Origami: Arrow illusion

So, you know how things in mirrors always have left and right reversed?  This origami model is no exception.

An origami arrow in front of a mirror. The arrow points to the left, while the reflection points to the right.

Arrow Illusion, my design.

The arrow illusion was inspired by a much more impressive optical illusion, the Ambiguous Cylinder Illusion.  Video below the fold.

[Description: a series of illusions using objects that look like cylinders, but whose mirror reflections look like squares.  Whenever the objects are rotated 180 degrees, they look like squares, but their reflections look like cylinders.]

YouTube suggested a few responses to this video, with people recreating the illusion with 3D printers and explaining how it works.  Although, I’m not sure why they bothered, when the author of the illusion, Kokichi Sugihara, literally published an academic paper on the subject!  (Incidentally, both of those video responses got the math wrong.)

Anyway, I obviously don’t have a 3D printer, so I wanted to design an origami version of the illusion.  At first I wanted to make an ambiguous cylinder, but curved origami is hard, and it was a bit too much math even for me.  So instead I went with the first example in Sugihara’s paper, an arrow.

Update: If you’re interested in making this model, I show folding diagrams below.  However, I later redesigned the model to be easier, so see this page for the updated diagrams.  You may print these diagrams for yourself, but if you would like to distribute them please ask me for permission (and proper pdf copies).

Page 1 of arrow illusion diagram Page 2 of arrow illusion diagram



  1. Bill Buckner says

    Mirrors don’t reverse left and right. (If the reversed left or right, then why not up and down? There is nothing special about the horizontal direction). What they actually reverse is front to back.

  2. says

    @Bill Buckner,
    Generally when we look in a mirror, we interpret what we see as a left-right reflection + 180 degree rotation (which is indeed equal to a front-back reflection). What’s special about the left-right reflection is that it’s more intuitive to imagine a 180 degree rotation around a vertical axis (an everyday activity) than a 180 degree around a horizontal axis (a gymnastics activity).

    The arrow illusion is a twisted satire of our intuition, exposing the hypocrisy at the very core of our being. 😉

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