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Crease 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 unfolded square to the folded form, compressing hundreds of creases, and sometimes hours of folding, into a single diagram! Small wonder, then, that to many people, the concept of an origami crease pattern as a form of origami instruction is more than a little reminiscent of a famous Sidney Harris cartoon in which a scientific derivation is described by the phrase “then a miracle occurs…”

As the complexity of origami has increased, crease patterns have become much more popular as a means of conveying origami. Part of the reason is that it’s a lot easier to draw a single crease pattern than to draw a detailed step-by step folding sequence. Part of the reason is that many origami composers (including myself) construct crease patterns as part of their design process, so the finished crease pattern comes “for free.” And part of the reason is that with the general rise in folding ability worldwide, a reasonable number of people now have the skill to “read” a crease pattern and fold the encoded form.

The profile of CPs has been raised in recent years through the “Crease Pattern Challenge” feature in Origami Tanteidan Magazine, and nowadays, it is almost de rigueur to add a thumbnail of the crease pattern to the origami figure’s label at origami exhibitions. We should note, however, that while the ubiquity of crease patterns is recent, the concept itself is decades old: many of the pioneers of the modern art from the 1960s and 1970s — notably Neil Elias — frequently recorded their compositions as crease patterns, at least in their private notebooks.

To the non-origami person, the sequence that transforms a sheet of paper into a beautiful folded object can seem miraculous. Even to the origami aficionado, however, the idea that a single drawing of the creases conveys the full folding sequence can seem equally miraculous. But in fact, a crease pattern can sometimes be more illuminating than a detailed folding sequence, conveying not just “how to fold,” but also how the figure was originally designed. And thus, it can actually give the folder insight into the thought processes of the origami composer in a way that a step-by-step folding sequence cannot.

So the value of crease patterns goes beyond saving time for lazy diagrammers. But in fact, there’s another reason why some compositions are published as CPs; it’s not just that the composer doesn’t want to spend the time drawing up a step-by-step folding sequence. It may be that the composer doesn’t even know of a step-by-step sequence. In fact, one may not even exist! Many modern origami designs, particularly if they were designed using tree theory, circle packing, box pleating, or any of the other tools of modern design, are designed in an “all-or-nothing” way. The creases all work together when they are fully folded, but it is often the case that there are no intermediate states — no subsets of the creases — that can be folded together, which would form the individual steps. For such a model, the only way to assemble the model is to precrease all of the creases, then gently coerce them all to come together at once with a minimum of bodging. That method of assembly, as it turns out, is almost always the approach used for folding a model from a CP.

So, while it is often possible to fold an entire model from a CP and a photograph, there is a bit of a puzzle to the activity. The first thing to realize about a crease pattern is: it may not show all the creases, depending on the folding genre. Mathematical and geometric crease patterns usually show all the creases, but representational origami rarely shows every crease in the finished form, as it would make the crease pattern impossibly busy. Instead, the crease pattern gives the creases needed to fold the “base,” that is, a geometric shape that has the right number and arrangements of flaps. At the very least, it is still left up to the folder to add thinning and shaping folds; but there can also be quite substantial manipulations of the base that are not reflected in the crease pattern and these, like shaping folds, are left to the folder to puzzle out.

One difference between CPs and diagrams is that CPs rarely use both the standard mountain (dash-dot-dot) and valley (dashed) lines. While the standard patterned lines work well for step-by-step diagrams in which each diagram only contains a few action lines, in crease patterns that may contains tens or hundreds of mountain and valley folds, the standard line patterns are very hard to distinguish. One of the keys to being able to read a CP is to be able to identify large-scale features of the pattern from some distance away. This means that we need to be able to clearly distinguish mountain and valley fold lines from far away, and the standard line patterns just don’t work: they dissolve into a morass of busyness.

Thus, crease pattern authors use different line styles than step-by-step diagrammers, but there is not yet a single established style. Over time, I've experimented with several different styles, and you will see that experimentation reflected in the patterns to the right. Most recently, for maximum readability, I have adopted the style of using solid black lines for mountain folds, and colored dashed lines for valley folds. This style keeps valley lines consistent with step-by-step styles and provides clear distinction between line styles in both color and black-and-white printing.

Crease patterns can also show additional information that illuminates the design or is helpful for the actual folding. It is sometimes helpful to show creases that aren’t actually folded, either because they help convey information about the structure, or they may show how to construct key reference points. For mirror-symmetric models, I will often show precreases or the fundamental geometry on one side of the pattern and the full pattern on the other. It is also helpful at times to highlight the hinge creases and/or to show the circle/river packing; you'll find a few examples of both here.

On this page, you'll see all of the crease patterns that I have on the site. (I don't have a CP for every composition, just these. If there are no published diagrams listed for a design, this is the closest you're going to get to instructions.) Click on an image to see a larger photograph of the folded artwork; click on the crease pattern to see a larger pdf image of the crease pattern. Puzzling out crease patterns can be fun; if you get hooked, there are many more scattered around the internet. Even if you don't try to fold from them, crease patterns are beautiful, intriguing, and inspiring in their own right. Enjoy!

Crease Pattern Links

There are several good sources for crease patterns on the web. Here are several links to pages of interest.

Gerwin Sturm's Guide to Box Pleating
A very nice guide to how to interpret and fold box-pleated crease patterns. Scroll down to find the links.

Satoshi Kamiya
Satoshi has composed what are probably the most challenging models in the world of origami, many of which are described by some of the most invigorating crease patterns.

Brian Chan
A deserved star of American origami, Brian has created a variety of new designs using tree theory and other techniques.

Grupo Origami Patrones
A Spanish-language Yahoo group devoted to the study of crease patterns.

Diego Quevedo
A Spanish-language blog about crease patterns and their interpretation.

Crease Pattern Gallery

Click here for a display listing of crease patterns for many of my designs.