Origami Tessellations

hierarchical

Originally uploaded by goran konjevod.

Goran Konjevod has done a lot of work over the last few years combining math and art - the output is fantastic things like this new piece, called “Hierarchical”.

I love the way it all flows from a strict, ordered process and yet produces such an organic, vibrant result. From a distance I would have a hard time believing this is paper, much less a single uncut sheet of it!

Goran also has an exhibition running currently in Phoenix, AZ, which includes this work.

I’m looking forward to my next opportunity to check out his art in person - probably at the Origami USA convention this June in NYC. Maybe I can even get him to share some of his design secrets!

I am in love with The Institute for Figuring. If you’re at all interested in geometric art, tessellations, chaos, fractals, or really anything- you should become a member. It’s highly worthwhile.

Crocheted Hyperbolic Plane, copyright IFF

From their website:

The Institute For Figuring is an educational organization dedicated to enhancing the public understanding of figures and figuring techniques. From the physics of snowflakes and the hyperbolic geometry of sea slugs, to the mathematics of paper folding and graphical models of the human mind, the Institute takes as its purview a complex ecology of figuring.

It’s like someone took EVERYTHING out there that I find interesting, and wrapped it up into a non-profit with a cool website, publications, and speaking events! Fantastic stuff.

To whet your appetite, there’s a rather good article on mathematical paper folding on their site currently:

The Institute For Figuring // Online Exhibit: Mathematical Paper Folding

Enjoy!

Ben Parker (brdparker on flickr) has posted a great collection of waterbomb tessellations recently- 132 photos, in all! Ben says this is all part of a tutorial/write-up on waterbomb based tessellations, which I am eagerly looking forward to reading.

Quite a few of us on Flickr have been folding all sorts of waterbomb-esque tessellation things in the last few months, although the real breakthroughs with this sort of technique comes from the “flagstone” tessellations of Joel Cooper, who has been creating magnificent works of art in this style for years. It is only recently that others of us have been able to sort out some of the methods of this type of construction, and of course we all seem to have approached it from different ways.

Many of the pieces posted here by Ben are not flagstone tessellations, following the intricate style popularized by Joel (great example here), but instead some interesting 3D pieces that remind me a lot of the work of Polly Verity and Ray Schamp. Also, I see a bit of Frank Van Kollem in some of these pieces, as well. But many are new and different, and resemble nothing I have seen before, and that’s always of great pleasure to me. New works are always wonderful to experience.

Many of the photos are low-res, but that’s the breaks when you’ve got a free account on flickr- sounds like a great opportunity for someone out there to step up and sponsor a Pro account, in my opinion…

If you’re a flickrite, I highly recommend adding Ben to your contacts list, so you don’t miss gems like this when they come along.

-Eric

Here’s a few sample photos:

I saw this amazing sliceform torus on YouTube, thanks to a link from Jorge Jaramillo (commented on this great set of sliceforms by Joan Michaels Paque.) I shouldn’t be browsing around Flickr, as I’m on a self-imposed Flickr hiatus, but Sunday’s a day of rest, so I treated myself to a few minutes of browsing

The coolest part of the video is the way the model folds flat and pops back into 3D!

The creator of this fantastic sliceform says this, on the YouTube commentary:

This torus has been made as a Sliceform.

It is a paper model made from two sets of slices of the torus.
It folds flat because the intersection of each set of slices acts as a hinge.
The slices are cut so that one set includes the Villarceau circles.
For more on Sliceforms do a web search with Google.
See www.tarquinbooks.com for books of models to cut out and ways to explore the mathematics of surfaces using Sliceforms.

Check it out, it’s worth a look. Lots of great people are doing sliceform stuff these days [1][2][3], maybe it’s time to give it a go?

If you’re looking to get started into Sliceforms, most definitely check out this website:

http://www.mathsyear2000.co.uk/explorer/slice/index.shtml

It covers what they are, how they are made, has templates for downloading, the whole thing. This is definitely a great opportunity to put a CraftROBO to work…

Announcing a new version of Tess (1.4)

Originally uploaded by Paper Mosaics.

Alex Bateman has released a new version of his landmark software, Tess.

Tess allows you to create all sorts of tilings, and modifications of those tilings- so you can explore possibilities without having to fold it all out in paper, first! Also, this new version provides PDF export capability, which is a major plus for windows users.

Tess is a Perl application, and will run on any Perl-capable system with a bit of tweaking. (This means you, Linux/FreeBSD/MacOSX users.) Or, if you’re running windows, you can download a standalone version, which will run on it’s own without requiring any Perl resources. Both of these are available to download from Alex’s website.

Download the latest version of Tess!

Ron Resch photo from the 1960’s

Originally uploaded by EricGjerde.

Given to me by Joan Michaels Paque, as some wonderful background information on the work of Ron Resch. Fantastic! Thank you so much, Joan!

I don’t have a date on this one, but from his hair and clothing it looks almost like the early 60’s. Wow. Isn’t it amazing to see the tessellated structure from back then? This is fantastic to me.

Check out the three other photos including a great letter from 1978, on my flickr photo stream.

Ron Resch, curved folds (from RonResch.com)

I highly recommend you check out the fledgling website belonging to Ron Resch, a visionary mathematician and designer who was one of (if not *the*) first to explore the architectural potential of 3D tessellated structures in the 1960’s and 70’s.

Only lately have I been exposed to more of his work, and the more I see the more I want to know. He has a film- called “The Paper and Stick Film”- which is apparently quite a fascinating thing to watch. He has a link to purchase this from his website, but it still seems to be a non-functioning link. (The minute this becomes available I’m buying it!)

It looks like he updated his site with some more photos of his patents and some additional historical photos of things he has worked on, too, so if you’ve been to the site before I suggest visiting it again.

Tom Hull talked a good bit about Resch at the Origami USA convention this year, and really intrigued me to look further into his designs. Only recently have I started exploring 3D tessellations myself, and so seeing his innovative thoughts from way back when is really an eye-opener for me.

One thing that really hit me today as I was looking at his site (yet again) was this curving folded piece, made up of out pleats. I like the way it captures an essence- flight, perhaps, or maybe something a bit more ethereal than that.

Sometime soon I need to make a pilgrimage up to Vegreville in Alberta, Canada to see his giant Easter Egg, made for the large Ukrainian community on the High Prairies to celebrate their heritage. There’s some more information about that on his site as well, which is worth looking at. Do a google search for it too, you won’t regret it.

-Eric

Christine Edison posted this lovely waterbomb tessellation photo, and had asked who designed it. Ray Schamp mentioned Tom Hull’s wonderful intro to 3d tessellations class at the 2006 OUSA convention, where Ron Resch’s work was heavily discussed.

To facilitate further discussion on the topic, here’s Ron’s patent paperwork in PDF format- it’s expired and is now public domain. It’s quite nice to reference him, though, as he really is quite an ingenious creator. I need to buy a copy of his DVD that Tom was talking about. If I get one I’ll be sure to do a review of it.

Anyhow, here’s his patent:

Ron Resch, Patent # 3407558.

Oschene provides wonderful instructions, in his slick Sequenced Crease Pattern style, on how to make yourself a regular pentagon or decagon from a square sheet of paper.

If you’ve ever tried to fold pentagons or decagons, you might know that they are irritatingly difficult to work with, inspiring all sorts of bad language to come forth after the 5th or 6th attempt to fold them properly. So I’m very happy to see an easy to follow set of instructions on how to save myself a whole lot of pain.

Thanks, Phillip!

You can get the diagram instructions from his website. (As he pushes the limits of sane blog header lengths in the process. What a URL!)

It’s been one year since the Origami Tessellations photo pool was created, and we’re nearing 1000 photos with close to 100 members- with over 20 members who have actively contributed material to the group!
This makes me really happy; when I started using Flickr a while back there really wasn’t origami tessellation content on here, and now there’s a healthy, growing community of friendly, fun people. This is all possible because of the positive, sharing spirit you have all shown to each other, and to new members joining in.
I’d like to thank you all for being a part of something wonderful, and I hope we continue to share, contribute, and grow for years to come!

Please feel free to comment on the discussion page on Flickr (or here, if you want!)

-Eric