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Box pleatingby Marc Kirschenbaum
Neal Elias has been one of my biggest creative influences. Even though his most creative period occurred during the mid 1960ís through the mid 1970ís, his influence has been strong enough to affect people creating in the 1990ís. When looking at a work by Elias, the viewer is often struck by an incredible sense of composition, which was often heightened by the use of colour changes. Elias was among the first creators to fold multi-subject models, and he was able to do this with more grace than most creators could do with single subject models. Milestone models of his have included "Llopioís Moment of Truth," which portrays the famous bull fighting scene, all from a single sheet of paper. He has also produced various dancing couples, instrumentalists with their instruments, and an incredible series of famous peopleís busts.
Perhaps Neal Eliasí greatest contribution to origami was his development and popularization of a style known as box pleating. This style came about in the 1960ís to meet the apparent craving of more technically elaborate models. Up until that point, most models had been developed using the classic bases, whose use was starting to seem limited. Box pleating was perhaps the first origami style that allowed for a systematic means of creating appendages.
Recently, in the realm of technical folding, the classic bases have not died yet. Instead, new life was breathed into them by folders such as John Montroll, Robert Lang and Peter Engel in America, and by Jun Makawa in Japan. These people hit upon ways to break down the classic bases into their simplest structural elements, which they could then work with to produce a seemingly unlimited number of appendages. This new geometrically oriented style is perhaps the next major systematic means for appendage creation since box pleating. This new style was perhaps also the reason box pleated models have been much less popular in recent years. Is the new geometric style better than box pleating, or are more creators simply more excited about having a newer style to work with?
Before any of these questions can be answered, it would be appropriate at this point to define box pleating. Again, box pleating is a style of folding, so within that style, a range of procedures will be found. There are, however, a number of commonalties between models that fall into the box pleated genre. These models make extensive use of folds that are orthogonal to each other, with some folds at forty-five degrees, to allow for the structure to be collapsed flat. David Lister has made a distinction between models that use such folds for a three dimensional structural purpose, versus using such folds for forming appendages. Lister regards models that fall into the former category as being box folded. Since the techniques for box pleating and box folding are often used within the same model seamlessly, I prefer to simplify the categorization to just calling all such models box pleated.
At its most basic level, one of the simplest box pleated bases would be the waterbomb base. The flaps of the waterbomb base share a common characteristic with the flaps of most box pleated bases; they terminate as 45-45-90 degree triangles. The folding sequence for this base is not obviously box pleated. Most of the folds are at forty-five degree angles. The orthogonality comes from that the edges of the flaps are from the sides of the square, which are indeed orthogonal to each other.
Designers who employ box pleating will rarely have anything that resembles a waterbomb base in their models. This is because the flaps of this base are wide and cumbersome, and few models call for flaps with those qualities. Using box pleating techniques, it is easy to take a simple box pleated base (such as the waterbomb base), and make the flaps have a higher aspect ratio (i.e., appear to be longer). If you were to sink the tip of a waterbomb base in halfway, the flaps would then become twice as long as the height of the base (prior to sinking, both the height and appendage length were equal). If you have the patience, designers have taken such sinking to extremes to produce appendages with extremely high aspect ratios. If you sink into twentieths, the resulting flaps will be twenty times as long as their height.
You can get increasingly complex structures by linking up such waterbomb-like modules. By starting with a long enough rectangle, you could form multiple waterbomb bases which can be joined by their edges. These sub-bases could receive the same sinking treatment as described before. This is a very cut and dry technique for creating subjects with many appendages (such as insects). If you start with a 3x1 rectangle, that will give you eight long appendages, which will suffice for many insects.
Box pleated models are often not so explicit in their instructions. The diagrams for box pleated models often take on a blue print style; a crease pattern is shown, and the folder is expected to follow it. A diagram might show a square with iterations of squares of mountain and valley lines, connected at their corners with more fold lines. This would just be asking for the folder to form a multiply sunk waterbomb base.
Sinking is just one of the ways in which box pleating can be carried out. Often the paper is pleated (like a fan), and then the pleats are stretched. This technique, appropriately enough, is called stretch pleating. You can try this out for yourself by first precreasing a square into eighths, both vertically and horizontally. Take the square, and pleat it together like a fan, with the coloured side on the exterior. Hold the fan shape in the upright position, looking at the white side, and grasp the top two original corners. Pull these corners apart from each other, and begin to fold them in half along their diagonals. These folds should terminate at the first interior crease (which in this case is 1/8 inwards). Next, bring the top edge down. If you turn the model over, and treat the interior rectangle as in the previous steps, the top corners of the square will begin to become distinct appendages. Repeating this iterative process until there is nothing left to stretch, will give you two long appendages on top, and a fan-like appendage at the bottom. It is noteworthy, in this instance, repeating the stretching procedure on the fan-like appendage will result in the equivalent of a waterbomb base sunk into fourths.
The above is only one example of stretch pleating. Since pleats can be stretched from the middle as well as from their ends, it is possible to arrive at appendages of varying lengths and structural configurations. It is often very easy to control the length of an appendage, as each iteration of stretching increases the length of the appendage one unit (a unit is the width of the pleat used). Experimenting with the techniques used by people such as Elias, should give any budding creator enough technique to arrive at most subject matter with relative ease.
From what I have said, one would think box pleating would satisfy most creatorís need to have a systematic means for base creation. For some people it has, but it does raise the question as to why newer systematic techniques were developed. Speaking as a creator who used to use box pleating techniques almost exclusively, I know why I switched to more geometric means of expression.
Box pleating does have some inherent problems, which might not have been obvious from this discussion. Often, a lot of precreasing is required, which can be quite tedious. It is not uncommon for the diagrammer to require the folder to precrease the paper into divisions greater than twenty. Wile some people might not find this process as boring as I do, most people will agree the resulting creases found along the length of the appendages are unsightly.
It is possible to precrease carefully enough, so as not to spoil your appendages with extra creases. Still, for many applications, the appendages derived from box pleating leave much to be desired. Such appendages look like a strip of paper that terminates abruptly as a right triangle, and in some cases, as a squared off rectangle. Such appendages do not suit most natural subjects well; their appendages often taper off naturally. Birdbase-like flaps would be better suited for such applications. Of course, it is possible to shape box pleated appendages, but the process tends to be awkward.
From a design perspective, box pleating can be restrictive in nature. It is very difficult to adjust proportions, especially when dealing with groups of appendages. If you wanted to make a group of appendages larger on a birdbase-like flap, you could simply use more of the flap, and use the same folding sequence to produce a larger version of the same group of appendages. This is possible, as you are really just starting with a triangle that is a larger version of the one you originally used. Such a luxury is not afforded to the designer when box pleating. To get larger appendages, the designer can not just simply use more of the paper and use the same folding sequence. This is because he would then be dealing with a rectangle of different proportions; a new folding sequence would then be in order. Often, the only solution is to begin with a rectangle of different proportions.
The relative lengths of appendages are difficult to control as well. Since the lengths of appendages are governed by the unit size chosen (which is the width of the appendages), a small enough unit is needed to get the desired variance in appendage sizes. This can sometimes result in appendages that are too thin.
Limiting oneself to 90 degree and 45 degree folds will also limit the number of appendages obtainable from a given area. Utilizing more acute angles in the overall structure would provide more room to add appendages, but then the structure would not be box pleated. Designing with only box pleating techniques can be a significant compromise on a modelís structure.
It would seem I have painted a very bleak case for using box pleating, when more flexible design techniques are available. As it turns out, box pleating is still used today, with good reason, and more importantly, to good effect. Even when box pleating is not the ideal route to approximating a subjectís form, becoming well versed with such techniques is an ideal stepping stone towards understanding the more advanced geometric techniques. I have very few regrets about my excursions in box pleating when I was younger. The design techniques I used then were much more straightforward than the more elaborate geometric things I do today. This was possible, as I utilized one of the most straightforward design methodologies around. It is the limitations of box pleating that can make a modelís structure more obvious and easier to understand.
For all of its inherent limitations, is there room for innovation in box pleating? I think there is, as I have seen some new directions that have yet to be fully explored. Most box pleated models have their line of symmetry running along the length of the rectangle. When a square is used, very few people orient their model along the diagonal. Using the square in the diamond formation provides lots of new ideas that have yet to be explored with box pleating. Similar techniques can be used, but since appendages tend to terminate differently, new solutions must be explored.
The most effective users of box pleating have exploited its biggest trait. Virtually all of the elements created through box pleating do not converge to a point. Folders have created various repeating patterns and textures with box pleating techniques. Patterns such as brick walls have been created, and similar patterns have been integrated into animal models to produce porcupines and dinosaurs with a full set of spikes. Colour changes are possible too. One of the most effective applications of this came from Steven Casey, who produced a chessboard from a single square.
Other noteworthy innovators in box pleating include Fumiaki Kawahata and Jeremy Shafer. Kawahata is noteworthy for successfully integrating box pleating techniques with more modern geometric techniques. Shafer (who also has utilized other techniques in his works), has seemed to catch the essence of Elias, with his adventurous choices of subject matter. Among the many things he has accomplished through box pleating, include a skeleton of geometric structure, and a Star of David with a woven look.
These are not the only creators who have exploited the benefits of box pleating. Designers of origami are still using the techniques developed in the 1960ís, and they do not appear to be phasing out any time soon. While the more modern techniques afford the creator more flexibility, box pleating is often the best way to go when forming models with non-converging patterns. Innovative geniuses such as Elias have left us a wealth of techniques to explore, so we should not ignore them.
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