Posts
Below are the latest posts on this site. Click the subject listings to the right to see individual categories of post.
I also have some book, magazine, and journal publications in math and science: see journal articles here, my books here, and a listing of all external publications here.
Careers in Origami
A version of this article previously appeared in OrigamiUSA’s The Fold online magazine. Perhaps you’ve heard that there are professional origami artists. Yes, there are a few: myself, Joseph Wu, Michael LaFosse, Paul Jackson, and Sipho Mabona for starters. (And lots of others: if I’ve left you out, my apologies—it’s assuredly not a complete list.) […]
Continue ReadingComputational Origami
This page contains links to computational tools useful for origami design and for combining origami with mathematical or scientific applications. See here for additional links about origami math, science, and technology. See here for additional links not specifically related to mathematical and scientific origami. If you’ve got a computational origami tool you’d like listed, send […]
Continue ReadingGot Videos?
I am regularly asked if I would create video instructions for my origami designs. Sorry, I’m not currently set up to make such videos myself. However, if you’re a videographer and would like to hire me to demonstrate and/or do hand-modeling of folding (something I’ve done several times for commercial clients), please contact me and […]
Continue ReadingPolypolyhedra in Origami
These images show what the (first) 54 polypolyhedra would look like if created using the Ooh and Ow unit joints (Ow being Francis Ow’s mechanism for joining struts at angles up to 90 degrees, Ooh being my own similar mechanism for larger angles). Polypolyhedron 1. Polypolyhedron 2. Polypolyhedron 3. Polypolyhedron 4. Polypolyhedron 5. Polypolyhedron 6. […]
Continue ReadingPolypolyhedra in Dowels
These images show what the (first) 54 polypolyhedra would look like if created using round dowels of the maximum possible diameter. Polypolyhedron 1. Polypolyhedron 2. Polypolyhedron 3. Polypolyhedron 4. Polypolyhedron 5. Polypolyhedron 6. Polypolyhedron 7. Polypolyhedron 8. Polypolyhedron 9. Polypolyhedron 10. Polypolyhedron 11. Polypolyhedron 12. Polypolyhedron 13. Polypolyhedron 14. Polypolyhedron 15. Polypolyhedron 16. Polypolyhedron 17. […]
Continue ReadingPolypolyhedra
Background In 1999, I became interested in a family of origami modulars composed of interwoven polygonal frames and/or polyhedral skeletons, the most famous of which was devised by Tom Hull, which he titled Five Intersecting Tetrahedra, now commonly known by its abbreviation, FIT. (See here for a description.) The underlying polyhedron—a compound of five tetrahedra […]
Continue ReadingScience Links
This page contains various and sundry links to web pages that combine origami with mathematical or scientific applications. See here for links related to computational origami (software for origami design and analysis). See here for additional links not specifically related to mathematical and scientific origami. Please let me know if you find any broken links […]
Continue ReadingMiscellaneous Links
This page contains various and sundry links to international origami societies and other origami resources on the web. See here for links relating specifically to mathematical and scientific origami. Please let me know if you find any broken links. Origami Societies These are the largest international origami societies. The linked pages also have links to […]
Continue ReadingOptigami
In the design of optical systems that incorporate multiple reflections of converging and diverging beams, tedious graphic layout procedures are followed to assure that mirror dimensions are correct and that structural elements do not interfere with the ray bundles. A change in dimension, location, or angle of any one of the system elements requires a […]
Continue ReadingEyeglass Telescope
Photograph of the Eyeglass prototype on its test range at Lawrence Livermore National Laboratory, Livermore, California. Image courtesy Rod Hyde, LLNL. Picture the solar system’s largest telescope, a telescope as long as the island of Manhattan, incorporating a lens the size of a football field: an instrument possessing the resolution to examine earth-like planets around […]
Continue ReadingAirbag Folding
What could origami possibly have to do with automotive airbags? Quite a lot, it turns out. Sorry, your browser doesn’t support embedded videos. Animation of an airbag deployment for which the mesh was generated using an origami design algorithm. The origami creases appear in the flattening you see in the first seconds of the animation. […]
Continue ReadingOrigami Conferences
Since 1989, there have been several highly successful international scientific conferences exploring the interactions between origami, mathematics, science, and (since 2001) education. The conferences take place at irregular intervals—basically, whenever a general chair and sponsoring organization decide that the time has come for the next. Beginning in 2015, the OSME series of conferences is guided […]
Continue Reading4OSME
2006-10-16 Update: 4OSME was a rousing success! Over 165 people attended some 70 talks. The 4OSME proceedings has been published by A K Peters, Ltd (now part of CRC Press). Several media groups covered 4OSME. See photographs and a trailer from Green Fuse Films’ Peabody-award-winning documentary on origami (portions of which were filmed at 4OSME), […]
Continue ReadingMaking of Mitsubishi
The Artist’s Commentary In October, 2005, I was contacted by MJZ, a production company in Los Angeles, who were working on a new commercial about the Mitsubishi Endeavor SUV for the advertising firm BBDO. BBDO’s concept was to have the car drive through an “origami world.” They needed an origami artist to design and fold […]
Continue ReadingCommercial Art
I have created a range of commissioned works for commercial projects, some of which are shown on this page. They illustrate just a bit of what is possible with origami used for commercial advertising. (See my page on monumental origami for further examples.) To make a figure look right for advertising, various origami genres can […]
Continue ReadingMonumental Origami
“Redpath Pteranodon,” a 4-meter (16′) wingspan origami Pteranodon installed at the Redpath Museum, McGill University, Montreal, Canada. Paper custom made by Papeterie St.-Armand, Montreal, Canada. The term “Monumental” in “Monumental Origami” refers to size: this is large-scale origami, intended to make a visual impact from a distance. The uses of monumental origami are several: it […]
Continue ReadingDesign Challenge at OrigamiUSA
In 2003, Daniel Robinson, Satoshi Kamiya, and I were sitting together at the OrigamiUSA annual meeting, talking about the process of composition and design and comparing thoughts and ideas. Brian Chan’s “Kraken Attack”, from 2006. I should mention that this is not at all unusual. Origami, unlike many other fields, is remarkably collegial, and the […]
Continue ReadingDesign Challenge 2010
The 2010 challenge was: Cars and Trucks. In recent years, we’ve stuck with the natural world, but this year we decied to visit man-made objects. A selection of the year’s entries are shown below. Brian Chan and I each took on sports cars, with the idea of doing the wheels in a way different from […]
Continue ReadingDesign Challenge 2009
The 2009 design challenge was one of the four nonhuman great apes: Gorilla, Orangutan, Chimpanzee, or Bonobo. The last few design challenges have been very open-ended, which has allowed artists to display great creativity in subject. For this next challenge, however, we decided to constrain the subject to emphasize implementation—and in particular, to challenge the […]
Continue ReadingDesign Challenge 2008
The 2008 design challenge was a prehistoric non-dino from an uncut square. What does that mean? Well, there are many, many dinosaurs in origami, but there are also many prehistoric creatures that are as cool, or cooler, than dinos, but have not yet been realized in origami. So whether one is an aficionado of the […]
Continue ReadingDesign Challenge 2007
The 2007 design challenge was to fold an entire plant from an uncut square. There are many origami plants (you can see several in my own gallery), but nearly all origami plants are either composite, i.e., from multiple sheets of paper, or only partial plants (like a leaf, or blossom). The challenge this year was […]
Continue ReadingDesign Challenge 2006
The topic of the 2006 design challenge was a sailing ship. It wasn’t that this topic hadn’t been done before; the symbol of OrigamiUSA is a simple traditional sailboat, and on the complex side, Pat Crawford’s brilliant “Full-Rigged Sailing Ship” is one of the most well-known origami figures in existence. But Crawford’s ship dates from […]
Continue ReadingDesign Challenge 2005
Attack of the Hermit Crabs! At the 2004 OrigamiUSA convention, Satoshi and I examined each other’s Eupatorus (and unmercifully razzed Dan Robinson for his no-show). It had been an enjoyable challenge, and so we decided to try it again for the following year. The subject we chose was a hermit crab—a type of crab that […]
Continue ReadingDesign Challenge 2004
The original design competition was for a Eupatorus gracilicornis beetle, which makes a good subject for origami because of its large number of hornlike protrusions. ( See here for some examples of the real thing.) Although 3 of us originally agreed to take on this subject, Daniel Robinson was otherwise occupied, so only Satoshi Kamiya […]
Continue ReadingCrease Patterns for Folders
In recent years, a new form of written instruction has become common within the modern art of origami: the crease pattern (often referred to by its abbreviation, CP). Conventional origami diagrams describe a figure by a folding sequence — a linear step-by-step pattern of progression. Crease patterns, by contrast, provide a one-step connection from the […]
Continue ReadingCrease Patterns as Art
If one takes the narrowest possible dictionary definition of the term, a “crease pattern,” or CP, is nothing more than a set of lines that is a representation of some subset of folds in an origami shape, real or imagined. But it can be, is, more; the deeper question is, what does a crease pattern […]
Continue ReadingSanta Monica Bronze Sculptures
In 1999, I was commissioned by Brailsford Studio (San Diego, California) to create four works as part of the public art component of the Downtown Transit Mall project commissioned by the City of Santa Monica and the Big Blue Bus. I developed original origami designs for four animals representative of the habitats in and around […]
Continue ReadingAngle Quintisection
This figure shows the key step in performing an origami angle quintisection—division into equal fifths—by folding alone. Within the mathematical theory of origami geometric constructions, the seven Huzita-Justin axioms define what is possible to construct by making sequential single creases formed by aligning combinations of points and lines. It has been mathematically proven that there […]
Continue ReadingHuzita-Justin Axioms
At the First International Meeting of Origami Science and Technology, Humiaki Huzita and Benedetto Scimemi presented a series of papers, in one of which they identified six distinctly different ways one could create a single crease by aligning one or more combinations of points and lines (i.e., existing creases) on a sheet of paper. Those […]
Continue ReadingOrigami Suppliers
The Origami Source Everyone’s first stop for origami supplies should be The Origami Source, OrigamiUSA’s own one-stop shop for books, paper, and related origami supplies. The Source carries books and paper from around the world, offers a unique file download store selling books and magazines in PDF form, and has friendly and great customer service. […]
Continue ReadingOrigamiUSA’s The Fold
Starting in November, 2010, I began writing a regular column on crease patterns (with occasional forays into other topics) for OrigamiUSA’s then-new online publication, The Fold. You’ll need to be a member of OrigamiUSA to read the articles, but in my highly biased opinion, it’s well worth the cost (not just for my articles, but […]
Continue ReadingTreeMaker
Background In 1989, I wrote an article for the magazine Engineering & Science about the state of technical folding, which, even then, seemed to be progressing by leaps and bounds due to an infusion of scientific and mathematical principles. In recounting some of the connections between origami, math, and technology, I wrote: Computing succumbed to […]
Continue ReadingTessellatica
This page contains the current release of Tessellatica, a Mathematica notebook for the design and analysis of origami with particular emphasis on origami tessellations. You’ll need a current version of Mathematica to use it. Beginning with Tessellatica 11.x, the version numbering matches that of the version of Mathematica that it is tuned for. Specifically, the […]
Continue ReadingOrigami Simulation
Background In the 1980s, I made the acquaintance of Jacobo (Jack) Fastag, a graduate student like myself who was interested in exploring the interactions between computers and origami. We both had hit upon the idea of exploring the ability to simulate origami folding on a computer, and each set out to write our own origami […]
Continue ReadingReferenceFinder
Background Update (2024): Mu-Tsun Tsai has created a web-based version of ReferenceFinder (and fixed a longstanding bug in the original source code along the way). He is continuing to develop this version: follow it here. You can also find the original source code (with bug corrected) on my own GitHub repo. During the development of […]
Continue ReadingMore Skin in the Game
I think we may have the beginnings of a trend! A few years ago, a fan liked my Origamido Koi so much that he had its crease pattern tattooed onto his arm. Well, we have another fan of skin, ink, and origami!. Yesterday Jamie Kruger asked to use the crease pattern of my Songbird, opus […]
Continue ReadingTessellatica and Web-Love from Wolfram
Wolfram gives me some web-ness: Above the Fold: Mathematica Transforms Ancient Art of Origami By coincidence, today I also learned that my 6OSME paper on Tessellatica was accepted (along with some others). So come to Tokyo in August, 2014 to get your free copy! (*) (*) Actually, you’ll be able to get a free copy […]
Continue ReadingDrupalizing
One of my side activities is managing the website of OrigamiUSA, which is based on the Drupal content management system. Earlier this year, we upgraded the site from Drupal 6 to Drupal 7, a process that was not lacking in adventures. At our local Tri-Valley Drupal Users Group meeting, I presented “Lessons Learned in a […]
Continue ReadingMy Friend Went to the Philippines and Lost All Her Money and All I Got Was This Lousy Email
The following are all actual emails; only the names have been changed. Thus spake “Jane Doe” <jane_doe@gmail.com> on 9/26/13 5:31 AM: I really hope you get this fast, I could not inform anyone about my trip, because it was impromptu. I had to be in Manila, Philippines for a program. The program was successful, but […]
Continue ReadingFlight of Folds and Shoot of Stars
Incredible photograph by Bill Stengel of our 10′ Flight of Folds sculpture in stainless steel (collaboration with Kevin Box); currently at the Turquoise Trail Sculpture Garden in Cerrillos, NM.
Continue ReadingFolding on the Water
I recently had the pleasure of going on a Lindblad Expeditions cruise in Southeast Alaska where I saw more amazing wildlife that I could have ever imagined. During lulls between bubble-netting humpbacks and beachcombing brown bears, National Geographic photographer Rich Reid was giving tips, techniques, and demonstrations, and at one point he set up a […]
Continue ReadingSpeaking of Butterflies
One of the oldest, simplest, and to my mind, most deceptively difficult of all origami subjects is the butterfly. It is so simple, because all you really need are two wings: one can make a quite recognizable one with just two folds. And there are many origami butterfly designs out there, notably Yoshizawa’s iconic creation. […]
Continue ReadingThis Doesn’t Taste Right
Photo taken by Mary Jane Kettler of my “Morpho Flight” butterfly at the Lady Bird Johnson Wildflower Center last year. I picture the conversation between the two harvestmen as going something like this: “Billy! We got one! and he’s not even moving!” “Wait…something’s wrong…What sort of cruel hoax is this?” (*) (*) Yes, I know […]
Continue ReadingSo That’s What’s Inside
The traditional Japanese origami crane is such an unusual shape, it makes one wonder why whoever first folded decided on calling it a crane, and also, why they gave it that particular shape. Well, now we know the answer: it’s shaped that way because that’s its skeleton, as the photo below shows. This fantastic model […]
Continue ReadingNow, That’s Settled
To recap the story: in 2009, I learned that a painter named Sarah Morris had been taking my crease patterns, recoloring and renaming them, and then selling them as her own work (without credit or permission). Needless to say, that was not happy-making, and after some unsuccessful attempts to engage her in rectifying the situation, […]
Continue ReadingSarah Morris Works Attribution
As noted here, as of March 1, 2013, the group of origami artists and Sarah Morris amicably settled our dispute over her usage of our origami crease pattern artworks. Most terms and conditions of the agreement are confidential, but as part of the agreement, the following will happen: Ms. Morris’s work Angel [Origami], 2009 shall […]
Continue ReadingSarah Morris Copyright Infringement
2013-03-21 Update: The dispute has now been settled. See details below. For several years, American artist Sarah Morris created a series of paintings on the theme of origami in which she took origami crease patterns by several international origami artists, changed the color scheme, made up her own names for them, and then sold and […]
Continue ReadingI Get Swag
You know when you’ve really made it in a field when people start sending you free stuff in hopes, I suppose, that your famousosity rubs off on the freebies. My moment of made-it-ness happened a few weeks ago, when I was contacted by the good folks at the X-acto (TM) Precision Instruments company, who were […]
Continue ReadingA Subject that Sucks
…blood, that is. In April, 2012, I was approached by the New Yorker magazine to create an origami mosquito as an illustration for an upcoming article. They knew me in part because I’ve done some origami illustration work for Wired magazine, which is part of Conde Nast, the parent company of them both. (Possibly a […]
Continue ReadingGhost Deer
I haven’t posted in quite a while, mostly because I’ve been bodaciously busy traveling on assorted origami business. The latest (and current) trip was to set up my exhibition at the Lady Bird Johnson Wildflower Center in Austin, TX. We set everything up Thursday, then came back Friday morning for some finishing touches. I’d folded […]
Continue ReadingDoodling with Sensei
As you may have seen, the Google Doodle for March 14, 2012 is made of origami and celebrates the 101st birthday of Akira Yoshizawa, the father of the modern origami art. Origami has a multi-century history as a folk art in Japan, and Yoshizawa was not the only, or even the first, of his countrymen […]
Continue ReadingSkin in the Game
There’s an anecdote that often makes its way into business/marketing presentations, about the difference between “interest” and “commitment.” The example given pertains to a bacon-and-eggs breakfast. The chicken had an interest; the pig was committed. This sort of differentiation doesn’t come up in the origami world very often. Most origami aficionados pursue the art as […]
Continue ReadingI Haz a Cover
It is not unknown for musicians to use origami for cover art (Jay Ansill‘s album “Origami,” with a range of Elias figures on it, comes to mind), and I always like the combination. Origami and music just naturally seem to go together. Sometimes that is, for me, literal; the occasional 16-hour day in the Origami-d’oh! […]
Continue ReadingDogs, Design, and a Farewell
There is an old joke about the difference between cats’ and dogs’ relationships with their owners: to a dog, their owner is God, while to a cat, the cat is God. To our 14-year-old black lab, Meg, every human being she ever met was a God, and they all preached the same theology: “And God […]
Continue ReadingThe Two Cultures
In early 2010, I was invited to give a talk at a conference organized by philosopher Rob Pennock at Michigan State University, celebrating the 50th anniversary of a famous lecture by British novelist C. P. Snow, titled “The Two Cultures.” In this lecture, and a subsequent book, Snow bemoaned the widening gulf between the sciences […]
Continue ReadingThe Fold: Hexabox
My newest installment for OrigamiUSA’s The Fold is up: Crease Pattern: Hexabox It’s a rotationally symmetric, solid-flanged shape based on a cool idea of Jeannine Mosely’s. Looks like this: I’ve used this basic notion for a lot of geometric solids, including several inspired by Southwestern pottery. Most of the curved ones require their creases to […]
Continue ReadingThe Haverhill Fritillary
Some figures take hours or days of careful design; others are quick doodles based on exploration of an idea. My latest posting is one of the latter. It started out as just a technical puzzle: “can I add A to B?” But it turned out to have a nice and relatively novel folding sequence, so […]
Continue ReadingInside the Origami-D’oh! Studio
Origami-D’oh! (J): What you say when the paper rips after 6 hours of precreasing. It’s fall here in Alamo, and the massive oak tree outside is doing its annual best at burying the Origami-D’oh! Studio in leaves: I sometimes get questions about what goes on inside the forbidden city here. I think people might imagine […]
Continue ReadingThe Truth that even Truthers Deny! Part 3
The shocking revelation of responsibility Yes: the perpetrator of 9/11 was, indeed: And if that doesn’t convince you this was all planned, well, then nothing will. ← Previous: the horrifying story!
Continue ReadingThe Truth that even Truthers Deny! Part 2
The horrifying story encoded in our currency! Our story begins with the $5 bill. It was a clear day, and two towers rose into the sky… But there was a cloud gathering…it was a shadow of foreboding. And suddenly, one of the towers was struck near the top! An explosion and cascade of debris! Then, […]
Continue ReadingThe Truth that even Truthers Deny! Part 1
How origami and American currency proves that the U.S. government orchestrated 9/11 I know, you read that headline and say, “Whoa. That is some serious qhat you’ve been chewing.” But all I can say is this: if you look beyond the “facts,” and the “evidence,” and the “physics,” and the “rationality,” and the “reason,” it […]
Continue ReadingOrigami Diagramming Conventions
Diagramming, Part I These articles were written in 1989–1991. Despite many changes in the origami world over the following decades, the recommendations remain basically sound. I’ve updated a few bits with some footnotes. Origami is an international phenomenon that has moved far beyond its traditional boundaries of Japan and Spain. Its practitioners are found world-wide, […]
Continue ReadingPaper
I am often asked what kind of paper to use for origami. There is no single answer; it depends on what you’re folding. On this page, I’ll talk a little bit about the most common types of paper for origami and my own experiences with them. Traditional Papers Found Paper One of the things that […]
Continue ReadingGoogle’s Doodle: Akira Yoshizawa
The Google Doodle for March 14, 2012, honored Akira Yoshizawa, the father of modern origami, on his 101st birthday. The Doodle featured the Google logo, folded from origami (each letter folded from a single uncut sheet), decorated with origami butterflies folded from one of Yoshizawa’s most famous and iconic designs. In the week or so […]
Continue ReadingChildren’s Books, Nature Poems and Activities
My wife, Diane, is a naturalist, teacher, and children’s book author. See her website here.
Continue ReadingBugaboo Spire, Northeast Ridge
As we have done for several years, Larry Sverdrup and I set out to do a new climb this July. Larry is quite an avid outdoorsman and his pet project for many years has been to climb as many as possible of the climbs in the book 50 Classic Climbs (which is affectionately, and nowadays […]
Continue ReadingA Familiar Name
Written in 2009. See also Connections. So here I am, in Ithaca, NY, giving a talk at their Light in Winter Festival. It’s my usual math + origami + science + technology + all-this-stuff-is-tied-together spiel. At the end of the talk, there’s the usual Q&A, and then the formal stuff breaks up and individuals walk […]
Continue ReadingConnections (with apologies to James Burke)
This was written in 1997. See also A Familiar Name. In 1992, I left my job researching lasers at NASA’s Jet Propulsion Laboratory in Pasadena and moved to a small company in San Jose called SDL, which designs and manufactures a wide variety of the type of laser called a “semiconductor laser.” San Jose is […]
Continue ReadingHow to Teach a Fold
This article originally appeared in British Origami Magazine, August, 1985. Those who don’t invent (the “unwashed heathen” to the creative folder) are usually quite disgusted by the inventor’s smug posturing, and look forward to their moment of revenge—the teaching session. Creative folders who also teach their own folds are utterly insufferable—they make use of “only”s, […]
Continue ReadingRules for the Creative Folder
This article originally appeared in British Origami Magazine, June, 1985. If you ask a paperfolder, he will tell you that the reason he goes to the annual origami convention in Britain (or New York, or Pago Pago, wherever) is to share the fellowship of other folders; to improve his own craftsmanship; to boldly go where […]
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