Polarised ice pic

ice blades

Like our bubble pictures this is not really an illusion, but I am fascinated by natural shapes.  It’s a picture of blades of ice, and what you see here is about three inches across.  The colours come from taking the picture in polarised light, as the crystal blades were forming in a shallow dish of water in a freezer.

Want to try your own pictures? The preparations are not trivial, but there’s nothing a school science section couldn’t handle.

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Which way around is Mercury going?

Does Mercury look like he’s rotating clockwise or anti-clockwise?  That may depend on whether you look at the left hand figure, or the silhouette.  That right hand silhouette figure can appear to rotate either way round.  Some viewers find that it flips from clockwise to anti-clockwise spontaneously, but others may find it hard to make it flip from one rotation to the other at all.  If it doesn’t change easily for you, try waiting till the outstretched arm is pointing top left, and then try to imagine the hand coming towards you (for an anti-clockwise turn) or moving away from you (for a clockwise one).

When the silhouette figure turns clockwise, it’s rotation mirrors the red figure.  When it flips anti-clockwise, the two figures appear to go round the same way, but with the silhouette figure rotating half a turn out of sync with the red figure. I find the change fascinating, like the figures are doing some kind of old style dance, but two different ways.

The rotation of the right hand figure is ambiguous because in silhouette it presents exactly the same image whichever way it turns. Add the reflections and shadows of the red figure and it can only be going one way around.

I made the individual frames for the animation by taking successive still photos all around a reproduction of the original sculpture.  (The original was made by Italian sculptor Giambologna just over four hundred years ago, and is in a museum called the Bargello in Florence, Italy).

Big Ben leaning over!

Big Ben

Does Big Ben look like it’s leaning over more in the right hand image than in the left hand one?  It can take a double-take to spot that the two pictures are identical. I find it a fantastically strong illusion.

It’s a demo of a new illusion found by Frederick Kingdom and colleagues (you’ll need to scroll down that link to get to their bit – look out for an even more than usual Leaning Tower of Pisa). Their discovery is a new version of the size-constancy illusion. This is my second demonstration of it – a few posts back I used a picture of a historic streetlamp. But here’s an example that looks stronger to me, with a better known subject.

Update 10 Oct 2011.  Big Ben really is leaning over! But not (yet) as much as it appears to lean in this illusion.

A tessellation pioneer

You probably know the tiling patterns of M.C.Escher.  But how about Koloman Moser?  Here are a couple of his designs.

 

Moser tilings

Moser was working in Vienna, Austria, a hundred years ago.  (He died in 1918).  I don’t know where he would have learned to do tessellating designs, that is, designs with motifs that repeat the way jigsaw puzzle pieces fit together, with no gaps or overlaps.  If you have checked out our tessellation tutorial, you’ll know that the secret of these designs is that the edge of each “tile” of the pattern must be able to be snipped into pairs of identical line segments.  Here’s how it works with Moser’s fish design.

Moser design demo

To the right you can see that the fish outline can be divided into three pairs of segments, a yellow pair, a red pair and a blue pair.  In the yellow pair, the top line is just repeated lower down to make the pair, in a move called a translation.  The red and blue pairs are a bit more complicated.  In each pair, the lower line segment is a mirror reflection of the upper segment, but shifted downwards.  That kind of shifted reflection is called a glide reflection.  It’s a fact that any motif whose edges can be snipped into one pair of segments that repeat by translation, connected as here to two parallel pairs whose edges repeat by glide reflection, will tessellate perfectly.  And that’s just one of 28 recipes for motifs that tessellate.

The second Moser design is based on a superficially simpler recipe, but it’s very, very clever.  In fact, it’s fiendish …..

So much so that I’ve had to correct the commentary at 13 May 2012! ….

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