Folding waynew origami Robert Lang
my talk is flapping birds and Space
Telescope’s
and you would think that should have
nothing to do with one another but I
hope by the end of these 18 minutes
you’ll see a little bit of a relation it
ties to origami so let me start what is
origami most people think they know what
origami is it’s this flapping birds toys
cootie catchers that sort of thing and
that is what origami used to be but it’s
become something else it’s become an art
form a form of sculpture
the common theme what makes it origami
is folding is how we create the form now
it’s very old this is a plate from 1797
shows these women playing with these
toys if you look close it’s this shape
called a crane every Japanese kid learns
how to fold that crane so this art has
been around for hundreds of years and
you would think something that’s been
around that long so restrictive folding
only everything that could be done has
been done a long time ago and that might
have been the case but in the 20th
century a Japanese folder named
Yoshizawa came along and he created tens
of thousands of new designs but even
more importantly he created a language a
way we could communicate a code of dots
dashes and arrows harkening back to
susan Blackmore’s talk we now have a
means of transmitting information with
heredity and selection and we know where
that leads and where it has led in
origami is to things like this this is
an origami figure one sheet no cuts
folding only hundreds of folds this too
is origami and this shows where we’ve
gone in the modern world naturalism
detail you can get horns antlers even if
you look close cloven hooves and it
raises a question what changed what and
what changed is something you might not
have expected in an art which is math
that is people applied mathematical
principles to to the art to discover the
underlying laws and that leads to a very
powerful tool the secret to productivity
in so many fields and in origami is
letting dead
people do your work for you because what
you can do is take your problem and turn
it into a problem that someone else’s
has solved and use their solutions and I
want to tell you how we did that in
origami origami revolves around crease
patterns a crease pattern shown here is
the underlying blueprint for an origami
figure and you can’t just draw them
arbitrarily they have to obey four
simple laws and they’re very simple easy
to understand the first law is to color
ability you can color any crease pattern
with just two colors without ever having
the same color meeting the directions of
the folds at any vertex the number of
mountain folds the number of Valley
folds always differs by two two more or
two less nothing else if you look at the
angles around a fold you find that if
you number the angles in a circle all
the even-numbered angles add up to a
straight line all the odd-numbered
angles add up to a straight line and if
you look at how the layers stack you’ll
find that no matter how you stack folds
and sheets a sheet can never penetrate a
fold so that’s four simple laws that’s
all you need in origami all of origami
comes from that you’d think can four
simple laws give rise to that kind of
complexity but indeed the laws of
quantum mechanics can be written down on
a napkin and yet they govern all of
chemistry all of life all of history if
we obey these laws we can do amazing
things so an origami to obey these laws
we can take simple patterns like this
repeating pattern of folds called
textures and by itself it’s nothing
but if we follow the laws of origami we
can put these patterns into another fold
that itself might be something very very
simple but when we put it together we
get something a little different this
fish 400 scales again it is one uncut
square only folding and if you don’t
want to fold 400 scales you can back off
and just do a few things and add plates
to the back of a turtle or toes or you
can ramp up and go up to 50 stars on a
flag with 13 stripes and if you want to
go really crazy a thousand scales on a
rattlesnake and this guy’s on display
downstairs
look if you get a chance the most
powerful tools in origami have related
to how we get parts of creatures and I
can put it in this simple equation we
take an idea combine it with a square
and you get an origami figure what
matters is what we mean by those symbols
and you might say can you really be that
specific I mean a stag beetle it’s got
two points for jaws that’s got antennae
can you be that specific in the detail
and yeah you really can so how do we do
that well we break it down into a few
smaller steps so let me stretch out that
equation
I start with my idea I abstract it
what’s the most abstract form it’s a
stick figure and from that stick figure
I somehow have to get to a folded shape
that has a part for every bit of the
subject a flap for every leg and then
once I have that folded shape that we
call the base you can make the legs
narrower you can bend them you can turn
it into the finished shape now the first
step pretty easy
take an idea draw stick figure the last
step is not so hard but that middle step
going from the abstract description to
the folded shape that’s hard but that’s
the place where the mathematical ideas
can get us over the hump I’m going to
show you all how to do that so you can
go out of here and fold something but
we’re going to start small this base has
a lot of flaps in it we’re going to
learn how to make one flap how would you
make a single flap take a square fold it
in half fold it in half fold it again
till it gets long and narrow and then
we’ll say the end of that that’s a flap
I could use that for a leg and arm
anything like that
what paper went into that flap well if I
unfold it and go back to the crease
pattern you can see that the upper left
corner of that shape is the paper that
went into the flap so that’s the flap
and all the rest of the papers leftover
I can use it for something else well
there’s other ways of making a flap
there’s other dimensions for flaps if I
make the flap skinnier I can use a bit
less paper if I make the flap as skinny
as possible I get to the limit of the
minimum amount of paper needed and you
can see there it needs a quarter circle
of paper to make a flap there’s other
ways of making a flaps if
put the flap on the edge it uses a half
circle of paper and if I make the flap
from the middle it uses a full circle so
no matter how I make a flap it needs
some part of a circular region of paper
so now we’re ready to scale up what if I
want to make something that has a lot of
flaps what do I need I need a lot of
circles and in the 1990s origami artist
discovered these principles and realize
we can make arbitrarily complicated
figures just by packing circles and
here’s where the dead people start to
help us out because lots of people have
this have studied the problem of packing
circles I can rely on that vast history
of mathematicians and artists looking at
discs packings and arrangements and I
can use those patterns now to create
origami shapes so we figured out these
rules whereby you pack circles you you
decorate the patterns of circles with
lines according to more rules that gives
you the folds those folds fold into a
base you shape the base you get a folded
shape in this case a cockroach and it’s
so simple it’s so simple that a computer
could do it and you say well you know
how simple is that but computers you
need to be able to describe things in
very basic terms and with this we could
so I wrote a computer program a bunch of
years ago called Tree Maker and you can
download it from my website it’s free
runs on all the major platforms even
windows
and you just draw a stick figure and it
calculates the crease pattern it does
the circle packing calculates the crease
pattern and if you use that stick figure
that I just showed which can kind of
tell it’s a deer it’s got a antlers
you’ll get this crease pattern and if
you take this crease pattern you fold on
the dotted lines you’ll get a base that
you can then shape into a deer with
exactly the crease pattern that you
wanted and if you want a different deer
it’s not a white-tailed deer but you
want a mule deer or an elk you change
the packing and you can do an elk or you
could do a moose or really any other
kind of deer these techniques
revolutionize this art we found we could
do insects spiders which are clothes
things with legs things with legs and
wings things with legs and antennae and
a folding a single praying mantis from a
single uncut square wasn’t interesting
enough then you could do two praying
mantises from a single uncut square
she’s eating him I call it snack time
and you can do more than just insects
this you can you can put details toes
and claws grizzly bear has claws this
tree frog has toes actually lots of
people in origami now put toes into
their models toes have become an origami
meme because everyone’s doing it you can
you can make multiple subjects so these
are a couple instrumentalists the guitar
player from a single square the bass
player from a single square and if you
say well but guitar bass that’s not so
hot do a little more complicated
instrument well then you could do an
organ and what this is allowed is the
creation of origami on demand I’m so now
people can say I want exactly this and
this and this and you can go out and
fold it and sometimes you create high
art and sometimes you pay the bills by
doing some commercial work but I want to
show you some examples everything you’ll
see here except the car is origami
density she got a date
so they were Emily
so it was a little hasty so they want to
see what she
sorry what though she was do you the
2006 Mitsubishi Endeavor was a powerful
3.8 liter v6 and available all-wheel
drive a mythic combination of beauty and
beast Mitsubishi driven is thrill just
to say this really was folded paper
computers made things move but these
were all real folded objects that we
made and we can use this not just for
visuals but it turns out to be useful
even in the real world surprisingly
origami and the structures that we’ve
developed an origami turn out to have
applications in medicine and science in
space in the body consumer electronics
and more and I want to show you some of
these examples one of the earliest was
this pattern this folded pattern studied
by Cory ami or a Japanese engineer
studied a folding pattern realized this
could fold down into an extremely
compact package that had a very simple
opening and closing structure and he
used it to design this solar array it’s
an artist rendition but it flew in a
Japanese telescope in 1995 now there is
actually a little origami in the James
Webb Space Telescope but it’s very
simple the telescope is going up in
space it unfolds in two places it folds
in thirds it’s a very simple pattern you
wouldn’t even call that origami they
certainly didn’t need to talk to origami
artists but if you want to go higher and
go larger than this then you might need
some origami engineers at Lawrence
Livermore National Lab had an idea for a
telescope much larger they called it the
eye glass the design called for
geosynchronous orbit 25,000 miles up a
hundred meter diameter lens so imagine a
lens the size of a football field
there were two groups of people who are
interested in this planetary scientists
who want to look up and then other
people who wanted to look down the
weather you look up or look down how you
get it up in space you got to get it up
there in a rocket and Rockets are small
so you have to make it smaller how do
you make a large sheet of glass smaller
well about the only way is to fold it up
somehow so you have to do something like
this this was a
small model folded lens you divide up
the panels you had flexures but this
patterns not going to work to get
something a hundred meters down to a few
meters so the Livermore engineers
wanting to make use of the work of dead
people or perhaps live origamist s–
said let’s see if someone else is doing
this sort of thing so they looked into
the origami community we got in touch
with them and I started working with him
and we developed a pattern together that
scales to arbitrarily large size but
that allows any flat ring or disk to
fold down into a very neat compact
cylinder and they adopted that for their
first generation which was not a hundred
meters was a five meter but this is a
five meter telescope as about a quarter
mile focal length and it works perfectly
on its test range and it indeed folds up
into a neat little bundle now there is
other origami in space Japan aerospace
agency flew a solar sail and you can see
here that the sail expands out you can
still see the fold lines the problem
that’s being solved here is something
that needs to be big and sheet like at
its destination but needs to be small
for the journey and that works whether
you’re going into space or whether
you’re just going into a body and this
example is the latter this is a heart
stent developed by Zhang Yu at Oxford
University
it holds open a blocked artery when it
gets to its destination but it needs to
be much smaller for the trip there
through your blood vessels and this stem
folds down using an origami pattern
based on a model called the water bomb
base airbag designers also have the
problem of getting flat sheets into a
small space and they want to do their
design by simulation so they need to
figure out how in a computer to flatten
an airbag and the algorithms that we
developed to do insects turn out to be
the solution for airbags to do their
simulation and so they can do a
simulation like this those are the
origami creases forming and now you can
see the airbag inflate and find out does
it work and that leads to a really
interesting idea you know where did
these
come from well the heart stent came from
that little blow-up box that you might
have learned in elementary school it’s
the same pattern called the water bomb
base the air bag flattening algorithm
came from all the developments of circle
packing and the mathematical theory that
was really developed just to create
insects things with legs the thing is
that this often happens in math and the
science when you get math involved
problems that you solve for aesthetic
value only just or to create something
beautiful turn around and turn out to
have an application in the real world
and as weird and surprising as it may
sound origami
may someday even save a life thanks