Amazing optical illusion and Spirograph


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Make the outside an oval and the circles in the shape of a triangle and you have a rotary engine.

y = sin(wt).


“did you know that there’s a direct correlation between the decline of Spirograph and the rise in gang activity? Think about it.”


I was going to ask, is that an optical illusion or just math?

Since the illusion requires that the velocity of the dots is being adjusted as they travel along the straight line, I’m voting “math”.

Um… by using one dimensional X and Y values (by definition lines) as the axes of a two dimensional plane, with X’s value changing based on radius * sine(time) and Y based on radius * cosine(time), it plots a circle. Why is this illusion particularly surprising? Linear data plots circles all the time. In fact, for each frame, if you took the horizontally oscillating dot, and moved it up or down to match the height of the vertically oscillating dot, it should plot the circumference of the larger circle.

It’s a fun illusion, no mistake.

But I had an actual Spirograph, back in the day, and as memory serves (it’s been a l - o - n - g time), you would only get that result if the inner wheel had exactly half the teeth of the outer ring, and the pen were positioned at the exact outer edge of the inner wheel…

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