My dad wanted this on his blog. He said it was about geometry. I said it was dog art. He said the best you could say is that it was dog graphics. But we agreed on the dog part, so he had to capitulate.
A tessellation is like a jigsaw puzzle where all the pieces have the same shape but they still fit together without any gaps. The squares on a tile floor would be one example. The figure below is a more complicated tessellation which is composed of identical 9-sided polygons but has a 3 dimensional feel, appearing a bit like two snakes wrapping around eachother:
Cover image on Grünbaum/Shephard book: Tilings and Patterns
Click on the above image to see it larger and, for more information, see the description at my dad’s flicker page, here.
If it were possible to make a tessellation where each piece was a dog then you would have a dog tessellation. For a long time I didn’t think such a thing could exist. I knew about that Dutch master graphic artist named Escher. He did lots of tessellations where the pieces were animals, so I asked the old man if Escher ever did one with dogs. My dad has seen just about all the Escher art there is to see and he said there weren’t any with dogs. There was a pretty nice one with fish he said and he showed me this one, which isn’t too well known:
Escher–Fish on Textile–1942 (big)
Well, that’s that, I thought. But then one day the old nose got to sniffing and pretty soon sniffed out an Escher piece with dogs. Yup, thought I, there are some advantages to being a dog. I’m pretty sure Escher had it in a notebook or some private file, because its not done as carefully as the public work he exhibited, and parts of the red have faded since he made it, way back in 1938. But a dog tessellation it is, and possibly the first one ever made. Have a look:
I was pretty happy there were some red dogs in there, since, as you must know by now, I’m a red dog too. Those dogs really look like dogs and yet they fit together perfectly. I take my hat (figuratively speaking since I don’t actually have a hat) off to Escher. Maurits Cornelis Escher lived from 1898 to 1972. The official Escher web site, where you can see lots of his other work, is here.
Nowadays lots of clever people have created tessellation art similar to Escher’s tessellations with animal images. People today have the huge advantage of using special computer software to help them design and create the images. But you won’t see many woodcuts, and for my taste Escher did it best.
Here then are some modern dog tessellations. The first three are by Japanese graphics design artist Makoto Nakamura
Makoto Nakamura–dog tessellation 1–1993 (big)
Makoto Nakamura–dog tessellation 6–2004 (big)
To me those dogs look too much like rabbits. Here is the last example by this artist.
Makoto Nakamura–dog tessellation 7–1988 (big)
You can find a huge variety of other graphic art at Makoto Nakamura’s page, most of it not dog tessellations. Just click here.
The next image is a dog tessellation by Yoshiaki Araki, who appears to me to have been a youngster in Japan when he did tessellations. Information about this artist is scarce, but my reading of tea leaves leads me to believe that he parlayed his interest in tessellations to an interest in Kleinian and Fuchsian groups and computer graphics, got a PhD at Keio University, and found bigger fish to fry. This is guesswork, not fact, so don’t quote me, and if you must be sure to say you heard it from Rita the dog.
Yoshiaki Araki–dog–date unknown (big)
For the last dog tessellation, here is an image by a 10 year old girl named “Kaitlyn C”, who won some sort of prize for it.
Kaitlyn C–age 10–Dog Tessellation (big)
This concludes my post on dog tessellations. If you want to see more you can certainly find them on the Internet, but I would urge you to try and create one for yourself.
Rita the dog