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Cycloid illusion: Are these dots really moving in a circle?

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In this Brusspup mind-bender, you may think you see a circle of eight white dots rotating around the inside of a larger red circle, but you’re actually witnessing something else, and you may not believe it unless you see it explained… but then you still might not believe it.

To quote Phil Plait: “For most illusions there’s a moment when your brain can see what’s going on and the illusion shatters, but not with this one.”

“If you want the math, then here you go: The shapes made this way (tracing the motion of a point on a circle as it rolls) are called cycloids, and there are a lot of varieties: epicycloids, hypocycloids, and others, depending on how the inner circle is rolled…

“I’ll note that when a circle rolls along a straight line, if you watch a single point on it you can break the motion up into two dimensions: Horizontal and vertical motion. These motions aren’t constant, but depend on the sine and cosine of the time elapsed. They start off motionless, accelerate to a maximum speed in the middle, then slow back down to zero … and in each direction, the point moves linearly! It’s only when you combine them that you get the cycloid.

That’s how this illusion works. By mimicking this trigonometric motion, your eyes and brain are fooled into thinking the dots are acting together, portraying the rim of a circle. But they aren’t; their motions are related but independent of one another (what’s called “parametric” in mathematics).”

Related watching: more optical illusions, including Kokichi Sugihara’s impossible motion illusions, as well as Brusspup’s amazing anamorphic illusions and the Amazing T-Rex Illusion.

via Bad Astronomy.

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