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MatheMUSEments
Morphing Art
By Ivars Peterson
Muse, November 2000, p. 26.
When you're riding along on your bike or in a car, you
sometimes see the word "ONLY" painted on the roadway
just before an intersection. The white letters look normal from
where you're sitting. But if you were standing beside the "ONLY"
instead of riding toward it, the letters would look stretched out.
It's only when you look at them at the proper angle that they
don't look distorted.
Artists have long used the same idea to create visual puzzles.
A viewer sees an object in a picture correctly only if he or she
finds the right angle at which to look at it. Such distorted
pictures are called anamorphic images.
One of the most famous examples is a painting called The
Ambassadors by the German artist Hans Holbein the Younger. It
shows two young men standing in front of tables overflowing with
books, instruments, and globes. At their feet, the artist painted
a weird shape that turns out to be a grinning skull when you hold
the picture at a slant (see
www.abcgallery.com/H/holbein/holbein16.html
).
You can create your own slant picture. You start with a piece
of paper ruled into square cells and another ruled with the same
number of trapezoids—squares that are stretched out in a special
way. Draw your picture on the square grid. Then carefully copy
the contents of each square of the original grid to the
corresponding trapezoid of the other grid. You'll find that
you'll need to stretch the lines of your drawing to make sure
everything fits together. You end up with a stretched-out version
of your original picture, but if you look at it from the right
angle, it'll look undistorted again.
Some artists have tried more elaborate schemes. It's possible,
for example, to draw or paint a picture you can understand only
if you look at its reflection in a mirror shaped like a cylinder
or a cone. The mirror takes the distortion out of the image.
About 200 years ago, anamorphic paintings for cylindrical or
conical mirrors were popular toys in both Europe and Asia. You
can still find examples in some museums. Nowadays, you can buy
anamorphic jigsaw puzzles, which you can assemble and view with a
special mirror to reveal a hidden image. And artists have created
amazing pictures that must be reflected by shiny spheres,
mirrored pyramids, or other mirrored shapes to show their true
identity.
It's a neat game of hide-and-seek for the eye.
Learn more about anamorphic images at physics.uoguelph.ca/morph/main.html.
You can buy MorphMagic anamorphic jigsaw
puzzles at www.tessellations.com/.
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