Tessellations

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Tessellations

Postby vivian maxine on March 21st, 2016, 4:58 pm 

When you lay a tesselated floor, the design is repeated throughout but what about the colors? Suppose you are doing triangles inside each other and you pick three colors for those triangles. Would the innermost triangle have to always be the same color, the middle triangle another repeated color, etc.? Or can you alternate where you put each color?

Second question: Can you actually use many different colors but the same repeated mosaic?

Thank you.
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Re: Tessellations

Postby Dave_Oblad on March 21st, 2016, 6:31 pm 

Hi Vivian,

As a hobby, I build a lot of 3D Models. I have to apply Tessellations often to provide some flexibility in Organic Models at the junctions where there is twisting, compression and stretching.. The colors/textures are controlled by a separate photographic map overlay that is applied to the Model at the time of Rendering, usually. The model contains information for aligning the Photographic Map for eyes, feet, back and belly etc.

Green.jpg
Overlay Map of a Gecko Lizard

This help?

Regards,
Dave :^)
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Re: Tessellations

Postby vivian maxine on March 22nd, 2016, 7:20 am 

You are far ahead of me, Dave. What you speak of is new to me and different. What I was referring to is a two dimension design using one pattern repeated over and over to the end. Like laying floor tiles. I knew how the patterns had to go but had never seen anything about color. I finally found it this morning at:
https://en.wikipedia.org/wiki/Tessellat ... and_colour . Apparently the artist gets a choice but if the colors are varied, it is not a true tessellation.

Thanks much, Dave.
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Re: Tessellations

Postby zetreque on March 27th, 2016, 9:41 pm 

Because of the title of this thread, the past several days I have been thinking about "tesseract" and I finally figured out where I heard it from. "A Wrinkle in Time". Related to tessellations I think because it's based on them? :)

http://www.tor.com/2011/12/15/there-is-such-a-thing-as-a-tesseract-a-wrinkle-in-time/
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Re: Tessellations

Postby vivian maxine on March 28th, 2016, 6:28 am 

zetreque » March 27th, 2016, 8:41 pm wrote:Because of the title of this thread, the past several days I have been thinking about "tesseract" and I finally figured out where I heard it from. "A Wrinkle in Time". Related to tessellations I think because it's based on them? :)

http://www.tor.com/2011/12/15/there-is-such-a-thing-as-a-tesseract-a-wrinkle-in-time/


It has been so long since I read A Wrinkle in Time that I barely remember what it was about. I shall have to do some reviewing. I know it was a good story of children off to rescue there father from somewhere in outer space? Or, knowing about Time now, maybe somewhere along the Time line? Seems he couldn't get back. Gee, maybe I'll read that again. Thanks for reminding me of it.
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Re: Tessellations

Postby vivian maxine on March 28th, 2016, 6:50 am 

A tessellation?

But, as the three soon realize, something is very wrong here: nearly every child (with one exception) bounces a ball or jumps rope in perfect unison. The doors all open and close at once. Everyone has a place, a part, a cog in a great pulsing machine. In Camazotz, L’Engle presents a genuinely chilling picture of evil: conformity.
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Re: Tessellations

Postby zetreque on March 28th, 2016, 12:01 pm 

vivian maxine » Mon Mar 21, 2016 1:58 pm wrote:When you lay a tesselated floor, the design is repeated throughout but what about the colors? Suppose you are doing triangles inside each other and you pick three colors for those triangles. Would the innermost triangle have to always be the same color, the middle triangle another repeated color, etc.? Or can you alternate where you put each color?

Second question: Can you actually use many different colors but the same repeated mosaic?

Thank you.


I don't see why not? If you live in a casino state, you will see lots of different fancy weird patterns of carpet over the years. All kinds of repeating patterns with different colors. Some "tiles" will have certain colors and their repeating "tiles" different colors. I wonder if the patterns confuse people into throwing their money away more or faster.
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Re: Tessellations

Postby vivian maxine on March 28th, 2016, 12:36 pm 

I hadn't thought of that but it may work. When I see those, I find myself spending a lot of time just checking them out. If you stare long enough, you'll see the patterns actually changing. I can't think exactly how to describe it but the design that you see suddenly breaks apart and its parts form a new and different design.

I wonder. Does tessellation take a very creative mind or a very non-creative mind? it certainly takes a creative mind to get started but, once you know what geometrics you plan to use, it is just repetitious - more alertness needed than creativity. That is unless you vary the colors. I did one with varied colors - which the Wiki article said is not true tessellation - and looking at it keeps your eyes dancing. There is no place to settle as there is when the colors are as repetitious as the pattern. I think I like it more.
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Re: Tessellations

Postby vivian maxine on March 28th, 2016, 1:08 pm 

zetreque, do you have access to the Oxford dictionary? If I read this right, the answer to your question is no. Tesseract is from the Greek tessera, a variation of "four" , a small quadrilateral tablet. In math it is a four-dimensional hypercube.

Tessellation is from tessella, from Italian and Latin and means the pattern we've been talking about - the repetition of a given pattern into a mosaic. I read somewhere that true tessellations use only squares or polygons but that is obviously no longer true. The one I just colored is an arrangement of paper clips.

However - there's always a however - with those two definitions, there is also "tessella" from Latin and defined as a "small tessera".

Then there is "tessaraglot" which is from Greek and pertains to four languages. So, maybe the answer is yes if you go back far enough.

We even have Tessa (tax exempt as a special savings account)

Now you see why I asked if you have access to the Oxford dictionary. :-)
"
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