# Illusion explained

September 9, 2014 • 9:16 am

Well, sort of, because it’s long and complicated, and you might not want to go through it. This drawing, which I presented yesterday, is a version of the Café Wall Illusion (the link tells you how it got its name). The lines look curved, but are really straight, as you can check with a ruler or piece of paper:

It also comes in a version lines that don’t appear wavy, but tilted:

The explanation is given in an online paper (reprinted from Perception [1979]) by Richard Gregory and Priscilla Heard.  It involves the luminescence of the squares, the width and luminescence of the separating “mortar” lines, and the degree of offset of the squares.

If you click on the screenshot below, you can go to a site where you can vary these things with slider buttons, and see how they affect the illusion:

## 7 thoughts on “Illusion explained”

1. jsoon71 says:

Hello. Cool illusion. One small error noted: the effect depends on the contrast, width, and luminance, rather than luminescence, of the squares and mortar lines.

2. Hmm. Of course the width and offset of the squares is involved, but that’s not really an explanation.

I don’t have time to read it, but I wonder if the paper says anything about the wavy-line version resembling the phenomena of constructive and destructive interference. The “bulges” in the wavy-line version occur when black squares more-or-less line up and would correspond to constructive interference; the “nodes” appear where the squares more closely resemble checkerboard arrangement and would correspond to destructive interference.

3. I have an hunch that we won’t have a satisfying explanation of this until after we’ve got a mathematical model. (Do we?)

Here’s an experiment I think I’d like to see done. It’d be perfect to do with college students.

Generate an example of the illusion. Have the subjects adjust a set of not-parallel lines to approximate the appearance of convergence / divergence / spacing / etc. until they think they’ve got a good match. Repeat with many different variations of the parameters.

I expect there’d be a good deal of consistency from subject to subject and for a solid formula to be derived that predicts the appearance of the not-actually-converging angles. With that in hand, it should then be possible to start looking for physiological phenomena that provide a good match….

Cheers,

b&

4. jsoon71 says:

One of my colleagues has done some research in this area (see McCourt, M. E. (1983). Brightness induction and the Cafe Wall illusion. Perception, 12, 131 142), and I have it from him that the Border Locking explanation proposed in the Gregory & Heard paper has not survived scrutiny. He directed me to the paper below, which provides an (at least partial) explanation based on spatial filtering processes occurring in the retina:

http://www.perceptionweb.com/abstract.cgi?id=p5646

Consistent with Ben’s proposed approach, I believe their spatial filtering based approach was likely suggested by a combination of behavioral experiments clarifying the perceptual conditions that produce/eliminate the effect (like the Gregory and Heard paper), together with a refined understanding of how the retina processes light.

5. Roberto Aguirre Maturana says:

Sorry if this have been mentioned before in WEIT or in the publication but…have you looked to this drawing with your eyes crossed, like a 3D stereogram? It looks even better.