Author Archives: Stuart Anstis

About Stuart Anstis

Professor of Psychology at UC San Diego. Ph.D. from Cambridge, supervised b Richard Gregory. Published about 170 papers on visual perception, especially illusions. A Humboldt Fellow, a visiting Fellow at Pembroke College, Oxford, and recipient of the Kurt Koffka Medal for outstanding contributions to vision research.

Second Order Motion


Early Study of Second Order Motion

I made this movie  clip in the 1970’s, when I had more hair than brains.  Randomly- spotted vertical rods were held in a frame so that they could move up and down along their own length but not sideways.  When I slowly pulled the rug out from under them, they fell in sequence, so that a contour (defined by vertical motion) moved to the left.

I then turned the machine upside down and cranked the handle.  The rods, resting on the barley-sugar twist table leg, moved up and down sinusoidally, producing a travelling wave of second-order motion.  Since this ‘motion grating’ was defined by texture, not by luminance, a Reichardt motion detector would be blind to it.  Observers could see it quite clearly.  I looked for a motion aftereffect but found none.

Bicycle Spokes


The sectored grey disk steps around clockwise. The thin grey spokes never change their brightness or position, yet they appear to drift around counterclockwise.  Gaze at the centre for 20s, then stop the movie, and you will see a clockwise motion aftereffect in the spokes, so we are stimulating low-level neural motion detectors.  Below: A spoke appears to move only when a sector of the same luminance effectively jumps across it.

As a demonstration, the disk jumps back and forth through one sector width (darkest sector made green to show better).  Look carefully within the red rings, where the spokes are the SAME grey as the sectors that flank them, and you will see the sector borders move OPPOSITE to the  overall sector movement.  The locus of these tiny counterclockwise movements runs clockwise around the rotating disk.

Flying Bugs and Induced Movement

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No flies on Rama: The flying bugs illusion
These two bugs fly clockwise along circular orbits of the same size, in all 3 movies. They are in counter phase; one is at 6 o’clock when the other is at 12 o’clock.
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Now the right orbit looks twice as big as the left orbit, because the CW moving background is in phase with the LH orbit but in counter-phase with the RH orbit, which it enhances.
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The orbits look elliptical, wide on the left and tall on the right.  The background moves CCW and is in counter-phase with the horizontal components of the left fly but the vertical components of the right fly.

El Greco

What if El Greco were astigmatic?

Why did El Greco (1541-1614) paint such elongated figures?  Could he have suffered from a visual astigmatism that optically stretched his visual field?  Art historians strongly doubt it, and logicians ague that this is a fallacy because any visual defect would affect sitter and painting equally and would cancel out.


I converted a volunteer into an ‘artificial El Greco’ with an experimental telescope that expanded the world horizontally.

When asked to copy a square, she drew an exact square copy, but when asked to draw a square from memory, she drew a tall, El Greco-style rectangle. This might suggest that El Greco’s portraits from life would be normal, but his portraits from memory would be elongated. However, the volunteer adapted over two days to the visual distortion; a series of her drawings of a square from memory gradually became perfectly square. So even an astigmatic El Greco could have painted in normal proportions if he chose. His elongations arose from his mannerist style, not from defective vision.



Motion undershoot. Bar rotates through 180°, from 12 to 12 o’clock.  But it appears to move only from 1 to 11 o’clock.

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Same as the ring but for linear motion. Red and green bars are in the same position but appear to be offset. Try tracking them with your eyes; your eyes feel as if they move, but they really don’t!!

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Same idea here! Right-angled cross looks wonky because moving sector edges shift the cross arms more than moving middles of sectors.

Reverse Phi


The four spots move back and forth in exact synchrony, in the direction shown by the arrow.  The two upper spots are correctly seen as moving in the direction of the arrow.  However, the two lower spots change their polarity between black and white as they shift.  These are perceived as moving backwards, toward the earlier stimulus and opposite to the true displacement.  This is reverse phi.  It is consistent with Ted Adelson’s motion energy model (JOSA 1985).

Both movies are identical and both rotate clockwise.  But in the right movie the dots are black and white on alternate frames, and appear to rotate counterclockwise.  This is reverse phi (Anstis 1970: Anstis & Rogers 1975), in which the motion energy does go counterclockwise.
Gaze at the centre of each movie for 20s, then stop the movement.  Which way does the movement aftereffect go?  CCW in the left-hand movie of course.  But CW in the right-hand movie, appropriate to the perceived motion direction, not to the physical dot displacements.
This shows that reverse phi does adapt neural motion detectors; possibly in brain area MT (V5).

In this reverse phi movie, made by PATRICK CAVANAGH, the spokes reverse their polarity on every movie frame.  Thus the inner ring actually steps counterclockwise (track a spoke with your eyes to check this) but it seems to rotate clockwise.  The opposite is true for the outer ring.  Adapt to the motion for 20s, then stop the motion (by clicking twice on the central fixaton spot).  In the motion aftereffect, the outer ring appears to move CW and the inner rinig CCW — appropriate to the illusory reverse phi, not to the physical displacement.

Four-Stroke Cycle

Each little disk is a four-frame movie, all with the same face, in a sequence positive-positive-negate-negative.  Gaze at the central fixation point for ~30w, then click on the same fixation pout.  The motion will stop and you will see a strong motion aftereffect in each disk.  So the four-stroke cycle is stimulating low-level cortical motion detectors.

Obama seems to move to the left and Trump seems to move to the right.  Neither changes his average position.

Vertical four-stroke drift:  Currencies

Rotating landmarks

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Vertical movement
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Horizontal movement
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Each movie is four frames long, in the sequence positive-positive-negative-negatives.

All Kinds of Motion

When the black and white bars switch places, on a dark surround (left) the white bar appears to jump, but on a light surround (right) the black bar appears to jump. The bar with the higher contrast wins out. The mid-grey at which the motions balance is the arithmetic (not geometric) mean of the black & white, suggesting linear, not logarithmic processing of luminance. (Anstis & Mather, Perception 1986).

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Ambiguous apparent motion. The two spots move either vertically or horizontally. Can you control the direction by willpower?

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Proximity: Motion is seen between nearest neighbors, horizontally on the left, vertically on the right. Shorter motion paths win out.

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The motion path changes gradually from a tall, skinny rectangle to a wide, flat rectangle. Perceived motion is always along the shorter side of the rectangle. Proximity wins.

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Visual inertia drives ambiguous apparent motion. Each spot appears to follow a horizontal path, not jumping up or down halfway across. Straight motion paths are preferred to going round corners.

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Do these all move together or do they move individually?

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The center dot simply flashes on and off but it gets entrained by the other dots and seems to disappear and reappear from behind the green square. [V.S. Ramachandran]

Kinetic Edges

Although the three windows are actually aligned vertically, the central window appears shifted to the right, in the direction of the drifting dots that it contains.

Eight circular windows, arranged in a circle, contain random dot textures that move counterclockwise. Although the windows themselves are not moving, they appear to rotate together like a ferris wheel. This is a stronger version of the illusion demonstrated above — it introduces continuous illusory movement, not just a static illusory shift. Also, after fixating for a while, you may perceive the windows fade out and disappear.