Dog Tessellations

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 Grünbaum/Shephard book (on dads flickr)

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

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:

Escher--Dog Tessellation--1938

Escher–Dog Tessellation–1938

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

5 by 6 dog tessellation

Makoto Nakamura–dog tessellation 1–1993 (big)

Makoto Nakamura--dogs 6

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--dogs 7

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

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

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.

Good luck!

Rita the dog

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21 Responses to “Dog Tessellations”

  1. Esther (mom) Buddenhagen Says:

    HI, Rita,
    These tessellations make me a bit dizzy. But once again I’m impressed by the breadth of your knowledge and your wonderful way with words Did you make up the word tessellation? What words have you made up? Do you realize you may be creating entire chains of being by making up words? Moving back and forth and reweaving history? I don’t think I want to create dog tessellations. I’d rather take photos of the ones in our family, especially you. You are my favorite dog and your blog is my favorite blog.
    Love, Mom

  2. Moira Says:

    Great post! I borrowed it for my blog today. Check it out on Dog Art Today…

    http://dreamdogsart.typepad.com/art/2008/08/mc-escher-the-dog-artist.html

    I also recently subscribed to you in my feedreader as I think we have a similar passion for dog art.

    By the way you might also be interested in my recent film “Dogs in Art” that includes the painting on your header The Greyhounds of the Comte de Choiseul by Gustave Courbet.

    View it here…

    http://dreamdogsart.typepad.com/art/2008/06/dogs-in-art-a-new-film-by-moira-mclaughlin.html

    : )

  3. Rachel Says:

    I love these, especially the second and the fourth ones. They make me a wee bit dizzy though.

  4. Moira Says:

    Hi Rita -

    One of my readers is looking for a print of the M.C. Escher Dog Tessellation for his home. I checked the Escher website and didn’t see it. Do you have any idea where he could purchase one? Thank you.

  5. Dog Tessellations « Newton Excel Bach, not (just) an Excel Blog Says:

    [...] Posted on August 31, 2008 by dougaj4 An intruiging tessellation from a dog with a way with words Cover image on Grünbaum/Shephard book: Tilings and [...]

  6. rita314 Says:

    Moira– thanks for the plug over on your real dog blog. Some irony there, I’m the real dog, but you have the real dog blog. Sorry, no clue where your reader could buy an Escher dog pic. They may be rare, knockoffs probably abound though.

    Rachel, Thanks for dropping by. Glad you found something you liked.

    Newton et al. thanks for the link back .. my dad say someday tadpoles won’t be his last post.

    Ma, thanks for writing again. No I didn’t make up the word ‘tessellation’. I only make ‘em up when they need to exist but don’t.

    Rita.

  7. Recent Links Tagged With "mcescher" - JabberTags Says:

    [...] public links >> mcescher Dog Tessellations Saved by TheDailyBuzz on Sun 26-10-2008 Museum of unworkable devices Saved by TexasTopModel on [...]

  8. Hop David Says:

    Rita,

    Here is another dog tessellation:

    http://www.tabletoptelephone.com/~hopspage/Dogtessel.html

    Regards,

    Hop

  9. rita314 Says:

    Thanks, Hop David. That is a fine dog tessellation indeed!
    BTW, dogs are never ornery (‘cept Cosi, of course).

  10. bruce bilney Says:

    Hello Rita, I love tessellations too and I’ve done quite a few myself including one of Dogs, the Black Dog of Depression (which can be reversed to be the White Dog of Levitation too.) See mine at http://www.ozzigami.com.au, go to Tessellations page in particular. It may take a while to load, it’s an old site, but quite a goodie in some ways. You didn’t make up the word tessellation, no, in fact the word tessellae (tiles) comes from Latin, the Romans got it from the Greek tesserae (mosaic pebbles) so it’s at least 2400 years old. But I do claim to have made up the word tessellanimation, of which I’ve done just one, Quantum Leap, tessellated Kangaroos in motion, as you may see. Makoto Nakamura did an earlier DOG one, Quantum Dog, I punned a little on his name when I did mine, tee hee. I adore Dogs, I think they are dreadfully underestimated – Did you know that they are now known to be able to smell some kinds of cancer, and to foresense incipient heart attacks in humans? But having raised joeys (baby kangaroos) I adore them too, and I think their motion is the most graceful of all land animals, no argument, so I am both humbled and proud at having been able to express my adoration in terms of eternally-jumping roos in tessellation. Kangaroos are the best at tessellating in still designs too.
    Escher’s best Dog tess is called Bulldogs, though I do like the Hound-like one of his that you show.
    Patrick Snels has a tessellations site, google ‘ tessellations knights ‘ will get you to the page I mean, he has HUNDREDS of designs there by many tessellators, including several designs by me, in fact my design Big Game is the No.1 most-hit-on to my glee.
    Finally, do I understand you to say that you are a Ranga? (i.e. redhead)? I am. Look up ranga on the Net, what fun. DUNheads of all shades give us a hard time but I reckon it’s just that they’re jealous and burn their eyes on our fire. They can’t help it. Red Power Rules eh!

  11. rita314 Says:

    Thanks Bruce, you are a real tessellator! My dad has a tessellanimation over on his blog, something about poly wogs if I remember correctly. But he got if from somewhere else, and just put it on his blog mostly to see if it would work after the blogging software had its way with it.

    I hope I never smell any cancer, life is tough enough around here without that! Is Escher’s bulldogs on line, I don’t think I’ve seen it?

    Didn’t know I was a ‘Ranga’ but for sure I’m red, pretty much all over! Yup, red power!

    Your friend,
    Rita

  12. bruce bilney Says:

    Dear Rita,
    Iwould think that those “poly wogs” (tadpoles in Australia) are the wonderful tessellanimation of Patrick Snels, whom I mentioned in my last missive. Google ” tessellations knights “, it will come up #6 in his big list in which my ” Big Game ” is the very first as I said before. Patrick calls them Animated Reptiles but I wrote to him telling him I thought they were too slithery for reptiles, I said they had to be amphibians as your Dad thinks too. They form the most fluid of all tessellanimations, but I think my Quantum Leap Kangaroos are untouchable anyway. You may see them on my website in 6 colours, but they are easier to follow in the simpler version found on the list on Andrew Crompton’s tessellations site.
    “Red all over” eh! Sounds evocative! Have you looked at my blogsite? http://ozzigami.blogspot.com/ A good bit about Rangas there.
    What’s your Dad’s blog? And, where away do you live? I’m in Adelaide, Australia. Oh yes, look up Redhead Day in Breda, Holland, it’s an annual event now each September, gee I’d like to get there this year.
    Bruce

  13. kim Says:

    You are an Amazing dog drawer you should be famous because you are not famous now right i am so kind aren’t i

  14. german Says:

    its very beutiful and nice.

  15. rita314 Says:

    Thank you german. I am glad you like it.
    Your friend,
    Rita the dog

  16. kelsey Says:

    you need to explain how to make them and then email me please

  17. Daniel Wyllie Says:

    Hi rita. You must see my tessellation. Have fun. :-)

    All bark and no bite

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