Robert Lang, one of the world鈥檚 leading artists in origami 鈥� Japanese paper folding 鈥� just happens to be a physicist who loves animals and math. He puts mathematics into his folded animal sculptures by using his MacBook Pro, TreeMaker and ReferenceFinder 鈥� two freeware programs he created 鈥� and Wolfram鈥檚 Mathematica, to convert simple stick figures into full-blown origami crease patterns.
According to Lang, 鈥淭he cool thing about origami is that it is a very mathematical art. In many arts, there鈥檚 pure artistic skill. In origami, it鈥檚 almost half and half. You can do things with pure art, you can do things with pure math, but if you put them together, you get far more satisfying results than either one alone.鈥�
Lang loves to design and fold creatures of such realism and complexity that it seems impossible that each is composed of a single sheet of paper, no cuts, no glue. In 2007 he folded a single sheet of 4.25m-square piece of paper specially made at Papeterie Saint-Armand in Montreal, into a life-size model of a Mesozoic flying reptile, complete with claws and talons.
After a rough first winter adjusting to temperature and humidity fluctuations in the gallery, this Pteranodon has been strengthened with rods to glide gracefully above the Redpath Museum鈥檚 dinosaur skeleton at 成人VR视频.
Lang notes that applying mathematical principles to origami has enormously advanced the art. Though origami is several hundred years old it has been limited to simple creations such as paper cranes or boats. 鈥淭he modern art form,鈥� he says, 鈥渨as born in the 20th century when a Japanese artist named Akira Yoshizawa started creating new figures of artistic beauty that inspired other origami artists to expand their horizons.鈥� Yoshizawa also created an instructional language that then enabled them to share their creations and build off of each others鈥� work.
For small shapes, Lang prints out the pattern and tests it. For monumental animals such as the Redpath Museum Pteranodon, he exports his Freehand illustration to a generic format such as eps and imports it into Mathematica.
鈥淚 love Mathematica,鈥� Lang says. 鈥淭reeMaker is a surgeon鈥檚 scalpel 鈥� a very narrow tool that does what it does incredibly well, but nothing else. Mathematica is the world鈥檚 largest Swiss Army knife. You can do anything in it: analyze, compute, simulate, visualize. And almost any project that involves something I鈥檝e never done before probably involves Mathematica at some point. 鈥淲ith Mathematica,鈥� Lang continues, 鈥淚 can import things. I can manipulate them, I can do visualization. I can solve equations, I can do algebraic manipulations and 3D renderings. I can plot surface graphs. It鈥檚 just mind-boggling.鈥�
For the Pteranodon, Lang wrote a quick Mathematica program that displayed its stick figure structure and a corresponding crease pattern. 鈥淏y changing the points in the crease pattern,鈥� he says, 鈥淚 could see its effect on the dimensions of the stick figure. I could make the wings longer, the neck shorter. The current version of Mathematica has live sliders so you can adjust them to find the perfect dimension on the crease pattern. You just watch the crease pattern and shape of the folded thing move in response to the sliders.鈥�
The other way to have designed the Pteranodon, Lang says, would have been to change a dimension on a piece of paper, fold it for two hours and see what the result looked like. 鈥淏ut with my two or three hours of investment in programming, I go 鈥榖adoop鈥� and see the result. And that鈥檚 just incredible.鈥�
Lang鈥檚 other monumental origami works include a Heron that is almost 3 times its normal size for the Masterworks of Origami exhibition at the Mingei International Museum, a life-size orchestra for the paper company Norske Skog and displayed before it was accidentally destroyed at a pulp and paper trade show, and most recently, a larger-than-life-size origami representation of a famous Japanese woodcut in which a magician tosses into the air a sheet of paper, which turns into a crane and flies away. This exhibition was installed at the Zeum children's museum in San Francisco.
Lang is a physicist with more than 40 patents to his credit, yet he is still surprised by the wide range of practical applications for computational origami 鈥� from space telescopes the size of football fields and automotive applications like folding airbags to medicine and consumer electronics.
- Learn more about .
- Read , published in The New Yorker on February 19, 2007.
All quotes and citations were taken聽from and from a profile on the .