Any valid flat crease pattern can be colored using only two colors without any adjacent regions sharing the same color.
The second secret is the concept of the as the primary artifact of design. Traditionally, folders followed step-by-step diagrams. Lang, however, often works backward: he first computes the complete crease pattern—the ghostly network of mountain and valley folds that contains all the information of the final model. To the untrained eye, a Lang crease pattern looks like a dizzying blueprint of a futuristic building. But to him, it is a map of molecular precision. Each line represents a constraint solved. By using a computer program he developed called Treemaker , Lang can input a stick-figure drawing of a desired creature, and the software outputs a crease pattern that, when folded, yields proportions accurate to within a fraction of a millimeter. This inverts the creative process: the artist no longer discovers the folds sequentially; he designs the final shape and then computes the exact sequence required to achieve it.
Optimizing the folding algorithms of airbags so they deflate and inflate safely within milliseconds.
For highly complex subjects like insects with numerous segmented legs or armor, Lang explains . This technique restricts all creases to horizontal, vertical, or 45-degree grid lines. While it can produce bulky models, box pleating offers an incredibly predictable and structured way to distribute paper for ultra-complex structures. 3. Hex Pleating and Tilings origami design secrets robert lang
Before the late 20th century, creating a new origami model was an art of gradual modification. If an artist wanted to create a bug, they would tweak an existing base, hoping to squeeze out enough paper to form legs or antennae.
Origami Design Secrets by Robert J. Lang: The Book That Revolutionized Paper Folding
Lang did not just write down these theories; he wrote the software to implement them. Origami Design Secrets serves as the conceptual manual for , a freeware program developed by Lang. Any valid flat crease pattern can be colored
How to get started with Lang's free design software, or Tessellotica
Whether you are a casual folder looking for a challenge or a mathematician interested in geometric theory, this book is a masterpiece. Here is everything you need to know about it.
Aligning the circles along specific geometric axes, often resulting in elegant, diagonal crease patterns. Lang, however, often works backward: he first computes
The book focuses on the "underlying structure" of origami rather than just specific models.
For centuries, origami was a tradition of passed-down patterns. In the late 20th century, a revolution occurred. Folders began applying geometry to paper, realizing that the medium wasn't limited to simple shapes—it could produce any subject with infinite complexity.
At its heart, Lang's book is a reaction against the "cookbook" method of origami instruction, which provides step-by-step diagrams for a limited number of models without explaining the underlying "why". Instead, Origami Design Secrets is an educational and philosophical guide that aims to teach the structural and geometric concepts behind all origami.