- Hi, I'm Robert. J Lang, origami artist and physicist.
And today I've been challenged
to go through levels of complexity with origami.
[invigorating music]
There's many ways to define complexity for origami.
It could be the total number of folds in the design,
it could be the number of folds
you have to bring together at once.
I'm gonna use a combination
of those two measurements and illustrate it
by going through different levels of complexity in a cicada,
one of the classic traditional subjects of origami.
As a disclaimer,
this is my interpretation of complexity
as it applies to origami.
Cicadas are very familiar in the Japanese culture,
in part, because in summertime they make a huge racket.
Not just in the countryside, but even in downtown Tokyo
the sound of cicadas can be deafening.
Within the origami world,
they have a particular significance,
because Yoshizawa, the great Japanese origami master,
considered his own cicada to be his greatest creation.
And so many origami artists
have felt the need, or the desire,
to create their own version of this iconic insect.
My level one would be the traditional Japanese cicada,
because it's one of the simplest folds in all of origami.
It's just a handful,
maybe one, two, three, four, five, six, seven, eight steps,
all simple folds,
and yet it reads very strongly as a cicada.
This can be folded by almost anyone in just a few minutes.
It consists of nothing but Valley Folds,
the simplest fold in all of origami.
Although it only has a handful of folds,
there's a few places where you can put
your personal stamp on it
by making Judgment Folds,
folds that don't have a specific reference point.
In particular, the angle at which you fold down the wings,
and then the angles at which you fold down
these two corners on the top
are done pretty much by eye.
By adjusting those folds positions,
a person can adjust the character
and the finished shape of their cicada.
For level two, this is a little bit more complicated,
because it incorporates a few more judgment folds.
But notably, it has a fold called a Petal Fold.
That petal fold is built
from two folds called Swivel Folds.
We'll start the same way,
in fact, this'll be based pretty much
upon the traditional cicada.
But now, we wanna do a few things differently.
We'd like to make the wings longer.
If I fold it down with a valley fold,
that's all the length I can get from my wing.
But if I'm willing to do a more complicated fold,
I can get longer wings.
And that more complex fold
is called a Swivel Fold.
And so, with my more complicated fold,
I'm gonna move it down and create this little pocket,
which I will then flatten.
When I fold the flap down,
I'll have to fold it
underneath the pocket formed here.
But if I do that,
I can fold it down,
and then tuck some of it underneath,
and that's a Mountain Fold.
And then the last little bit
is I fold the valley fold down,
but then fold the paper back.
I'm gonna leave a little bit of color exposed here.
And the reason I'll do that,
is that when I then fold the edges inside,
same as I did before,
my cicada will have colored eyes.
So although this is still quite stylized, geometric
and a little bit abstract,
I think it's closer to the form of a real cicada,
and it reads a little bit better as a cicada.
For level three,
we're still doing a fairly simple abstract cicada,
but we've added a few more folds of complexity
and we've added some Squash folds,
which allow us to shape the wings relative to the abdomen
and give a little bit more of a teardrop shape
which matches the wing shape of an actual cicada.
I'll do a squash fold.
Lift a flap up,
I put my finger inside, press it flat.
That's a new fold.
It actually combines making multiple folds,
'cause I'm creating a fold here and here,
the same time that I'm bringing it down.
It's a Combination Fold,
but that allows us to achieve
a little bit more shaping.
We're adding what are called Crimped Folds,
which let us both create distinct eyes
and also give the body a little bit
of three dimensional roundedness.
So gonna do a crimp,
that's putting a valley
and a mountain right next to each other
and the mirror image on the backside.
So there's the crimp on the front,
do the same on the back,
press 'em to set the crimp.
And then I'm gonna fold the corners underneath,
which will lock the crimp in place,
and then that also allows me
to open the model out.
As we add details to the origami design,
we travel along a continuum from abstract,
the highly realistic.
This is my level for design,
which is a cicada designed
by the great Akira Yoshizawa.
From this point onward,
the folding is sufficiently complex
that I'm not gonna fold them from start to finish,
but I'll fold through until we can see the base
and the basic structure.
The reason we have such a big jump from three to four
is we're going from representations without legs
to representations with legs.
A cicada has six legs,
so our number of legs needs
to make a big jump right there,
go from zero to six.
So just as we need to make
a big jump in the number of legs,
we'll also need to make a big jump
in the complexity of folding.
- This level four design, by Yoshizawa,
he used a rectangle that takes eight bird bases
and put them together into a rectangle.
[paper crinkles]
This is the crease pattern for the bird base,
and you see this star shaped motif.
And that little star shaped motif is repeated eight times
in this crease pattern,
that when folded looks like this.
So a row of two across and eight along
makes it possible to fold this fairly complex base,
that it has enough flaps to get all of the legs,
as well as the wings and other features at the cicada.
This is my level five design.
It's a cicada that I developed back in the 1980s.
It coincidentally shares a lot of its structure
with Yoshizawas in that it's built
from a rectangle that has an array of bird-based patterns,
but the next step in this march of realism
will be to put in the antenna.
Even though the antenna
are quite small on a cicada,
they're definitely noticeable,
and so we do that by adding two more bird bases
to the pattern in the rectangle.
Make the rectangle a little bit longer,
add a few more features,
and then we can get antenna,
as well as eyes, wings, and legs.
So one of the steps up in creating the base,
we have to fold some layers together,
and then unwrap one layer
that's wrapped around another.
This layer's wrapped around another.
And then, I unwrap it
so that it comes down.
And this layer, that gets turned up.
That gives another base
that's pretty similar to the Yoshizawa base,
but it has two long flaps
and crucially, the addition of two small points
one here and one here.
And so this step of unwrapping is the next step
in this sequence of cicada designs.
This is my level six.
Now, even though rectangles started
to become pretty common in the '60s and '70s.
The 1980s in the world of origami
people felt like it was an aesthetically desirable thing
to use squares.
Most traditional origami designs came from squares.
There's a certain geometric elegance to a square.
So even though rectangles allowed us
to create more complex shapes
like cicadas with legs and antenna,
we thought, can we do that from a square?
But getting points like legs, long skinny appendages
that come from the interior of the paper,
require quite a bit more
in the way of planning and design
and also in the complexity
of the folding steps themselves.
This design used some additional folds
we haven't seen yet called Rabbit Ear Folds,
and they're pretty easy,
but it also required a fold called
a Closed Unwrap and a Closed Sink.
And these are now quite famous
in the world of origami for their difficulty.
[paper crinkles]
I wrap the layer from back to front.
These are pretty difficult to do
without ripping the paper,
it's called a Closed Sink.
I'm going to put this point inside
in a way that locks the edges together.
And I have to do that,
by opening it up
a little bit and then refolding.
And when I'm done, the point is gone
and there's a little pocket,
and the edges are locked together.
But the reason we use them,
is it allows us to create combinations of points and flaps
that in this case will give us the legs
that we want from a square.
This is my level seven design,
and we can also do a side by side to this one
to see how things improve,
but it's folded completely differently from level six.
One of the things we'd like to do
to increase the realism
is to make all of the legs very thin and delicate,
have none of them come
from the interior of the paper.
But the only way to ensure that happens,
is to start planning the design from the beginning,
so that the legs don't come from the center.
And to do that,
we use a new technique called Circle Packing,
in which all of the long features of the design
are represented by circles.
So each leg becomes a circle,
each wing becomes a circle,
and things that can be big and thick
like the head or the abdomen,
can be points in the middle.
The basic folds of origami
like mountains and valley folds
have had names for years, even decades.
And some of the other combinations
of two or three mountains and valleys
have also been given names like Reversal or Rabbit Ear.
But as we move up the level of complexity,
we find that we need to start putting together groups
of folds in unique ways
that have never been done before.
And so these folds don't even have names,
because you might not encounter
that exact combination ever again.
But in many cases,
these new combinations of folds arise
when we're trying to create a new point
from somewhere in the interior of the paper
and that happened in this design,
which bumps its level of complexity up
one more than the previous.
This is level eight Shizuoka cicada.
It's one step up from level seven,
because it has even thinner, more delicate legs
and more graceful teardrop shaped wings.
This required yet another new design.
In all the previous designs,
we could fold the model sequentially.
Start with a square, do one step at a time,
maybe do a few folds at a time,
but we could break the folds down into a sequence.
But in some designs,
you might have 10s,
or even hundreds of folds
that all have to come together at once.
And when that happens, we call that a Collapse.
I've got my six legs here,
two flaps for wings, a long flap for the body,
these cross pleats would be used to segment the body,
and then some extra paper up here for the head,
and I can use these corners to create antenna.
And there's our finished Shizuoka Cicada.
For my level nine version of a cicada,
I thought we would move to a Juvenile Cicada,
because it has some additional features
that demand additional complexity.
One is that a Nymph Cicada
has proportionately longer legs.
So we need to get longer flaps,
but we still have to make them very, very skinny.
But most notably,
it has a lot more structure on the claws.
It's got a pointed front claw,
and then a spine at the base of each claw.
We can also add segments,
distinct segments for the abdomen.
To make this happen,
we go again to the technique
of box pleating or square packing.
And this time, we'll have a lot more little figures,
a lot more squares, a lot more objects to pack
to get all these small features,
the spines, the eyes, the scale.
That gives rise to a more complex crease pattern,
one that has more folds.
And then that fold too,
requires a collapse to bring it all together.
We have a square or a rectangle
for every little pointy bit on the shape.
So we have little squares for the spines,
little squares for the claws,
large ones for the legs,
small ones for the antenna, and so forth.
And we have to pack all of those into the square.
And then from that packing,
we construct the crease pattern
that has not only more up and down
and side to side folds,
and that therefore gives rise
to this crease pattern with more folds
and a more complicated collapse.
This is my level 10 design,
which is a Flying Cicada.
And what makes this more complex now
is that it has four major flaps
that come from the interior of the paper:
head flap, abdomen, and two of the legs.
The reason we need those extra flaps,
is because now it's flying.
We need four really large flaps
to make the wings.
Cicadas have four wings.
Four large wing flaps
take up most of the side edges of the paper,
and so then we have to get other features
from the interior of the square.
The folds that generate
those middle points are harder, they're more complex.
The fact that we have four of them now,
more than we've ever had before,
is what puts this into the next level of complexity.
My level 11 design is a cicada.
We're back to the classic pose.
But this deceptively simple design
actually has the most complex folds
of everything we've done before.
Just in terms of the design,
this is actually a step backward in complexity,
because it's just an array of bird bases.
But in terms of the complexity
of actually folding,
this is the most complex
of anything that we've looked at.
It contains closed sinks, mixed sinks,
mixed wraps, combinations of all these folds,
and a very large number of them.
So, many, many individual folds.
Those middle points require much more complex folds
than any of the steps
that we've done leading up to this,
and that's what makes this
the highest level in this series.
Those are my levels of complexity.
You might have your own levels for origami
or whatever your pastime might be.
Wanna thank Wired for giving me this opportunity,
and wish all of you happy folding.