|Post is a part of a larger series (Uniaxial base):|
Every origami model in its essence has a base. No matter how complicated or simple a model is, the base is always an initial step. In traditional origami, there are only a handful of bases and all traditional origami models were derived from them.
Folding a base is in most cases very simple. But, on the other hand, the transition from the base to a final model is not that easy because there are many different approaches possible. That becomes more than obvious when you consider how many fundamentally different models have the same base in its core.
Type of traditional origami bases
Origami has been practiced in Japan for centuries. During that period a number of so-called traditional bases were devised. But today, only four of them are viewed as traditional origami bases. These are Kite, Fish, Bird, and Frog bases. They are named after the models based on those bases.
But, what is peculiar about those four bases are the fact that they are unusually similar. So similar that it seems they are constructed from a single element. From a simple triangle (look at figure 1). You see, the difference between these bases is only in the number and the position of that one particular element.
Take a good look at figure 1, and you will see that the Kite base, the simplest base of all, consists of two such basic elements, while the Frog base, the most complex one, consists of sixteen such basic elements.
As you can see in figure 1, all traditional bases are very similar, because all of them are constructed from one particular type of triangle. This triangle is clearly marked on all bases. I hope it is now clear that the difference between bases is only in the number of triangles used. This fact seems obvious but it was completely obscured to origami artists until Eric Kenneway first drew the attention of Origami society to this fact.
Nevertheless, whether these bases are similar or not, they were only what origami artists had at their disposal. And despite that, they managed to create wonderful models. Some of them are so fascinating and beautifully designed that connection to its underlying base is almost invisible. Kangaroo by Hagiwara Gen or Elephant by Enomoto Nobuyoshi are perfect examples.
What is particularly interesting is the fact that, even though these models use traditional origami bases as its starting point, they were not designed so long ago. They are quite new. So they are showing us two things. First, they show us that traditional origami bases could be still useful and second that in traditional origami, unlike the modern one, real art is not in the base itself but all subsequent steps.
Picking the base
To create the desired model, one has to pick a base that suits his or her needs. In most cases, the number of flaps chosen base poses is the main determinator. You see, the choice is severely limited because we have only four bases at our disposal. Sometimes none of the bases is good enough. For instance, if we try to design an animal with four legs, a head and, a tail, a bird base wouldn’t be sufficient due to the small number of long flaps. Bird base has only four long flaps while we need six. Not long ago the problem was virtually unsolvable. At that time, it was not uncommon to design an animal without a leg. A good example is the traditional origami giraffe (look at figure 3).
Even though it may not be obvious from the figure, the giraffe has only one hind leg because it is based on a bird base. Believe me, a design like this one was normal and completely acceptable in those days.
Lack of flaps can be to some extent solved by implementing so-called blintzed bases. Blintz base (figure 4) is very simple but at the same time not very useful. You cannot do much with that base. But, on the other hand if combined with other traditional origami bases it really shines. This new approach, combination of blintz and some other traditional origami base was proposed by Akira Yoshizawa and George Rhoads. These two origami artists combine two traditional bases, namely, bird base and frog base, with a blintz base.
What they create are two new bases; a blintzed bird base and a blintzed frog base (look at figure 5). These bases have more flaps than any other traditional origami base and as such represent a major step forward in origami design.
A lot of models were designed using blintzed bases, but the most well known is crab by Yoshizawa.
For some time, origami authors considered these bases as silver bullets. Unfortunately, they are not. Not even close. You see, if you look at the crease patterns of these two bases you will realize that they indeed have more basic triangles than their traditional counterparts.
Unfortunately, even though the number of triangles is doubled, they do not have twice as many flaps. The question is why?
Present-day origami theory can give us the answer to that question. You see, nowadays, we know that all traditional origami bases are based on circles. Look at figure 7.
According to the theory, the number of circles directly determines the number of flaps. So, if you compare a traditional bird base and a blintzed bird base it is obvious that the number of large circles and consequently the number of large flaps is the same. What is different is the number of small flaps. Above that, if you take into account that large flaps in a blintzed bird base are roughly twice as thick, it seems that the price for having four additional small flaps (purple) is rather high.
The situation with a blintzed frog base by Akira Yoshizawa is somewhat more favorable.
Here we have four additional long flaps, nine in total. Yoshizawa pushed the boundaries even farther by creating a double blintzed frog base with 13 large flaps. No wonder why he chose this base for his famous crab model.
Another vastly popular method invisions to combine two traditional origami bases. For instance, by combining a bird base and a frog base a new hybrid base can be created.
This base is used in numerous models but my favorite one is Dragon by Jo Nakashima.
What is the main difference between the blintzed bases and the hybrid bases? None of the blintzed bases have an origami element called a river. As a matter of fact, none of the traditional origami bases don’t have it either. A river is one of the pillars of modern origami and strangely enough it is not present in traditional origami.
But, on the other hand, when two traditional origami bases are combined a river emerges.
In figure 10 you can see a crease pattern of the hybrid base. The green area that meanders between circles is a river.
As you can see, the river effectively separates two polygons from the rest of the model. Nothing similar could be found among traditional origami bases. What’s more, if you analyse any of the traditional origami bases a bit more, you will realise that all its flaps originate from the same point. But, It is clearly not the case here. In this hybrid base, two sets of flaps exist with two different points of origin.
But, as much as with blintzed bases, hybrid bases also have limitations. Since they are constructed from only four traditional origami bases, the number of combinations is severely limited.
The use of traditional origami bases is a very popular but somewhat limited approach. Its limitations can be to the same extent overcome by implementing blintzed and hybrid bases. But, even though origami artists have managed to create amazing models using nothing but traditional origami bases it became apparent that some fundamentally different approach is needed. Finally, in the 1990s, a new comprehensive approach was invented. This new approach, known as Circle packing, gave us tools to design new bases, effectively removing focus from the traditional origami bases altogether. Real artistry is now in base design, unlike traditional origami where skills are not in creating a base but in all successive steps.
Despite the fact that traditional origami bases are losing its importance, I still believe that understanding traditional origami bases is an important step toward origami mastery and as such should not be skipped. Of course, the true goal of every inspired origami artist should be the acquisition of modern and highly versatile techniques like Circle packing and Box pleating.