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Patterns - reflection, rotation and translation
& Comic Book Picture 16, Metamorphosis
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Nothing transforms an object more than being incorporated into a pattern. Nobody knew that better than the mid twentieth century artist Mauritz Escher, and you can see many examples of his experiments with patterns on the Escher Foundation website (in left sidebar, click on "picture gallery" and then on "symmetry").

Patterns seem simple - a matter of repetition of shapes. But there turn out to be surprisingly fascinating rules and constraints.

At the heart of every regular pattern there is an element that is not made up of regular repetition within itself. So for example, a whole face would not qualify, because it would include repetition by reflection - only a half face, like the one to the left, will do. There are actually just four ways that such an element can then repeat, combining with itself over and over, to cover the plane. It can just move in regular steps (translation); it can be reflected (like the two halves of a face); it can be reflected but offset (in what is called a glide reflection); or it can be rotated round a point (like the hands on an old analog clock face). Several of these kinds of repetition may combine.

For example, starting to the left with a letter P here, we make a pattern by first reflecting it, then repeating the result three times in a rotation through 360 degrees, and then repeating that result by reflection, into a hexagonal scheme.

There's an introduction to making patterns like these on my other site

Note the striking brilliance of the light from the lighthouse. That's an illusion, see the commentary to comic book picture 5, The Island.