Creator/Folder : R.J. Lang
Photo comes from the website of Ben Ball
with his authorization
Origami Design Secrets:
Mathematical Methods
for an Ancient Art



Last update : 20 august 2003

Publication : sept 2003

Creator/Folder : R.J. Lang
Photographer : K. Burczyk
with her authorization



Cover from the site A K Peters.
Buy the book on this site


Creator/Folder : R.J. Lang
Photo comes from the "Origami Interest Group" website by Marten van Gelder with his authorization

Here's the table of contents (the page numbers will be different).
Any section with a letter (e.g., "4.A Stealth Fighter") consists of folding instructions for the named model.

In addition to the 25 models with full instructions (and color photos), there are crease patterns for another 25 or so figures that either have been published elsewhere or will be published, in Origami Insects II. So the CPs that are not published yet will be a bit of a challenge, at least until I finish OI2.

Along with the folding diagrams, there's 100,000 or so words of prose and a couple of hundred figures about how to design.

Robert J. Lang



Download the
pamphlet here



TABLE OF CONTENTS :


1. INTRODUCTION 8

2. THE BUILDING BLOCKS OF ORIGAMI 15
2.1. Symbols and Terms 16
2.2. Basic Folding Steps 20

3. ELEPHANT DESIGN 43
3.1. Elephant Design 1 45
3.2. Elephant Design 2 46
3.3. Elephant Design 3 48

4. TRADITIONAL BASES 54
4.1. The Classic Bases 54
4.2. Other Standard Bases 56
4.3. Relationships Between Bases 61
4.4. Designing with Bases 64
4.5. Simple Variations on Bases 69
4.A. Stealth Fighter 72
4.B. Snail 72
4.C. Valentine 72
4.D. Hummingbird 72
4.E. Baby 72


5. SPLITTING POINTS 73
5.1. The Yoshizawa Split 73
5.2. The Ideal Split 78
5.3. Splitting Edge and Middle Flaps 85
5.4. More Complex Splits 90
5.5. More Applications of Splitting 96
5.A. Pteranodon 98
5.B. Goatfish 98

6. GRAFTING 99
6.1. Border Grafts 99
6.2. Strip Grafting 112
6.3. More Complicated Grafts 118
6.4. More Applications of Grafts 129
6.A. Songbird 1 133
6.B. KNL Dragon 133
6.C. Lizard 133
6.D. Tree Frog 133

7. PATTERN GRAFTING 134
7.1. Pleated Patterns 134
7.2. Pleated Textures 142
7.A. Turtle 157
7.B. Western Pond Turtle 157
7.C. Koi 157


Creator/Folder : R.J. Lang
Photo comes from the Gilad's Origami page
with his authorization


8. TILING 158
8.1. Uniaxial Bases 159
8.2. Splitting Along Axes 164
8.3. Tiles of Crease Pattern 168
8.4. Tile Assembly 170
8.5. A Multiplicity of Tiles 181
8.6. Stick Figures and Tiles 184
8.7. Dimensional Relationships Within Tiles 194
8.8. From New Tile to New Base 196
8.A. Pegasus 200

9. CIRCLE PACKING 201
9.1. Three Types of Flap 201
9.2. Overlaps 205
9.3. Connections to Tiles 206
9.4. Scale of a Circle Pattern 207
9.5. The Circle Jig 210
9.6. Symmetry 212
9.7. Selective Inflation 216
9.8. Circles and Rivers 225
9.9. Mathematical Circle Packings 226
9.10. Bases from Equal Circle Packings 231
9.11. The Margulis Napkin Problem 237
9.12. Comments 242
9.A. Emu 243
9.B. Songbird 2 243

10. MOLECULES 244
10.1. Tangent Points 244
10.2. Triangle Molecules 250
10.3. Quadrilateral Molecules 251
10.4. Waterbomb Molecule 252
10.5. Arrowhead Molecule 256
10.6. Gusset Molecule 259
10.7. Molecules with Rivers 262
10.8. Crease Assignment in Molecules 265
10.9. Putting it All Together 268
10.10. Higher-Order Polygons 275
10.A. Orchid Blossom 282


Creator : R.J. Lang
Folder & photos : N. Terry

11. TREE THEORY 283
11.1. The Tree 283
11.2. Paths 286
11.3. Scale 291
11.4. Subtrees and Subbases 292
11.5. Computational Molecules 296
11.6. Quadrilaterals 297
11.7. Higher-Order Polygons 301
11.8. The Universal Molecule 305
11.9. Other Techniques 311
11.10. Comments 316
11.A. Alamo Stallion 317

12. BOX PLEATING 318
12.1. Mooser’s Train 318
12.2 Box Folding 325
12.3. Box-Pleated Flaps 342
12.4. Square/River Packings 347
12.5. Filling in the Molecules 350
12.6. Bouncing Creases 362
12.7. Elias Stretch 365
12.8. Ortholinear Rivers 366
12.9. Holes and Plugs 367
12.10. Box-Pleating versus Optimal Bases 369
12.11. Comments 373
12.A. Bull Moose 375
12.B. Black Forest Cuckoo Clock 375

13. HYBRID BASES 376
13.1. Flats and Flaps 376
13.2. Multiaxial Bases 382
13.3. Grafted Kite Base 385
13.4. Mixing and Matching 389
13.5. Wrapping It Up 389
13.A. African Elephant 392

14. ALGORITHMS 393
14.1. Mathematical Model 393
14.2. Definitions and Notation 394
14.3. Scale Optimization 394
14.4. Edge Optimization 395
14.5. Strain Optimization 395
14.6. Optional Conditions 396
14.7. Stubs 398
14.8. Universal Molecule 399

A. REFERENCES 402
B. ACKNOWLEDGEMENTS 417
C. GLOSSARY OF TERMS 419
D. INDEX 429


Creator : R.J. Lang
Folder : Paula Versnick
Photo comes from the Gerard & Paula's site
with Paula's authorization.


List of models with folding instructions :

1- Stealth Fighter
2- Snail
3- Valentine
4- Hummingbird
5- Baby

6- Pteranodon
7- Goatfish
8- Songbird
9- KNL Dragon

10- Lizard
11- Tree Frog

12- Turtle
13- Western Pond Turtle
14- Koi

15- Pegasus
16- Emu
17- Songbird 2

18- Orchid Blossom

19- Alamo Stallion
20- Bull Moose
21- Black Forest Cuckoo Clock

22- African Elephant
23-24-25-
3 more short sequences embedded in one of the chapters


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Origami Insects 2

Last update : 7 july 2003





LadyBug - Creator/Folder : R.J. Lang
Photo : Gérard Blais with his authorization
Photo comes from the website of Origami-Montréal

Here are the models. None have appeared in books, but several have appeared in convention programs and several have their crease patterns in ODS. (The opus numbers won't appear in the book, they're just for clarification.)

As for how to get your hands on it, it will be published by Gallery Origami House, and you will be able to order it directly from them and (probably) from OrigamiUSA & BOS, probably in September.

Robert J. Lang

(7 july 2003 - Text published on the Origami-list)

Opus Title Opus Title
410
381
370
406
343
380
369
368
379

Butterfly
Acrocinus longimanus
Ant
Tarantula
Pill Bug
Cockroach
Dragonfly
Eupatorus gracilicornus
Scorpion

330
357
416
377
329
382
417
424
344
Flying Ladybird Beetle
Longhorn Beetle
Praying Mantis
Periodical Cicada
Flying Cicada
Flying Grasshopper
Kabuto Mushi
Hercules Beetle
Centipede

Discover photos of the models and buy the book here


Index Lang

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