Mixing Memory

Everybody’s seen Kanizsa’s triangle:


It’s a simple illusory figure illusion, first reported by Kanizsa(1). The illusion is likely caused by the processes that the visual system uses to separate figures from their ground(2), but to date there doesn’t appear to be any consensus about exactly how these processes cause the perception of illusory figures (here’s a list of several competing explanations).

Recently, researchers in the Human Technology Laboratories have begun producing 3D versions of the Kanizsa triangle:


These figures are created by starting with the original Kanizsa triangle, and adding three regions with different shades (luminances), which converge in the center of the illusory triangle (see the explanation here. Here’s what it looks like with the three little Pac-Man figures reversed, so that the contours of the triangle no longer appear (from here):


As if a 3D version wasn’t enough, two members of the HT Lab team, Pietro Guardini & Luciano Gamberini, won second place in this year’s Best Visual Illusion of the Year contest with moving 3D Kanizsa triangles (Kanizsa pyramids, I guess). You can see the moving pyramid here . All they do to make it look like the pyramid (which isn’t actually there, remember!) is moving, is move the edges of the different luminance regions around. Man, our visual system is easily fooled.

1Kanizsa G. (1955). Quasi-perceptional margins in homogenously stimulated fields. Rivista di Psicologia, 49, 7-30.
2Liinasuo, M. Rovamo, J., & Kojo, I. (1997). Effects of spatial configuration and number of fixations on kanizsa triangle perception. Investigative Ophthalmology & Visual Science, 38, 2554-2565.


  1. #1 Scott Belyea
    May 20, 2007

    I have no idea what the typical “reaction time” is to see the triangle in the basic illusion, but it took me a while. I looked for maybe 5 seconds, saw no illusion, and then scrolled down and read a bit. Scrolled back up … nothing. It wasn’t until I focused directly on the centre of the figure that the illusion appeared.

    However … it was not a triangle; it was a six-pointed star (“Star of David”). It took a bit of effort to actually see the illusion as a triangle.

  2. #2 Enigman
    May 20, 2007

    I was disappointed at first, thinking how weak the first-place illusion was, how there was nothing weird at all about a picture of a tower next to another picture of the same tower from a different angle (so that it looked like it was leaning more). Utterly fantastic. Whatever next?

  3. #3 Tim
    May 20, 2007

    I was at the vision science conference and this contest, and the reason this illusion got second place was because the guy showing it was hilarious… he was dancing and singing and his slides were very amusing. I didn’t even really get the illusion when I was there — its definitely not such a great illusion.

  4. #4 Chris
    May 20, 2007

    Tim, it’s a very simple illusion, but I think it’s awesome. That we see the boundaries of a triangle just because they’re suggested by three little pac-man figures is cool enough, but the fact that you can make those nonexistent boundaries 3D, and then move, blows me away.

  5. #5 buzz
    May 21, 2007

    To be honest, I think the illusion is hardly special. It is no more special, in my opinion, than arranging a few dots in a triangular formation to make it look like there’s a solid triangle.

    The wedges and pac man figures are glorified dots. They create contrast on the background, much like a black dots would on a white space. (I hope I’m clear with the explanation)

  6. #6 Max
    May 21, 2007

    Has anyone ever investigated the relative salience of these illusions? It seems like if we surveyed, say, 1000 people online, and asked them to rate the salience of each illusion from 1 to 5, and then normalized the rankings we would see two things.

    First, we could analyze the co-variance of the different illusion saliences and thereby infer a common mechanism.

    Second, we could find out to what extent people differ in processing visual information. The most interesting result would be if someone had a hard time seeing the triangle and an easy time seeing the tower, but others were the reverse.

  7. #7 Tim
    May 22, 2007

    Chris, I didn’t mean it wasn’t a cool illusion — it is! I just meant its hard to see for me (and apparently others, like Scott above). I can easily switch back and forth between seeing nothing interesting happen and seeing the pyramid, and the pyramid isn’t a very stable percept even when I see it.

  8. #8 Chris
    May 22, 2007

    Tim, ah, OK. It’s pretty strong for me. It might be interesting to look at individual differences in these sorts of illusions. At the very least, it might allow us to distinguish between the various explanatory hypotheses.

  9. #9 Kevembuangga
    May 23, 2007

    Even when the pacman figures are outward I can still the whole 3-walls corner reversing but the reverted perception isn’t very stable.

  10. #10 CA
    May 23, 2007

    I was really entertained by these illusions. Interststing that others had a hard time seeing them. I agree with you, chris, it might be real intersting for someone to study individual diffferences. Maybe it is like broccoli; some get it and some don’t; all related to genetic programming. Hey, that would be another interesting study if you find reproducible individual differences.

  11. #11 C A
    May 25, 2007

    I was really impressed with how strong the images are. Others weren’t. I agree, Chris, it would make an interesting study to look for individual differences. I wonder if it is like broccoli; some get it and some don’t. If it is like broccoli, the differences would be in the genes. Hey, familial differences would be another study.

  12. #12 Pietro Guardini
    May 31, 2007

    Hi everybody,
    I really appreciate your comments on our illusion. Just let me add something you may find interesting.

    The first issue here is studying illusory contours (IC) on heterogeneous backgrounds: there are more than 500 publications on IC, and in nearly all of them authors superimposed pacmen on white/grey/black backrounds. Let’s say we are studying IC formation from a new point of view (note that some authors already used this method).

    More important (as Chris wrote), there is no clear explanation of IC and using heterogeneous backgrounds can help. Occlusion cues (the open mouth of pacmen) play a crucial role indeed: in the Kanizsa triangle, you see an OPAQUE white triangle placed over three circles and an outlined triangle. But what happens when you can also see THROUGH the IC figure? It’s exactly what we have using non-homogeneous backgrounds.

    You may find interesting this:

    Purghé (1998) Can illusory figures be transparent and opaque at the same time? Perception 27(3) 337 – 340.

  13. #13 tory
    October 28, 2007

    this is cool i like the 1s wher its black pacmans and white pacmans since im left handed i can really tell what it is easier and faster cuz our minds r smarter lol but the black makes the triangle a popping out pyramid and the white is a going in pyramid this is so awesome

  14. #14 Jessie
    October 18, 2008

    you can make black a “going in” pyramid too.
    i’m also left handed.

  15. #15 mahesh
    May 15, 2012

    DOES THE RIGHT ANGLE MAKE US SAPIENS SAPIENS? I had a very interesting talk with a young woman who was recently diagnosed with Aspergers. her mind producers SQUARES in quilt-like patterns which she is compelled to express by drawing on paper. she’s been seeing squares in her mind even before she knew what one was. are we all seeing squares all the time, but we just don’t know it?

    squares do not occur in nature: pointied things do (teeth, mountain tops), oblongs do (faces, fingers, torsos, forearms, ears…). however, humans create squares EVERYWHERE: doors, windows, iphones, ipads, computers, playing cards, books… is a square (or a right angle) a PRIMITIVE CONSTRUCT wired into our brains, something that animals don’t have? is this what sets us apart from animals? is there a low-energy state in the visual perception of a right angle that is not in the others?

    if so, what about bees (hexagonal hives) and spiders (radially symmetrical webs)? why didn’t their regular pattern catch on and give them intelligence?

    human vision works this way: we detect the edges of an object, then we “fill in” the insides with the general colour that we perceive, i.e. we _recreate_ the object from our own primitives. we don’t do sharp points well — they “leak” color. there is a checkerboard visual illusion that shows this. why do we (i assume) still treat right angles as something special?

    anyone else with knowledge in neuroscience or aspergers who wants to weigh in?