ROB EASTAWAY: "Jurassic Park," we've all seen the film, but
very few people have read the book, including me.
I've not actually read the book, but I have looked at the
pictures because there's something in there that is
just kind of really weird, a little pattern, a beautiful
pattern that's very little known.
So I just wanted to share it with you.
So we're going to get to it just by--
I've just got a random piece of paper here.
It happens to be brown.
We're just going to fold this bit of paper in half.
So I fold it like this, crease it, and you've kind of got a
seagull there.
And if it forms a V, of course.
I mean, nothing surprising so far.
I'm going to be consistent here.
So I'm folding that which is your left over right, and I'm
going to do it again.
So fold it again, left over right, and crease it.
And if I sort of pull it apart now, OK, so we've got, reading
left to right, can you see there's a sort of peak, then
there's a valley, then there's a valley.
So we'll call this peak, valley, valley, OK?
Or and remember this for later, if I sort of close it
up a bit, it's a sauce spoon, OK?
So I fold it over once, and I fold it twice,
and I fold over again.
Now, can you predict what the pattern is going to be of
valleys and peaks?
Now, you'd probably think that something as repetitive as
this is going to be some really obvious pattern, and
it's either going to alternate, maybe valley-peak,
valley-peak.
Or you might think--
I to know-- it's going to create a little--
obvious little zigzaggy kind of pattern.
But that's not the case.
If I pull it out, it goes peak-peak; valley-valley;
peak; valley-valley.
So what's the pattern here?
And indeed, can you predict what's going to happen when I
fold it for a fourth time?
So we do one, and two, and three, and fold it a fourth
time, and unfurl it.
Well, it's kind of good to try and predict before you see it,
but here we go.
And now we've got peak-peak; valley; peak-peak;
valley-valley-valley; peak-peak; valley-valley;
peak; valley-valley.
It's kind of--
if not random, it's certainly not a really
obvious and easy pattern.
And if just start closing this up, and you turn these into
right angles, you can see that what's emerging is something--
well, something that's clearly not trivial, but it's
certainly not clear what's going on.
And this is where we turn to the book, OK?
Could you get yourself your nice cheap copy or brand new
copy of "Jurassic Park," and you turn to
page whatever it is.
And you have this page which says "first iteration," and
you've got this pattern.
So this is actually what you get when you fold our strip of
paper four times.
So if you call a fold an iteration, really you should
be calling this the fourth iteration.
I don't know why it's the first iteration
in here, but anyway.
The second question, of course, is what is it doing in
"Jurassic Park?" And there's a little cryptic reference at
the bottom of the page by Ian Malcolm who's the
mathematician who features in this story.
"At the earliest drawings of the fractal curve, few clues
to the underlying mathematical structure will be seen."
So he talked about a fractal.
So this is going to turn into a fractal of some kind.
Can you picture what that fractal will be?
I certainly can't, not without having seen it first.
If we keep folding our paper, which we're not going to do
because there's a limit to how many times even with a long
strip of paper you can fold it.
Another fold, what's called a second iteration here,
produces this pattern, which is--
I guess that what's kind of interesting is, without
crossing over itself, it joins and forms this little block,
this little rectangle and another square there.
I think the reason why there are fractals appearing in here
is that there's a sort of theme about the
unpredictability of systems and chaos, and the fact that
we've set up Jurassic Park, and all these creatures are
going to behave in a certain way.
And here's this doom-monger saying it could all go
horribly wrong because what we think is predictable could
turn out to be chaotic and so on.
So that's the metaphor, I think, that's being used.
So if I keep folding the paper, I
get the third iteration.
It's getting a bit more involved, but it's still hard
to see any pattern emerging from this.
And we go quite a lot of pages further before we get to
what's called the fourth iteration.
Actually, there's been a few more folds here, so the
numbers at the top are kind of going out the window.
But now we've got this big block just from folding the
paper right over left, and we zip ahead
to the fifth iteration.
Well, now you've got these kind of blocks appearing, and
they're a bit like lizards.
I don't think that's a deliberate reference to
Jurassic Park or anything, but there's some things which are
almost animal-like about this thing.
And you keep going to what's called the sixth iteration.
There are lots--
way more than you can fold a bit of paper.
You get this rather stunning pattern emerging.
And in fact, what you'll find is that each of these, the
main shape in the center, has been then rotated and rotated.
And typically, they're being rotated by 45 degrees, and the
dimensions are being reduced by the square
root of 2 each time.
Why folding a piece of paper could lead to something as
stunning as this is just--
you know, it's mind blowing.
We've all seen fractals.
There's lots of fractals that are famous.
This one, which is so easy to produce, is actually
remarkably little known despite featuring in "Jurassic
Park."
And we go all the way to the end, an infinite number of
folds of paper.
We get what's called here the seventh iteration, this
beautiful solid block.
And even more stunning is the fact you can picture sticking
another of these curves in.
They would sort of fit together like jigsaw pieces.
You can see another dragon curve outlined here.
So if you imagine you've got a black one and a blue one and a
yellow one, you could actually stick them together to make a
really cool kitchen floor tiling.
It would be a bit hard to do.
But to produce something like this, I don't think anyone
would predict that.
BRADY HARAN: That's pretty cool.
ROB EASTAWAY: Mm.
I love it.
And I love the fact that the whole world knows about
fractals, but whenever I show a group of people the dragon
curve, they say I've never seen this before.
And who would have thought that you could
get to it so simply.
[DINOSAUR ROARS]
ROB EASTAWAY: I think he likes it.
BRADY HARAN: If there are many sides, then the angles become
too shallow so that the next one would only
have a little bit.
I'm going to put in another polygon out here and match
that one there.
I'd end up with only a little sliver under there.