Thoughts on tesselation

[Barry Lee Hands]

someone was asking:
Could you tell us couple words about "tessellation and Keplers laws", please.
Where can I find more information about this one, please

Thank you

I thought you might like to hear my reply:

Vlad, you ask, Where can you find more info on this stuff? it is all over, but I figured this new way of layout (ancient) by studying Escher, the mosques of Egypt, Kepler and Isaac Newton, the ruins in Greece and Rome, the Ufizzi and the Vatican museums, until I saw it everywhere, in buildings, in the patterns of cloth and carpet and wallpaper, and almost went mad with it - but in a nutshell:
This is a tessellated deductive layout; that is it is actually designed on a repeating hexagonal pattern and there are no point of origin (that would be fractal).
Instead the leaves prescribe elliptical orbits ( Keplers' laws of planetary motion) around points of gravity in the dark matter. (negative space)
in this case, everything orbits the hidden point of gravity outlined by the orbits forming a small curved triangle in the center:
http://engravingschool.com/forum-pics/barry/OrbitinginductiveThreesegmenttesselations.jpg

Here is example of the original drawing, showing a detached tesselational hexagon at the bottom of the drawing:
http://engravingschool.com/forum-pics/barry/tesselationexperiments002.jpg

and some additional experimental tesselational figures, of which the series at the bottom was the start of the previous drawing, and as you can see, no stems (or scrolls) are required::
http://engravingschool.com/forum-pics/barry/tesselationexperiments001.jpg

"The horror... the horror" - Colonel Kurtz

[SVD]

Thanks Barry!

Saved off for further study.

It'll be interesting to compare what I've saved up with your book / DVD when you eventually build up to one.

Like so much else involved in engraving it seems like such a small, simple thing but then again, three little lines make a leaf...

[graniteguy52]

Barry,

Fascinating stuff ! It's doing as much for my brain as my morning coffee (or at least supplementing it).
I hope explanations like this lead you to authoring a book!

Gordon Alcorn

[ihsfab]

I have been diving into Celtic patterns here for the last few months and have noticed that it follows right along with what you have explained. Since I am not a math buff, I never knew what the theory was behind what I was creating just that if I started out with a geometric based shape the design would grow from there. Now I know why. Thanks again Barry:yo[1]:

[Barry Lee Hands]

You are welcome!

[Dave London]

:thankyou[1]: Barry
Great information , lots to study

[Archie Woodworth]

Berry,
Thanks ... more great work from your bench/drawing board. Thanks for taking time to share your knowledge with us.
Regards,
Archie

[Scott99]

Thankyou very much for the instruction.

scott99

[davidonthebeach]

I really like this. Thanks for sharing it.

~David

[mrthe]

Thank you Barry very helpful,this remember me the "Gaudi's Paseo de Gracia " floor tiles

http://engravingschool.com/forum-pics/barry/baldosas-paseo-gracia-barcelona.jpg

[WVEngraver]

Thank-you Paolo. You beat me to it. Here in the United States we do not have many places to see this timeless design concept. It certainly looks fantastic with the "renaissance" leaf design and personally I would love to have a Roman style bathroom tiled like this.

[SEngraver]

Hi,

Thank you Barry Lee and Mrthe.
SE:yo[1]:

[Dave London]

OK here is my first attempt, started with hexagons then overlaid the elliptical shape then added the leaves. This is a 200% blowup of a winchester frame.
What have I done right or wrong.

[Barry Lee Hands]

That works.
One " rule " for tessellation is you take the smallest reasonable area, and us it to decide whether to go with a square or hexagon, and the size of it.
Then, use that to develop the whole area.
And once you have the tessellation laid out, it can even be a background, and then you can drop a more major pattern in the middle of the tessellations.
and you can mix tessellation and fractal, I do it all the time.
The main thing that relates to gun or knife engraving is to THINK OF THE DESIGN ELEMENTS, because they have soooo much to do with developing a recognizable style, then arrange them to suit the space.

[Dave London]

:thankyou[1]: Barry
And more good info, I like leaf patterns Oak, Maple, made up.

[LVVP]

Thank you Barry for the reply, I am sure it is useful for everybody

Vlad

[charles starks]

Wow berry thanks .
At first I was having a real problem understanding what was happening . .
The problem for me was the word “tessellation”
To be honest I was going ; what the heck ???

But then I realized what I know this as is pattern repeat and shift . It took Mrthe’s photo for it to click .
After years upon years in the flooring industry , I could pick up issues near instantaneously . I would drive my wife nuts as every where I went I would point out where contractors had made mistakes
What I never realized however was the use of the hexagon . For some reason I had always pictured in the form of squares . IE whats commonly done in say carpets is that you have a pattern designed in multiple of squares . these are laid out side to side . Lets say those squares are 24x 24

Thus ending up with a pattern repeated width wise of 24inchs . . The next row of squares are shifted by ½ the demission of the square . .
The next row is then shifted back 12 which reproduces the original beginning pattern.
As such we say that a carpet has a 24 inch pattern repeat with a 12 inch shift .

When looking at designs on floors what this does is not only create a pattern that repeats itself in length and width but also in diagonal . So what often looks to be random colors is in fact not .. There is always a repeat . For most folks they never see it . But like you said , once its pointed out , you see it everywhere

That shift is what makes your hexagon . Very cool , thank you i never thougth of it like that :thumb[1]:

[Barry Lee Hands]

Thanks Charles, you know what I am talking about.
It doesn't really matter if its a square or a hexagon, except when you are designing it.

[Bert Edmonston]

Thanks for posting this. I had to bring the image into my cad drawing program to really figure it out. Once you boil it down to the basics it really becomes quite simple to figure the method out.

It appears to me there is a primary and secondary rotation point. The primary point being the rotational center for the loops with the two leaves on them and a secondary rotational point for the loops with one leaf on them.

[Barry Lee Hands]

That works.

[Otto]

I'm gonna take another look at the greenbriar that's growing through my chicken wire!

[rod]

Barry,

I have come to your posting a bit late, distracted by the birth of a bonnie wee grandson, Luke, last week. Mother and child both well!

This is a valuable and generous sharing of your tessellation journey, and a breath of spring approach to traditional ideas widespread in the craft. Of course, said traditional ideas are applied in masterful, elegant, and novel ways by many of our favourite masters, and I am delighted to admire and appreciate each new variation.

But the tessellation approach is indeed interesting. Your first illustration is attractive and complete, yet it is not symmetrical. I like that. With your permission, I need to cut a few practice plates for myself to better understand the approach?

Best

Rod

[Barry Lee Hands]

You bet, that is why I posted it.
I think that good artists borrow, and great artists steal.
Few of my ideas are new, and most are gathered from the midden heap of our predecessors in shards and just put together a little differently than the way I found them.

[redgreen]

Hey Rod, congratulations. I didn't want to say anything about the delinquencies from the primary pattern as some (no matter how well explained or intended) would feel it was an attempt to indicate error. As you have brought it to the surface I feel I may speak of it without undue ruffling of the wrong feathers. Perfect form requires that all secondary patterns use the unaltered 'primary' to create them. This leads to the rubber stamp or cookie cutter look that was pointed out earlier. Barry has broken perfect form to create a far more interesting design and a randomness that looks very natural to my simple untrained eye. I find the overall effect pleasing, the swirls created seem to cause an overall randomness that is very natural looking while maintaining a number of secondary patterns, most designers would not attempt to overlay a secondary design. To me it seems much like what I see in some Japanese art, a complex subject in a simple form that provokes near constant internal referencing beyond the surface decoration. As a creative and talented all around professional Barry seems to walk the fine line between creativity and pleasing the eye of the traditionalist, and as his success proves does an excellent job of it. And is willing to share and teach, you can't beat that.

Bob

[rod]

Thanks, Barry,

and Bob, I will chew on your interesting remarks as I try cutting a few practice plates in an effort to grasp what Barry is getting at. I have written in the past, that Barry's signature three element leaf series reminds me, somehow, of my young days wandering the Scottish hills and gazing into small streams, or burns as we say, to 'watch small fishes glide'. Leaves would drift down, some golden and some green, their movement partly governed by the flow of water, and its eddies, or spirals of current, influencing but not controlling the leaf's journey. The moving leaves were quite captivating to me, a deep spiral or scroll of water was at play, it influenced the leaves but they did not totally surrender.

Later, when I discovered the work of nature artist, Andy Goldsworthy, who lives in the Scottish Borders, I saw that he could capture moments of this dance.

Rod

[redgreen]

Hey Rod, you wax nostalgic most delightfully, I feel I'm nearly able to look over your shoulder into the vision of your past. Those days of youth when you may see the beauty of debris in the odd branch and possibly not be considered a fool. The blind harsh critics never change they will only 'see' beauty where they are told to see it, the endless swirl of life is just litter in a ditch until an 'expert' points to to it and declares it so, odd how they and far too often some 'artists' seem to insist you only see it as such or suffer their insult, admonishment and sometimes punishment.

Bob

[warren smith]

all of this interests me as well .. its very pleasing to the eyes..

[redgreen]

This is a wood block by Escher, it is a work of tessellation in metamorphosis, it seems to defy many of the 'rules'. The point was to show there are no real 'rules' for tessellation, between the combination of tiling, color and symmetry the only limits are ones own imagination and ability to bring it to light.

11337

Bob

[Terrezar]

This is brilliant! Thank you for posting this!

[Barry Lee Hands]

This is a wood block by Escher, it is a work of tessellation in metamorphosis, it seems to defy many of the 'rules'. The point was to show there are no real 'rules' for tessellation, between the combination of tiling, color and symmetry the only limits are ones own imagination and ability to bring it to light.

11337

Bob

Yes, that's a fractal tesselation hehe

[Andrew Ovalles]

Played around with this concept in coral draw. This should be a quick understanding of how tesselation works.

1. This is a vector copy I did of barry's first picture
http://engravingschool.com/forum-pics/barry/tile1_zps9ec24351.jpg

2. I took it an made the same multiple copy
http://engravingschool.com/forum-pics/barry/tile2_zpsfee2ad48.jpg

3. Then I rotated each one to a different side / angle. The arrows indicate which direction i turned
http://engravingschool.com/forum-pics/barry/tile3_zps39b7ab8e.jpg

4. Here it is touching (its rough but you should get the idea) Creating a nice patterned layout
http://engravingschool.com/forum-pics/barry/tile4_zps37a3c70b.jpg

I hope this helps folks understand a little better :)

[Andrew Ovalles]

One more post to show the ease of applying this to a project. Used an old picture template that roland baptiste once posted and applied this technique to holland and holland frame

1.template
http://i122.photobucket.com/albums/o280/andrewoval/practice1_zpsc717b3d7.jpg (http://s122.photobucket.com/user/andrewoval/media/practice1_zpsc717b3d7.jpg.html)

2. Used the same 7 hex pattern from the 4th photo in my previous post, duplicated them, and rotated them deleting the ones that didn't have any place in the photo.
http://engravingschool.com/forum-pics/barry/Pratice2_zpsccd784b7.jpg

3. I put an overlay of white over the template only covering the outside of the template while leaving the design in the middle untouched.
http://engravingschool.com/forum-pics/barry/practice3_zps78d56fcf.jpg

4. And finally I deleted all the hexagons and just left the design.
http://engravingschool.com/forum-pics/barry/Practice4_zpsa560feda.jpg

Jeez talk about what you can do when you have some freetime huh. Well thats all for today folks :yo[1]:

[redgreen]

That's a long stretch Barry,:biggrin[1]: I think you may get some hate mail from digital artists and mathematicians. :willy_nilly[1]: How about a new term? Something that describes a non-fractal visually interpreted as a fractal?


That's cool Andrew, I find it a bit awkward, your primary tiling is not symmetrical, was this purposeful? It certainly fooled me at first glance, completely unexpected. I thought you were attempting a random pattern using a symmetrical primary tiling.

Bob

[Barry Lee Hands]

One more post to show the ease of applying this to a project. Used an old picture template that roland baptiste once posted and applied this technique to holland and holland frame

1.template
http://i122.photobucket.com/albums/o280/andrewoval/practice1_zpsc717b3d7.jpg (http://s122.photobucket.com/user/andrewoval/media/practice1_zpsc717b3d7.jpg.html)

2. Used the same 7 hex pattern from the 4th photo in my previous post, duplicated them, and rotated them deleting the ones that didn't have any place in the photo.
http://engravingschool.com/forum-pics/barry/Pratice2_zpsccd784b7.jpg

3. I put an overlay of white over the template only covering the outside of the template while leaving the design in the middle untouched.
http://engravingschool.com/forum-pics/barry/practice3_zps78d56fcf.jpg

4. And finally I deleted all the hexagons and just left the design.
http://engravingschool.com/forum-pics/barry/Practice4_zpsa560feda.jpg

Jeez talk about what you can do when you have some freetime huh. Well thats all for today folks :yo[1]:

That's pretty good, however you should line up the stems so they make ellipses under the leaves.

[Andrew Ovalles]

Hey bob, Not by any means was my work symetrical, I had mentioned my first post that it was a rough design. In my 2nd post i just wanted to show what the grand picture would look like if you applied the idea to a project.

I'm now getting more involved in this thought process of tesselation because it is a good layout idea for future projects. I'm starting to understand that you can appy tesselation in many different ways than just how barry presented. Will see what the future holds but until then I think im going to continue to play around with it.

Barry, i've just started reading about kepler and escher and understand your references better. Hopefully soon i can do something interesting knowing what i know now.

[redgreen]

Well Andrew, the process that brought you to the design is well beyond my understanding, I'm just a simple minded old fool. The seven tiles used to make your primary pattern does not show me the pattern, apparently this discussion has gone far deeper than my simple understanding. I better step back and see hows its done by those who have a better perception of the concept, always ready to learn. :pop2[1]:

Bob