Archive for the ‘math’ Category

ORIPA update

February 16th, 2006

Roberto Soto posted this email to the Origami-L mailing list:

I just found this Java based program named ORIPA. It’s a program to create
crease patterns (or to draw existing crese patterns), but the funny thing is
that it can actually show youde finished model.

I was just wandering if any of you have heard or read about it before??

the link: http://mitani.cs.tsukuba.ac.jp/pukiwiki-oripa/

I had to reply to this, of course- ORIPA is a wonderful software tool, and deserves more attention from the western origami world. I was pleased to find that Jun Mitani had localized it to English, and made an English language page with instructions for how to get it working. That’s a lot of extra work for him, especially with a new baby at home, and I’m very grateful he took the time to do that.

Here’s my reply to the O-list.

I wrote a bit about this program on my site a few months ago:

http://www.origamitessellations.com/2005/12/12/figuring-out-things-with-oripa/

Jun Mitani’s program is quite an excellent one, which works out amazingly well for folding a lot of basic (and not so basic) models. There’s been a lot of traffic in the Japanese origami blog community about this particular app, with a lot of interesting pieces being produced with it.

here’s a few of them, via Technorati’s blog search:

http://www.technorati.com/search/ORIPA

also, Hideo Komatsu has been playing around with ORIPA quite a bit- his blog has a number of posts on his usage of it, especially as he tries to use it to diagram his work (it doesn’t often fold the patterns properly, and I believe he submits the bugs he finds to the author).

you can read his blog here:

http://d.hatena.ne.jp/origami

his blog posts on ORIPA:

http://d.hatena.ne.jp/origami/searchdiary?word=oripa&.submit=%B8%A1%BA%F7&type=detail (http://tinyurl.com/9gcwq, or search for yourself in the left hand search window)

you can run this through babelfish’s translation tool (not so good, though) which will lose the photos- make sure to view it in japanese first, as there’s lots of pictures.

http://tinyurl.com/arkbr (babelfish link, link text is much too long.)

However, there was a posting by Komatsu a while ago which I interpreted as saying that development on ORIPA was coming to an end. That may be completely incorrect, though, so don’t take my word on it.

Jun Mitani has localized the application for English as of version 0.16, which is a wonderful thing- you can view his english language page with instructions here:

http://mitani.cs.tsukuba.ac.jp/pukiwiki-oripa/index.php?ORIPA%3B%20Origami%20Pattern%20Editor

(or http://tinyurl.com/8ezde here if that link is too long, and wraps on your screen).

since the program is now available in english, it should significantly lower the barrier for more people to play with it. The application is very interesting- you can lay out a crease pattern, and it will tell you whether or not it will fold; furthermore, it will fold it and show you the final folded model. You can flip the model and see both sides, have it spread out the layers a bit to better see the folds, turn it to wireframe mode so you can see through the layers, etc.

There is also an upload board- kind of a wiki BBS page for discussing issues, uploading files, and the like. that page is here:

http://mitani.cs.tsukuba.ac.jp/oripa/upboard/upboard.cgi

All you need to make it run on windows is a reasonably recent Java install, and his program file (currently oripa016.jar). By all means download it and give it a try!

-Eric Gjerde
http://www.origamitessellations.com

Posted in design, diagrams, geometry, math, o-list postings, origami, weblinks | Comments (0)

Voronoi tessellation, test 1 (twisted)

January 25th, 2006

a test piece from a new working theory of pleating.

polygons are defined by the same methodology used to make Voronoi tessellations; borders are then used as a reference crease along with the central point of the polygon to create the appropriate “fold flat” crease pattern. in this case, you can see the original 1/2 pleat creasings, which were further divided into 1/4 width pleats.

This was a test using random polygons; other methods of more usefulness (applications for use with regular polygonal shapes) are in development.

much fruit on this tree, I think. I hope I am able to refine my ideas enough to make them usable.

if you find this idea interesting at all, please drop me a line at origomi [ at ] mac.com. I’d be happy to talk to you about it.

the untwisted version, below.

Posted in design, geometry, math, my work, origami, origami tessellations, paper | Comments (0)

Geometry without language

January 24th, 2006

The always fascinating Future Feeder points out a story in the January 20th issue of Science, about a tribe in Brazil’s Amazon jungle which has no language for geometry but still understands it, in some cases as well as American adults. (Although as an American adult, I’m not really sure that’s actually saying much. -Eric)

There’s something a little satisfying in knowing that the human mind is capable of intuitive leaps with or without a huge societal support structure in place to coddle it.

link is here; NY Times article is here.

Posted in geometry, math | Comments (1)

Origami Tanteidan Tokyo, Jan 2006

January 23rd, 2006

Posted in the “Information Corner” of the notes from the January Origami Tanteidan Tokyo meeting:

my apologies for the bad babelfish translation.

Information corner / Information

- Concerning the rigid body folding (crossing over Takahiko)
Whether or not from Yamatani’s broken line information which attaches with respect to plane surface, that rigid body folding possibility of the graphic method which decides was thought.
After details, being settled as a dissertation, again it announces.

(In regard to the rigid body folding, you can read Tom Hull’s article inOrigami Tanteidan magazine 86 and 87. Also you can refer to Tom’s article on his website.)

- 3rd diffraction paper engineering research sectional meeting (information: Crossing over Takahiko)
It was held at 2005 December 6 Nitto capital industrial university.
The Hagiwara research (mechanical engineering), the Nojima research (space engineering), Kuribayasi (the micro mechanism Takeuchi research) with, to engineering field of the Origami Tanteidan.
Applied example was announced. Lightweight high intensity core panel and circular membrane of large area ( etc.)
The tableware pet bottle & the book shelf etc. of the retraction receipt model and folding receipt type were introduced.

I’d love for someone who can do a better job of translating to please let me know what the proper translation is for this paragraph. I’m including it in the original language here, in hopes some kind soul will help us out.

情報コーナー/Information

●剛体折りについて　（渡邉尚彦）
平面上につけられた山谷の折線情報から，それが剛体折り可能かどうかを判定する図式解法を考えました．
詳しくは、論文としてまとまってから改めて発表します。
（剛体折りに関しては、探偵団マガジン86，87号TomHullさんの記事，Hullさんのサイト Rigid Origamiを参照．）

●第３回折紙工学研究部会　（情報：渡邉尚彦）
2005年12月6日東京工業大学で開催されました。
萩原研（機械工学），野島研（宇宙工学），栗林さん（マイクロメカニズム・竹内研）により、折紙の工学分野への
応用例が発表されていました。軽量高強度コアパネル、大面積の円形膜（ソーラーセイル等）の
巻取り収納モデル、折り畳み収納式の食器・ペットボトル・本棚などが紹介されました。

Why am I sharing all this information? because it’s talking about rigid folding, which is very applicable to many things, especially manufacturing and “industrial” use of origami techniques. It’s also very pertinent to tessellation folding, as much of what we do can be accomplished with rigid-folding techniques. Read Tom Hull’s article linked above for a better idea of what this is all about.

And the part that truly caught my eye is these folded examples, referred to in the quote above. Some very exciting ideas here!

[via] Hideo Komatsu’s blog

Posted in geometry, math, origami, origami tessellations | Comments (3)

Infinite Bird Bases

January 12th, 2006

I saw this new crease pattern from Darren Abbey today.

he says:

for my personal amusement, I diagrammed an extended version of my fractal origami model.

This version has seven levels.

When folded, it will have 16,384 points.

Not all of the creases are indicated, this is meant as an exercise for the student.

Darren, you are quite insane. it’s wonderful. looking forward to seeing someone (else!) fold it.

Posted in diagrams, geometry, math, origami, origami tessellations | Comments (0)

Peter Budai’s “Flammifer”

January 11th, 2006

I found this interesting design on Galen Pickett’s website, in one of the rather hidden(1) galleries(2) he has full of origami goodies.

It’s a model called “Flammifer” by Peter Budai, who I had never heard of until seeing this model. Here’s a great little writeup by David Lister from a few years back about him.

What I thought was the most interesting thing about this design is that I’ve folded something very similar to this, but with hexagonal instead of triangular square symmetry; but in all other respects it matches the doubling dual-sided pattern exactly.

I had thought about trying to fold this, since I know it’s possible, but I’m very pleased to see that it has been done and solved long ago!

Thank you, Galen, for posting all your wonderful photos online, and sharing some of your origami world with the rest of us.

And thanks also to Peter Budai for the wonderful design. I think this is a natural outgrowth from a very interesting line of origami exploration by Peter- he calls them “Infinite Folds“. this one is just 4 of these “infinite folds” put together. Many of these could no doubt be combined in the same way, and folded to a (theoretical) infinite level of recursion. Fantastic.

edit: fixed the typo. meant to say square instead of triangular. oops.

Posted in geometry, math, origami, origami tessellations, paper, weblinks | Comments (5)

Upcoming book from Tom Hull

January 4th, 2006

Digging around always seems to pay off- I found the LiveJournal page of Thomas Hull, origami mathematician extraordinaire.

He mentions that he has a new book coming out in the spring of 2006, called Project Origami : Activities for Exploring Mathematics.

Here’s a draft version of the cover (thanks, Tom!)

Looking forward to this one!

The summary, via the A K Peters website:

When it comes to mathematics, paper isn’t just for pen and pencil any more! Origami, the art and science of paper folding, can be used to explain concepts and solve problems in mathematics-and not just in the field of geometry. The origami activities collected here also relate to topics in calculus, abstract algebra, discrete mathematics, topology, and more.

Using origami, learn about:

• Solving Cubic Equations
• Bucky Balls and PHiZZ units
• Matrix models for folds
• Gaussian Curvature and much more!

These activities, which can enhance the classroom experience, also make great independent student projects and are perfect for math clubs or math circles.

and, if you’re a book geek…

ISBN: 1-56881-258-2

242 pages, no less!

Posted in diagrams, geometry, math, modular origami, origami, origami tessellations, paper, weblinks | Comments (2)

Chris Palmer’s Polypouches

January 2nd, 2006

I’ll be perfectly honest: I never understood what Chris Palmer was doing with his “PolyPouches”. I had tried going to his website a few times to find out information about his work (no luck there!) but all I found were these things he was calling PolyPouches, and it asked me to buy a subscription to find out more.

I just shrugged it off at the time, having no idea what they were thus not a lot of interest. However, the other day I came across this site which features photos from an Origami USA convention in 2001.

And by looking at this wide array of them, I figured it out- they are the shapes that are formed at pleat intersections; the kind that those of us just getting started in tessellations are discovering as we go along. He’s already mastered all of this, of course, but for us it’s new.

Once I realized that was what these were, it really opened my eyes to some of the possibilities inherent in 3d pleat junctures and just how many things are possible. It’s like he was making a catalogue of them for his own reference and decided that other people might find them interesting as well. I wish I knew more about them, but I don’t think that will happen.

Anyway, if you have folded tessellations with non-flat-folding pleat intersections (Melisande, Fredrik, Jane, etc) you might recognize some of them here. Take a look at some of the other ones as well, and notice what other possibilities are in store for all of us as we continue folding…

So I owe an apology to Chris for thinking these polypouches were not related to his previous tessellation work, as they certainly are! I wish I had more insight into his works and his design methodologies, without having to reinvent the wheel here; but I do respect his decision to keep his art (and income source) a private thing. It’s his choice, after all.

Thank you, Chris, for creating these works and giving us a glimpse of what must be a fascinating world of mathematical art you live in!

If you have issues with the images not working (the geocities host that the images are on is very bandwidth-limited) let me know and I will post alternate links to the images locally.

Posted in geometry, math, origami, origami tessellations, paper | Comments (3)

Duals

December 15th, 2005

Doing some reading online about tessellations; found this little snippet from this site.

The dual of a tessellation is formed by connect the centers of the shapes in a tessellation so that these segments do not pass through a vertex of the tessellation. The dual tessellations of the regular tessellations are themselves regular tessellations. However, the duals of the semi-regular tessellations are not semi-regular tessellations.

So, now I know the official way to discover the dual of the tessellations I am folding. Helpful!

Posted in geometry, math, origami tessellations | Comments (0)

any suggestions for folding this tiling?

December 12th, 2005

This tiling is really just causing me mental anguish. I’m trying to find an elegant way to fold it, and it’s just not happening so far.

(click the photo for a larger version)

Totally open to suggestions or hints from crowd on this one. it’s really interesting looking, too… what I have folded so far is fascinating (to me, anyway). I’d really like to find a way to make it go the distance.

Posted in WIP, diagrams, geometry, math, my work, origami, origami tessellations | Comments (0)

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