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Colorful Tessellation

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(Spell check?) A tessellation I made in my math class.
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© 2011 - 2021 AnScathMarcach
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Peter-Dow's avatar
Impressive.

I'm no art critic Cori - more of a mathematician - but I know what I like and I like this.

Can I ask about your inspiration for the tessellation pattern drawn in black lines?

Firstly, what would you call the basic tessellation element shape - "H-shape", "dumb-bell shape", what?

Secondly, did your math class teacher suggest some basic tessellation patterns and you picked that one and drew it and coloured it in (it's OK, I am British, that's how we spell "color", with a "u") or how did you come to pick that particular tessellation pattern? Maybe you just thought it up using your own imagination and genius?

I am curious as to whether that is a well-known basic tessellation pattern which appears in a mathematics or art book somewhere or whether this is original?

If I ever did redecorate I'd be happy to put up a wallpaper with that design on it!

I trust that you got full marks in your math class for this drawing?


Comment by Peter Dow
AnScathMarcach's avatar
Wow, you seem to take particular interest in it.
As for my inspiration, it wasn't much more than wanting to do something unique knowing nobody else was going to put more effort into it. I just decided to do a letter I shape since they fit together and I put some colorful gradients in.
I'm not sure how well known it is. I don't think I've seen it before. Our teacher did show us some other ones, but they were even more basic like hexagons and such.
If you would like to use it, feel free as long as you give me the credit. I appreciate your interest.
Peter-Dow's avatar
Yes your work is of particular interest to me because I am not one for commenting on works of art normally. I joined this Deviant Art site specifically to comment on this work of art though it is not the first time I have viewed the site I am not a regular visitor here.

Actually, I found your image via a google image search. I was searching for "tessellation" with other search terms, maybe "H" or "I" or "dumbbell" or something, can't remember exactly which when I found your image though I note I can still find your image listed if I google image search for "tessellation H"

Link - google search for "tessellation H" - [link]
(Your image appears in the 2nd page of results)

My particular interest is that I am thinking about an engineering design project (I am more of an engineer than a mathematician) in which the whole idea of a tessellation pattern similar to this occurred to me and I wondered if anyone had made good use of the pattern before and that's why I was searching for tessellation images. Your image really stood out from the others and caught my eye.

Ah, so you call the shape a letter "I" shape, the "I" here shown rotated by 90 degrees, on its side, so to speak. Did you start off drawing it with the canvas rotated by 90 degrees from how it is here and at some point decided it looked better this way around, where the "I" looks kind of like a squat "H" or a dumbbell shape? Or did you always have in mind an "I" on its side?

The rainbow colours are very striking. A non-artist engineer-type like me, more interested in the mathematics than the art would probably limit myself by default to use only one simple colour for each shape but to sharply distinguish the boundary of the shapes from each other would find that to colour any tessellation or any map of countries where each country was coloured with one simple colour I would not need to use more than 4 different colours to keep neighbouring shapes (British spelling of "neighbor") of a different colour to each of its neighbouring shapes.

In mathematics, this finding is called the Four Color Map Theorem, which is easy enough to state but not so easy to prove in such a way as to impress other mathematicians. Well no worries because who needs to impress mathematicians?
Wikipedia - [link]

I note that you have only used essentially two colouring schemes - each "I" shape is coloured using either one or the other of the schemes, either Red-Orange-Yellow scheme or Green-Blue-Purple scheme, but neighbouring "I" shapes don't have the same colour at any one point on the border between "I"s because your colour schemes are a gradient of colours. Thereby you manage to keep the sharp contrast between neighbouring shapes of the tessellation even though you only have used essentially 2 colouring schemes, albeit using multiple colours in each colouring scheme!

Yours is an elegant solution to the tessellation / map colouring problem which demonstrates that artists are not so fussed with pointless limits to what colours to use to colour maps with as mathematicians are!

This tessellation pattern is after all well known. Please read my other comment made at about the same time as your comment, so maybe you missed it, which shows that this tessellation pattern, or others quite like it, has been used many times before for a paving stone tessellation.

Thank you for permission to use your image. I will be sure to give you the credit if and when I do.
AnScathMarcach's avatar
Yes, I saw the other comment when I went to look back on the picture. What we did was cut out one shape and trace it over and over to make them all the same. The shape I cut out looked like an I, so that's what I associate it with.
Your information really is interesting. I didn't know something so simple would strike so much interest. I may even make a digital version soon that will look even better. You can add me to your Deviantwatch if you want to see it when I do.
Peter-Dow's avatar
I am pleased you find my comments interesting. Simple shapes are much easier to make when you are engineering something. If you look at the tessellated shapes they use for paving stones or tiles they tend to be fairly simple shapes. A really complex shape, even though it would tessellate fine would be more difficult to make in the real world.

I have uploaded my own "digital version" although my work uses my own very specific "I" shape.

I have dedicated my new work of art I have called "Tessellated I" to you Cori with my thanks for the inspiration your "Colorful Tessellation" has given me.

I have added you to my Deviantwatch and added you as a friend here.
Peter-Dow's avatar
Here's the link to my image. I just replaced the first version with a new one with my own watermark added.

[link]
Peter-Dow's avatar
Update: A quick google search uncovered pavement tessellations worldwide which use this shape.

"Pavement Tessellations" - webpage
[link]

This photograph, © Cathy Myers, may be of a pavement tessellation in Newburgh, New York.
[link]
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