grating of thesame height (Movie 17). Although this variant is as strongas the original one, Howe et al. (2006) regarded it as aproblem that the illusion is somewhat reduced in comparison to the standard one. We suggest that the reduction, if
any, depends on a weaker extinction effect because there isa relatively small amount of edges of high contrast.

Fig. 9. Frames of the enhanced version of the horizontally elongated variant. There is little or no positional illusion in theenhanced 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.
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

9

Akiyoshi Kitaoka and Stuart Anstis

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

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

Movie 18 shows the clearing-in-a-forest variant (Anstis,2004), in which little or no footsteps illusion is observed.
This observation indicates that the lateral sides of themoving blocks do not contribute significantly to the footsteps illusion.
The color-based variant
Variants of the ‘second-order’ footsteps illusion (Kitaoka& Anstis, 2015) can be explained in the same way. For
example, Movie 19 demonstrates the color-based footsteps
illusion, in which magenta or cyan rectangles appear toshow a footstep motion across a grating of red and green
stripes, although this footsteps illusion is rather weak for

10

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

Movie 18. A demonstration of the clearing-in-a-forest variant.
Each of the blue or yellow rectangles (60 pixels high × 20 pixels
wide) moves horizontally back and forth at a constant speed(1 pixel / 30 ms) across a white or black gap ­between gratingsof black and white rectangles (60 pixels high × 10 pixels wide
for each rectangle).

some observers. Edges of low color contrast (combination of similar colors: magenta vs. red, or cyan vs. green)
appear to move slower than edges of high color contrast(combination of nearly opponent colors: magenta vs.
green; cyan vs. red) or appear to move slowly or to be captured there (position capture). Movie 20 demonstrates theinverted version, which also shows a footstep appearance.
Moreover, the geometrical illusion is observed (Fig. 10),which is also thought to contribute to the color-based
footsteps illusion and the inverted one. Although the fourcolors are selected so as to have similar luminances, it
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

A review of the footsteps illusion

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 andforth 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 footstep motion.

Movie 20. A demonstration of the inverted variant of thecolor-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 therectangles. Even if observers fixate on the stationary cross, afootstep-like appearance is observed.

should be noted that there remains a possible involvementof luminance in this variant.
The contrast-modulated variant
Movie 21 shows a footsteps illusion defined by the difference in luminance contrast (Kitaoka & Anstis, 2015).
When moving edges of a square have a small difference incontrast, it appears to slow down, as compared to those
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

that have a large difference in contrast. It is suggested thatedges with a small difference in contrast might be hard to
be detected in visual processing and appear to slow down
or to be captured there.
Movie 22 shows its inverted condition, which, however, does not show a footstep motion or display a weak
one at best. This finding is unique as compared with theother inverted variants demonstrated so far. It is conjectured because stationary random-dot patterns anchor
the squares there. In contrast, the moving squares in thecontrast-modulated footsteps illusion (Movie 21) are perceived as transparent layers and are not anchored by random dots.
Moreover, the geometrical illusion is observed (Fig. 11).
It is suggested that it also contributes to the contrast-modulated footsteps illusion and the inverted one.
The offset-defined variant
Movie 23 shows a footsteps illusion defined by the difference in offset of abutting gratings (Kitaoka & Anstis,2015). Blocks contoured by abutting gratings with a small
offset appear to move slower than those with a large offset.
It is suggested that subjective contours with a small offset might be hard to be detected in visual processing andappear to slow down or to be captured there. Movie 24
shows its inverted variant, which shows a footstep motion.
Moreover, the geometrical illusion is observed (Fig. 12)
and is thought to contribute to the offset-based footsteps
illusion and the inverted one.
The kickback illusion and the kick-forward illusion
Howe et al. (2006) proposed a new motion illusion called
the ‘kickback illusion’. Movie 25 shows an instance inwhich blue rectangles move across a grating made up
of white pinstripes on a black background, while yellow
rectangles move across a grating of black pinstripes on awhite background. The spacing of two adjacent pinstripes
is the same as the width of each rectangle. When the edges
of a rectangle pass over pinstripes, the rectangle appear to
wiggle or jump backward. To be more specific, this effectoccurs both when the leading edge covers a pinstripe andwhen the trailing edge uncovers a pinstripe (Movie 26).
Howe et al. (2006) reported that most subjects reported
the backward speed to be considerably greater than theforward speed.
Although the kickback illusion is observed even if
rectangles move slowly (Movie 27), the geometrical illusion does not seem to be involved in this effect (Fig. 13).
Moreover, the extinction effect might take part when theedges move between pinstripes and slow down the rectangles, but it cannot explain the backward motion of the
kickback illusion.
Howe et al. (2006) stated that one would expect
the footsteps illusion and the kickback illusion to be

11

Akiyoshi Kitaoka and Stuart Anstis

Fig. 10. A footstep-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 rightedge 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.

Movie 21. A demonstration of the contrast-modulated
footsteps illusion. The pattern of random dots (1 × 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 × 60 pixels). The contrast of thehigh-contrast stripes (0 vs. 255 in a 256-level grayscale) ishigher 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 aconstant speed (3 pixel / 60 ms) across the stripes. Squares
appear to move fast or slow like a footstep motion. Notethat the difference in contrast between the high-contrast
stripes and the high-contrast squares is so small that somedisplays cannot properly demonstrate this illusion becauseof clipping.

mediated by the same mechanisms because of their geometric similarity, but that it is probably not the case. They
presented two pieces of evidence. One is that the kickback illusion disappears when yellow objects move acrosswhite pinstripes on a black background. The other is that

12

Movie 22. A demonstration of the inverted variant of thecontrast-modulated footsteps illusion. The contrast-definedsquares and the pattern of random dots are stationary andthe contrast-defined stripes move rightward at a constant
speed (3 pixel / 60 ms) behind the squares. Squares do notappear to show a footstep motion or appear to display aweak one at best.

the ‘kick-forward’ effect (Movie 28) is observed insteadof the kickback one when white objects move acrossblack stripes on a yellow background. The kick-forward
illusion also occurs both when the leading edge covers
a pinstripe and when the trailing edge uncovers a pinstripe. They suggested that the ‘kick’ part of the kickback
illusion is an example of the reverse phi (reversed phi)
phenomenon (Anstis, 1970; Anstis & Rogers, 1975, 1986;
Rogers et al., 2019).
Movie 28 shows an instance of the kick-forward illusion, in which moving rectangles appear to be accelerated
when their edges pass over pinstripes. This illusion gives
a strong impression of the footstep motion. The kick-­forward effect is observed even if rectangles move slowly
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

A review of the footsteps illusion

Fig. 11. The geometrical illusions observed in the contrast-modulated footsteps illusion. (a) The spacing of the upper two squares
appears 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.

Movie 23. A demonstration of the offset-based footsteps
illusion. Rectangular blocks made up of four thin line segments (1 pixel high × 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 footstep motion.

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

Fig. 12. The geometrical illusions observed in the offset-based footsteps illusion. (a) The spacing of the upper two blocks appears
to be larger than that of the lower two, although they are aligned vertically. (b) The lower spacing appears to be larger than theupper one.
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

13

Akiyoshi Kitaoka and Stuart Anstis

Movie 25. A demonstration of the kickback illusion. Blueor yellow rectangles (20 pixels wide) move horizontally backand 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 blackor white backgrounds, respectively. Rectangles appear tojump backward when their edges pass over pinstripes.

Movie 26. A demonstration of the kickback illusion to showthat 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 jumpbackward when it covers/uncovers a pinstripe.

(Movie 29) and the geometrical illusion does not seem to
be involved in this effect. These observations suggest thatthe strong impression of the footstep motion be renderedby the alternation between the deceleration caused by theextinction effect when edges move between pinstripes and14

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

the acceleration caused by the kick-forward effect whenedges pass over pinstripes.
Movies 30 and 31 show the inverted versions of the
kickback and kick-forward illusions, respectively. In thesecases, illusory motion can be explained in the same manner as those of the kickback or kick-forward illusions.
As Howe et al. (2006) suggested, the ‘kick’ part of
the kickback illusion or the kick-forward one cannot be
explained in the same manner as the footsteps illusion.
Their inverted variants cannot be explained so, either.
Although Howe et al. attributed the effect to the reverse
phi phenomenon (Anstis, 1970; Anstis & Rogers, 1975,1986) and we basically agree with them, we here specify
the illusion that yields the ‘kick’ part.
Movie 32 shows an instance, in which disks appear to
expand or contract when circumference contours appear
or disappear. Specifically, a blue disk in the upperleft square appears to expand when its white contour
appears, while it appears to contract when the contour
disappears. The expansion or contraction is illusory
because the blue disk does not change in size. Inversely,
a black disk in the upper-right square appears to contract when its white contour appears, while it appears to
expand when the contour disappears, although the black
disk does not change in size. In the same manner, a yellow disk in the lower-left square appears to expand whenits black contour appears, while it appears to contract
when the contour disappears. Inversely, a white disk inthe lower-right square appears to contract when its black
contour appears, while it appears to expand when thecontour disappears. This luminance-change-dependent
motion illusion was proposed as one of the basic effects
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

A review of the footsteps illusion

Fig. 13. There is little or no footstep-like positional illusion in the kickback illusion. Panel (a) shows the condition that the rightedge 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.

Movie 28. A demonstration of the kick-forward illusion.
Black or white rectangles (20 pixels wide) move horizontallyback and forth at a constant speed (1 pixel / 30 ms) in front ofa 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.

underlying the reverse phi motion and other phenomena(Kitaoka, 2006).
In the kickback illusion, when edges of a blue rectangle
pass over pinstripes, the leading blue edge hides a whiteline and the trailing blue edge uncovers another white line
(Movie 25). The former corresponds to the disappearanceof the white contours shown in Movie 32, while the lattercorresponds to the appearance of the white contours. The
same is true for the yellow one. The direction of this illusory motion is opposite to that of the moving edges andthe backward motion is observed in the kickback illusion.
In the kick-forward illusion, when edges of a black rectangle pass over pinstripes, the leading black edge hides awhite line and the trailing black edge uncovers another
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

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

white line (Movie 28). The former corresponds to thedisappearance of the white contours shown in Movie 32,
while the latter corresponds to the appearance of thewhite contours. The same is true for the yellow one. The
direction of this illusory motion is the same as that of themoving edges, and the acceleration of motion is observedin the kick-forward illusion.
The driving-on-a-bumpy-road illusion
Movie 33 shows an instance in which blue rectangles
move across a grating made up of black pinstripes on awhite background, while yellow rectangles move across a
grating of white pinstripes on a black background. The
spacing of two adjacent pinstripes is the same as the widthof each rectangle. When the edges of rectangles pass overpinstripes, the rectangles appear to be captured by the15

Akiyoshi Kitaoka and Stuart Anstis

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.

pinstripes, although Howe et al. (2006, their Stimulus 7cdemo) reported ‘a percept of almost completely smooth
motion’. The whole appearance is something like running a car on a bumpy road. Movie 34 shows the inverted
variant, in which stationary rectangles appear to be captured by moving pinstripes and to move with them when

16

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. Disks appear to expand or contract when theircircumference contours appear or disappear, although eachdisk does not change in size. For details, see the text.

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

pinstripes pass over both edges of a rectangle. Different
from the dramatic difference between the kickback illusion and the kick-forward illusion, the appearance does
not change even if the colors are exchanged so that
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

A review of the footsteps illusion

Movie 34. A demonstration of the inverted variant of thedriving-on-a-bumpy-road illusion. Blue or yellow rectangles (20 pixels wide) are stationary and a grating made upof 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 whenpinstripes pass under their edges.

Movie 35. Another demonstration of the driving-on-abumpy-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 theiredges pass over them.

rectangles are black or white and pinstripes are blue or
yellow (Movies 35 and 36).
It is suggested that the extinction effect occurs whenedges pass over pinstripes because they are of low contrast
and the position capture or motion capture are followed.
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

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 ofblue 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 (1pixel / 50 ms) behind the rectangles. The rectangles appear
to be captured by the moving grating and move with it whenpinstripes pass under their edges.

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

Moreover, one may point out a resemblance to the pausing-and-sticking illusion (Goldberg & Pomerantz, 1982),
a phenomenon that moving objects appear to pause when
they cross each other (Movie 37). Yet, there is a large difference in condition. The pausing-and-sticking illusion
is observed when fast moving objects collide, whereas
the running-on-a-bumpy-road illusion is observed when17

Akiyoshi Kitaoka and Stuart Anstis

Movie 38. A demonstration of the footsteps illusion based
upon reverse phi motion. Flickering rectangles (20 pixels
wide) whose color alternates between black and white movehorizontally 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 reverse phi
motion. In this movie, two of the rectangles started with thephase of phi motion (see Fig. 14), and 1,400 ms later theyswitch to the phase of reverse phi motion. Conversely, theother two rectangles started with the phase of reverse phi
motion, and 1,400 ms later, they switch to the phase of phi
motion.

moving edges pass over stationary pinstripes. Probably,
they are not the same illusion.
The footsteps illusion based upon reverse phi motion
The last one introduced in this article is the footsteps illusion based upon the difference in apparent speed between
phi motion and reverse phi motion (Movie 38). Rectangles
appear to move fast when they are in phi motion, while
they appear to move slowly or move backward when
they are in reverse phi motion. Figure 14 shows how to
install these phenomena in Movie 38. Phi motion refers
to a normal motion perception of an object in which theobject appears to move as it does, while reverse phi refers
to an illusory motion perception of an object in which
the object appears to move in the opposite direction to its
positional shift when the contrast polarity of the object
is reversed (Anstis, 1970; Anstis & Rogers, 1975, 1986;
Rogers et al., 2019). Although this variant resembles theoriginal footsteps illusion in appearance, the mechanisms
between them are quite different.
Rating of the footsteps illusion and its variants
To confirm the described phenomenal observations on thefootsteps illusion and its variants, the degree of ‘footstep
appearance’ in each movie was rated by seven observers.
First, each of the observers regarded Movie 1 that shows

18

Fig. 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 fromthe second to the third. They move 1 pixel from the third to
the fourth. They stay there from the fourth frame back to thefirst 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 (1,400 ms), followed by the phase ofreverse phi motion that is repeated five times, and vice versa.

the standard footsteps illusion as the reference stimulus thatshould be rated ‘10’. A rating of ‘0’ indicates completely
smooth motion. A rating of more than ‘10’ was allowed.
Observers rated twenty-seven movies (Movies 1–3, 5, 6,
10–14, 17–25, 28, 30, 31, 33–36, and 38) listed in Table 1.
Since this study was conducted in the period of the coronavirus lockdown in 2020, the first author asked observers
to rate them on their individual displays. The size of themovie (600 × 480 pixels) shown on each display and theviewing distance were recorded. The results are shown in
Fig. 15, which confirms these illusions. Moreover, it was
confirmed that the railroad-track variant (Movie 17) is asstrong as the footsteps illusion (Anstis, 2004), while theclearing-in-a-forest variant (Movie 18) shows little or nofootsteps illusion (Anstis, 2004).
List of the geometrical illusion involved in thefootsteps illusion and its variants
Although the involvement of a geometrical illusion in thefootsteps illusion has been pointed out (Sunaga et al., 2008;
Thompson & Anstis, 2005), we think this geometrical illusion is a variant of the ‘static displacements’ proposed by
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

A review of the footsteps illusion

Table 1. A list of the twenty-seven movies that were rated for the degree of footstep appearance
Movie

Variants (mean ratings)

1
2
3
5
6
10
11
12
13
14
17
18
19
20
21
22
23
24
25
28
30
31
33
34
35
36
38

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

Note: 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 ofcoherent motion as it is. The results are put in parentheses.

Fig. 15. Mean rating scores and errors (standard deviation [SD]) of the degree of footsteps appearance in the 27 movies.
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

19

Akiyoshi Kitaoka and Stuart Anstis

Fig. 16. The geometrical illusions, in which the spacing of the upper two rectangles appears to be larger than that of the lower
two, although they are aligned vertically. (a–c) The static displacement illusion proposed by Gregory and Heard (1983). (d) Avariant of the static displacement illusion corresponding to the geometrical illusion observed in the footsteps illusion. (e) Avariant 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 geometricalillusion observed in the offset-based footsteps illusion.

Gregory and Heard (1983). Figure 16a consists of four
dark rectangles in front of a light-gray background. Each
rectangle is flanked by black or white line segment at thelateral sides. This image shows a geometrical illusion thatthe spacing of the rectangles in the upper row appear to belarger than that of the rectangles in the lower row, although
they are aligned vertically. When the gray of rectangles is
exchanged with that of the background and black or lightflanks are exchanged with each other, the upper spacing
appears to be larger than the lower (Fig. 16b). The position of a dark rectangle appears to shift toward its blackflank and away from its white one, while the position ofa light rectangle appears to shift toward its white flankand away from its dark flank. F­ igure 16c is a combined
image in which the spacing of the upper dark-gray rectangles appears to be larger than that of the lower light-grayones. Even if, in Fig. 16c, the dark-gray is exchanged withblue and the light-gray is replaced with yellow, the illusion
does not change (Fig. 16d). The spacing of the upper blue
rectangles appears to be larger than that of the lower yellow ones. The geometrical illusion shown in this figure justcorresponds to the illusion shown in Fig. 2a.
Moreover, even if the dark-gray, light-gray, black, andthe white in Fig. 16c are exchanged with the magenta,
cyan, red, and the green that are adopted in the color-based footsteps illusion (Movie 19), respectively,
the illusion does not change. The spacing of the uppermagenta rectangles appears to be larger than that of thelower cyan ones (Fig. 16e). The position of a colored20

rectangle appears to shift toward the flank of the similarcolor and away from the flank of the different color. The
geometrical illusion shown in this figure just corresponds
to the illusion shown in Fig. 10a.
Furthermore, even if the black, dark-gray, light-gray,and white in Fig. 16c are exchanged with random-dot patterns of the lowest, second-lowest, second-highest, andhighest contrast that are adopted in the contrast-modulated footsteps illusion (Movie 21), respectively, theillusion does not change. The spacing of the upper
low-contrast rectangles appears to be larger than that of
the lower high-contrast ones (Fig. 16f). The position ofa low-contrast rectangle appears to shift toward its lowest-contrast flank and away from its highest-contrast one,while the position of high-contrast rectangle appears to
shift toward its highest-contrast flank and away from its
lowest-contrast one. The geometrical illusion shown inthis figure just corresponds to that in Fig. 11a.
Figure 16g shows the geometrical illusion corresponding to the offset-based footsteps illusion (Movie 23 andFig. 12a). The position of a rectangle appears to shift
toward its flank with a small offset.
We suggest that the geometrical illusion is involved insome but not all examples of the footsteps illusion. For
example, the footsteps illusion based upon the difference
in apparent speed depending on edge contrast (Anstis,2003) (Movie 6) or the enhanced version of the horizontally elongated variant (Movie 13 and Fig. 9) do not show
the geometrical illusion.
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

A review of the footsteps illusion

Classification of the footsteps illusion and its
variants
This article described the footsteps illusion and its abundant variants. It is thought that the illusions collected inthis article are not based on a single mechanism. There
are at least three groups in regard to supposed underlying
mechanisms (Fig. 17). The first group includes the original
footsteps illusion, its variants, and their inverted illusions(Movies 1–24). The second one contains the kickback illusion and kick-forward illusion and their variants (Movies
25–31, 33–36). The third one shows the footsteps illusion
based upon reverse phi motion (Movie 38). Moreover,the first group can be classified into subgroups dependingon the dimension of edge contrast: luminance-contrast
type (Movies 1–18), color-contrast one (Movies 19 and20), modulated-contrast one (Movies 21 and 22), or offset-contrast one (Movies 23 and 24).
For the first group, it is suggested that the footsteps illusion
and its variants be attributed to the geometrical illusion or
the extinction effect in addition to the difference in perceived
speed depending on edge contrast. This suggestion is consistent with Howe et al. (2006) who attributed the footsteps
illusion to the motion signals originating from (1) the moving edges, (2) the lateral edges (the upper and lower edges),and (3) the background edges in the vicinity of the moving
edge. It is postulated that the geometrical illusion depends onthe combination between (1) and (3), the extinction effect isrendered by the combination between (1) and (2) or between(1) and (3), and the difference in perceived speed depending
on edge contrast is solely based upon (1).
For the second group, it is suggested that motion illusion triggered by local luminance changes (Movie 32)(Kitaoka, 2006) should play an important part in acceleration or deceleration of moving rectangles. For the thirdgroup, a special combination of reverse phi (Anstis, 1970)
and phi motion presents a new demonstration of the footsteps illusion.
Conclusion
A common misconception is that when the mechanism
is different, the phenomenon is also necessarily different.
Conversely, we tend to think that if the phenomenon issimilar, the mechanism is also similar. However, it may
well be that the phenomena look similar but have different
mechanisms. Therefore, it is important to have a proper
understanding of phenomena.
This article collated a variety of illusions to be included
in a single category or a single phenomenon called ‘footsteps illusion’, although they are not claimed to be basedon a single mechanism. We think that this phenomenal
categorization matches the aims of Journal of Illusion that
focus on phenomenal aspects of perception. We believethat this review can, in the future, help us better understand how motion perception is achieved.

Fig. 17. A tree diagram of a classification of the illusions reviewed in this article. Movie numbers and ratings scores are put inparentheses.
Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612

21

Akiyoshi Kitaoka and Stuart Anstis

Acknowledgments
We thank Piers Howe and Hiroyuki Ito for giving helpfulcomments on this article.
Conflict of interest and funding
The authors have no conflicts of interest associatedwith this article. This work was supported by the JSPS
KAKENHI Grant (Grants-in-Aid for Scientific Research)
Number JP15H01984 awarded to Akiyoshi Kitaoka anda grant from the UCSD Pathways to Retirement awarded
to Stuart Anstis.
Review details
To view the editorial history for this article, please visit
the article landing page https://doi.org/10.47691/joi.
v1.5612References
Anstis, S. M. (1970). Phi movement as a subtraction process. Vision
Research, 10, 1411–1430. doi: 10.1016/0042-6989(70)90092-1
Anstis, S. M. (2001). Footsteps and inchworms: Illusions show that
contrast modulates motion salience. Perception, 30, 785–794. doi:
10.1068/p3211
Anstis, S. M. (2003). Moving objects appear to slow down at low
contrasts. Neural Networks, 16, 933–938. doi: 10.1068/p140167
Anstis, S. M. (2004). Factors affecting footsteps: Contrast canchange the apparent speed, amplitude and direction of motion.
Vision Research, 44, 2171–2178. doi: 10.1016/j.visres.2004.03.015
Anstis, S. M., & Rogers, B. J. (1975). Illusory reversal of visual depth
and movement during changes of contrast. Vision Research, 15,
957–961. doi: 10.1016/0042-6989(75)90236-9
Anstis, S. M., & Rogers, B. J. (1986). Illusory continuous motion fromoscillating positive–negative patterns: Implications for motion perception. Perception, 15, 627–640. doi: 10.1068/p150627
Anstis, S., Verstraten, F. A., & Mather, G. (1998). The motion aftereffect. Trends in Cognitive Sciences, 2(3), 111–117. doi: 10.1016/
S1364-6613(98)01142-5
Goda, N., & Ejima, Y. (1997). Moving stimuli define the shape ofstationary chromatic patterns. Perception, 26, 1413–1422. doi:
10.1068/p261413
Goldberg, D. M., & Pomerantz, J. R. (1982). Models of illusory pausing
and sticking. Journal of Experimental Psychology: Human Perception
and Performance, 8(4), 547–561. doi: 10.1037//0096-1523.8.4.547
Gregory, R. L., & Heard, P. F. (1983). Visual dissociations of movement, position, and stereo depth. Quarterly Journal of Experimental
Psychology, A, 35, 217–237. doi: 10.1080/14640748308402127
Howe, P. D. L., Thompson, P. G., Anstis, S., Sagreiya, H., &Livingstone, M. S. (2006). Explaining the footsteps, belly dancer,

Wenceslas and kickback illusions. Journal of Vision, 6, 1396–1405.
doi: 10.1167/6.12.5
Kitaoka, A. (2006). Configurational coincidence among six phenomena: A comment on van Lier and Csathó (2006). Perception, 35,
799–806. doi: 10.1068/p5319b
Kitaoka, A. (2014). Color-dependent motion illusions in stationary
images and their phenomenal dimorphism. Perception, 43(9),914–925. doi: 10.1068/p7706
Kitaoka, A. (2017). The Fraser-Wilcox illusion and its extension. In
A. G. Shapiro & D. Todorović (Eds.), The Oxford compendium ofvisual illusions (pp. 500–511). New York, NY: Oxford University
Press. doi: 10.1093/acprof:oso/9780199794607.003.0068
Kitaoka, A., & Anstis, S. (2015). Second-order footsteps illusions.
i-Perception, 6(6), 1–4. doi: 10.1177/​2041669515622085
Kitaoka, A., & Ashida, H. (2007). A variant of the anomalous motion illusion based upon contrast and visual latency.
Perception, 36, 1019–1035. doi: 10.1068/p5362
Murakami, I., & Shimojo, S. (1993). Motion capture changes to
induced motion at higher luminance contrasts, smaller eccentricities, and larger inducer sizes. Vision Research, 33, 2091–2107. doi:
10.1016/0042-6989(93)90008-K
Pinna, B., & Brelstaff, G. J. (2000). A new visual illusion of relative motion. Vision Research, 40, 2091–2096. doi: 10.1016/
S0042-6989(00)00072-9
Ramachandran, V. S. (1987). Interaction between colour and motion
in human vision. Nature, 328, 645–647. doi: 10.1038/328645a0
Rogers, B., Anstis, S., Ashida, H., & Kitaoka, A. (2019). Reversed
phi and the ‘phenomenal phenomena’ revisited. i-Perception,
10(4), 1–22. doi: 10.1177/2041669519856906
Spillmann, L., Saito, K., & Komatsu, H. (2016). Hajime Ōuchi – A mystery
resolved. Perception, 45, 371–374. doi: 10.1177/0301006616637433
Stone, L. S., & Thompson, P. (1992). Human speed perception
is contrast dependent. Vision Research, 32, 1535–1549. doi:
10.1016/0042-6989(92)90209-2
Sunaga, S., Sato, M., Arikado, N., & Jomoto, H. (2008). A static
geometrical illusion contributes largely to the footsteps illusion.
Perception, 37, 902–914. doi: 10.1068/p5689
Thompson, P. (1982). Perceived rate of movement depends oncontrast. Vision Research, 22, 377–380. doi: 10.1016/0042-6989​(82)90153-5
Thompson, P., & Anstis, S. (2005). Retracing our footsteps: A revised
theory of the footsteps illusion [Abstract]. Journal of Vision, 5(8),929. doi: 10.1167/5.8.929
Wade, N. (1990). Visual allusions: Pictures of perception. London:
Lawrence Erlbaum.
Wade, N. J. (2017). Hidden images. In A. G. Shapiro & D. Todorović(Eds.), The Oxford compendium of visual illusions (pp. 774–780).
New York, NY: Oxford University Press. doi: 10.1093/acprof:
oso/9780199794607.003.0113
Zenger-Landolt, B., & Koch, C. (2001). Flanker effects in peripheral
contrast discrimination – Psychophysics and modeling. Vision
Research, 41, 3663–3675. doi: 10.1016/S0042-6989(01)00175-4

All the movies and figures are also available from the webpage shown below.
http://www.psy.ritsumei.ac.jp/~akitaoka/footstepillusion-movies-figures.html

22

Citation: Journal of Illusion 2021, 2: 5612 - https://doi.org/10.47691/joi.v2.5612