Origami Paper

Rattlesnake, opus 539

Robert Lang began his foray in origami when he was six years old.  His teacher gave him a book detailing several fold designs.  Lang, at that time, viewed origami as both a mental challenge and a world of endless possibilities.  The reality, as little Robert Lang saw it, was that any free sheet of paper he could obtain was a potential toy in the making.  As Lang got older he never grew out of what he thought might be a childhood obsession.  Instead, he began to create his own folded figures and always had origami on the back burner as he went through the rest of his life.

In 1987 Robert Lang and his wife Diane moved to Ludwigsburg, Germany where he was executing his post-doctoral work in Applied Physics as part of a program with the California Institute of Technology.  While in Germany the couple made a stop in Black Forest, original home of the cuckoo clock.  After seeing the intricately carved clocks, Lang was inspired to fold his own version of a Black Forest clock from paper.  On the artist’s website, he freely admits that his “first cuckoo clock was fairly plain”[1] but that his second was better.  By the third version he had a novel design, very intricately folded.  Black Forest Cuckoo Clock, opus 182 was Lang’s first real smash hit in the origami world.

The design is folded from a single one foot by ten-foot rectangle of Zanders “elefantenhaut” paper down to a fifteen-inch high version of a Black Forest Cuckoo Clock.  Lang’s masterpiece is complete with a pendulum and pinecones at the bottom, leaves along the sides, and a stags head at the top of the clock.  The final design was so involved it took Lang three months to complete the folding instructions and another six hours to actually complete the folds.  But the work paid off.  Lang was flown to Japan to demonstrate his design on television and was beginning to be recognized as an international origami master. 1987 was pre computational origami for Lang, but the Black Forest Cuckoo Clock was still one of the most complex origami figures produced to date.

Though Lang was receiving international acclaim for his origami designs in the late 1980s and throughout the 1990s, he kept pursuing physics as a full time career.  After his doctoral studies, Lang went on to work for NASA’s Jet Propulsion Lab in 1988, then spent more than nine years at Spectra Diode Labs and eventually ended his full-time pursuit of physics at JDS Uniphase in 2001.  In that time Lang was credited with more than forty patents, most revolving around laser physics, and produced more than eighty technical papers.  To this day Lang holds technical positions in the field of physics, including Editor in Chief for the Journal of Quantum Electronics.

In the early 1990s Lang and another origami master Toshiyuki Meguro both independently recognized that origami was fundamentally a circle-packing problem.  In other words, mathematics was the key to complex origami design because each flap or appendage of an origami figure must originate from a circular section of paper.  The more circles one can fit on a page, the more intricate the figure can be.  Lang wrote a program named TreeMaker in the early nineties that was designed to formulate a “non-trivial origami figure based on a description of the number, lengths, and connectedness of the flaps.” [2] Within a number of months Lang had written the first version and by 1998 he had released TreeMaker 4.0, which could solve origami problems that Lang could not solve with traditional pen and paper.

ReferenceFinder is another program Lang wrote in the 1990s, meant to accompany TreeMaker.  Where TreeMaker works to solve the problem of the placement of circles on a page, ReferenceFinder works with the problem of folding an object once the crease pattern is mapped out.  Before ReferenceFinder origami artists were left with a trial-and-error approach to folding.  Even if they could map out the creases, they then had to figure out in what order to make the folds to create the intended figure.  ReferenceFinder uses seven folding operations to calculate the best possible folding sequence for a given figure.  Those seven folding operations are known as the Huzita-Hatori Axioms.  The Huzita-Hatori Axioms come from the discoveries of the first six axioms in 1989 by Humiaki Huzita, and the last one by Koshiro Hatori in 2001.  The axioms are essentially a set of mathematic rules that define how paper may be folded.  Because the axioms are expressible in equation form, Lang recognized the ability to create a computer program based on those formulas.  By 2003, and the third version of ReferenceFinder, all seven axioms had been integrated and could generate the folding sequence for virtually any set of crease patterns.

With TreeMaker and ReferenceFinder now in hand, and the use of a commercial precision laser cutter to score paper, Lang is able to create works of art that would not be otherwise possible.  One such work is Rattlesnake, opus 539, a private commission in 2008 that features a snake coiled in a defensive posture, tail up as if to shake its rattle as warning before it strikes.  The tail itself contains ten beads and the body features approximately one thousand scales.  The head contains nostril indentations and an open mouth.  The snake is folded from one uncut rectangle of brown Thai unryu paper[3] and at completion is approximately 8? in size.  The incredible precision of the folds and the intricacy of the hundreds of scales and rattle make the piece incredible and nearly unbelievable under the standard constraints of origami.

Lang’s complex origami is often referred to as computational origami because of his use of mathematics and the computer.   Without the mathematic discoveries of the Huzita-Hatori Axioms, the development of the computer as a tool for complex calculations, and without the laser cutter to aid in folds, Lang’s artwork would not be possible.  Lang is an example of a brilliant scientist porting his knowledge over to another field.  For that ability Jan Polish of Origami USA calls Lang the “renaissance man of origami.” [4]

[1] http://www.langorigami.com

[2] http://www.langorigami.com

[3] http://www.langorigami.com

[4] http://www.smithsonianmag.com

Tags: Computational Origami, Origami, ReferenceFinder, Robert Lang, TreeMaker

This entry was posted on Monday, March 8th, 2010 at 5:30 pm and is filed under Artist Profile, Grad School. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

Robert Lang Origami