An optical illusion created by Kohske Takahashi: All the lines are smoothly curving sine waves, but their shading and contrast with the background makes them appear to be sharp zigzags. Credit: Kohske Takahashi
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An optical illusion created by Kohske Takahashi: All the lines are smoothly curving sine waves, but their shading and contrast with the background makes them appear to be sharp zigzags. Credit: Kohske Takahashi

An optical illusion that will zigzag your brain

Contributed by
May 28, 2019

Our brains are kluged.

They’re a mishmash of evolutionary workarounds, upgrades, patches, and jerry-rigged connections between our senses and the kilogram or so of gray gloppy meat we keep inside our skulls.

Because of that they can be easy to fool. Our brains are adapted and trained to work a certain way, and if confusing inputs get sent to them, they get bollixed up. That’s the basic principle behind every optical illusion, really. Patterns of colors, contrasts, or shapes can be put together in a way that throws a monkey in the wrench of how our brains interpret them, and what we think we’re seeing isn’t what’s really there.

Kohske Takahashi, a professor at Chukyo University in Japan who studies cognition and perception, discovered a new illusion that is as much fun as it is baffling. Check this out:

An optical illusion created by Kohske Takahashi: All the lines are smoothly curving sine waves, but their shading and contrast with the background makes them appear to be sharp zigzags. Credit: Kohske Takahashi

An optical illusion created by Kohske Takahashi: All the lines are smoothly curving sine waves, but their shading and contrast with the background makes them appear to be sharp zigzags. Credit: Kohske Takahashi

OK, no biggie, right? It’s just a bunch of alternating pairs of lines, where one pair is curved and the other zigzagged, right?

Yeah, no. Here’s the fun bit: All those lines are smooth sine waves. In fact they’re all the same curve! There are two key differences between the lines. Look carefully at the smooth waves: The curves change shades from white to black, and the change occurs at the inflection point between them (halfway down the sloping curve). Now look at the zigzags: The shading change happens at the peaks and troughs.

The other difference is the background shading. In the middle, where the background is gray, the illusion is extremely strong. It’s almost impossible to see the zigzag lines as smooth curves. Now look at the upper left, where the background is white, or the bottom right, where it’s black: The illusion is far weaker. The zigzag lines look smoother to me there, though still not as smooth as the sine curves. The illusion is still working there, just not as well.

So what’s going on here? Well, no one is sure. Takahashi published a study of this illusion, and in his paper he notes that how our brain interprets curves (separating a straight line from a curve, for example, or two curves with different curvature) is relatively well understood. However, this zigzag illusion is new and not as easy to understand.

Top: Two pairs of the sine waves, where one appears smooth (top set) and one with sharp corners (bottom set). Bottom: Superposing the bottom set of lines on the top set shows they are exactly the same except for the shading.

Top: Two pairs of the sine waves, where one appears smooth (top set) and one with sharp corners (bottom set). Bottom: Superposing the bottom set of lines on the top set shows they are exactly the same except for the shading. Credit: Kohske Takahashi / Phil Plait

He set up different curves to see how well the illusion is perceived, and found that if the amplitude of the curve (the height between crest and trough) is too high or too low the illusion weakens. Where the shading changes is clearly important, as is the background, so contrast plays a role. He thinks that it may be that our brains uses one way to see curves, and another to see zigzags, and they compete with each other. Under certain circumstances they get imbalanced, and the zigzag wins even though the curvature is actually smooth.

Something I noticed is how, to me, the smooth curves look flat to me, just wiggly lines. But the ones I see as zigzags look more 3-dimensional, as if I’m seeing a set of zigzag-shaped steps; the contrast change between white and black looks like shadowing to me (that effect is really obvious to me in the second image above, where I cut out two rows of the illusion to compare them). It persists when I shrink the image and see it at full size, too. In fact I think it may be stronger if the image looks smaller. Takahasi discusses this in the paper, and even tested for it. He changed the contrast in a way that removed the perception of three dimensions (in the paper, see Figure 2, row 7), and the illusion persisted!

So clearly there’s more than one thing going on here. That’s usually the case with illusions; your brain has two ways to perceive something and they have to fight it out (like the Necker Cube illusion, one of my favorites since it’s so basic and if you concentrate you can make your perceptions of it change).

Want to melt your brain even more? One of my favorite animators, Cyriak Harris, animated the illusion such that the lines move horizontally but the shading doesn’t move… like a wave moving through vertical stripes of different shades. Watch:

Yeah, I know, right? Our brains are so odd.

I think about things like this when I watch scifi shows with AI, like androids. Since their brains will be designed by humans from scratch, it seems to me they would not see illusions the way we do. And they may have their own versions of them that we won’t see.

And aliens, too. When we finally meet intelligent aliens, will their fundamental perceptions of the world differ from ours in ways that are so vast that communication will be difficult, if not impossible? How will the stochastic constructions of their own brains (assuming they even have brains like we do) separate them from us in ways we cannot even fathom?

And this is the big reason I love optical illusions. They’re delightful and fun, of course, but they allow us to see the places where our own organic hardware and software have cracks. And the implications of this, when extrapolated even a little bit, are quite profound.

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