# Playing with patterns

In materials science class, we examined wallpaper patterns for symmetries. Atoms and molecules can pack according to a variety of crystal structures. Mathematics obviously loves patterns too. There are fractal tilings and tessellations. Who doesn’t love Escher? There are probably practical applications to tiling, but more importantly they are great fun that tickles the brain. Recently I took my first stab at pattern making depicting (what else?) water polo.

# M.C. Escher: revisiting a familiar name

M.C. Escher and Salvador Dalí are two of the greatest reality-bending artists. So, fittingly, the Salvador Dalí Museum in St. Petersburg, Florida recently hosted a special Escher exhibit. I’ve visited the Dalí collection many times, but I’d never seen Escher in person.

I had many Escher calendars as a kid. When I took crystallography, we studied the symmetries in Escher’s tessellations. I’ve always been interested in design and mathematics, and Escher is the purest intersection of the two. I was ecstatic to see the exhibit.

Before the exhibit, I was most familiar with Escher’s lithographs. Without too much elaboration, lithography is a high-fidelity technique which allows the artist to produce an image that is not directed by the mechanics of printing (I’m sure the method does direct some artistic choices, but as a non-expert, that’s my rough take on it).

The exhibit contained many of Escher’s woodcuts, which were new to me. Woodcuts are make by carving a plate of wood, coating the plate with ink, and pressing the plate to a page. The page will be white where the wood has been cut away and the page will be colored where the wood remained. Woodcuts have a distinctive style–they cannot render colors in between white and ink color. Multiple colors can be achieved with additional pressings, but the technique is inherently color-limited.Additionally, the resolution of the print is limited to the fidelity of the wood. These two aspects give woodcuts a distinctive artistic feeling. If you can’t tell, I’m currently a little in love with woodcuts.

Escher died in 1972, but thanks to Disney, his works remain out of the Creative Commons. However, I am allowed to use low-resolution works for discussion purposes. You’ll have to buy books if you want anything with much detail, though. Below are a few of my favorite Escher images that are available through Wikipedia, as I have linked them under the image.

Some of Escher’s early works were illustrations. There was a beautiful cathedral, half underwater. There were evil-looking creatures in forests. It was such a romantic side to an artist most think of as a master of geometry. Below is an example of one of his illustrations. Even though it’s of a conventional subject, the Tower of Babel, the perspective is beautiful. I love the lines; this work just wouldn’t be whole using a method besides woodcut.

Below was Escher’s first impossible reality. And look, it’s a woodcut! Hooray!

Still Life and Street: Escher’s first impossible reality

Below is one of Escher’s more famous images. It is a lithograph printing. See how various tones of gray are possible with this technique, as well as high-fidelity. It lends this images a very different tone than the one above. The lizard design is called a tessellation. Tessellations are plane-filling patterns. They occur in nature and area subject of mathematical study. Escher was inspired by the tiling work at the Alhambra in Spain, another example of tessellation.

Below is another Escher woodcut, done with several plates to achieve multiple colors. Even when Escher wasn’t exploring impossible realities of geometry puzzles, he chose interesting perspectives.