0:00:03 > 0:00:06OVERLAPPING VOICES
0:00:11 > 0:00:16This is the Giant's Causeway at the northern tip of Northern Ireland,
0:00:16 > 0:00:19and it's famed for these strange angular rocks.
0:00:25 > 0:00:30There are 40,000 of them crammed into this small area of coastline.
0:00:31 > 0:00:35What makes them so striking is that they're so regular, so simple,
0:00:35 > 0:00:40they just don't seem to fit in to this rugged natural environment.
0:00:45 > 0:00:49The mystery of these hexagonal rock formations has inspired
0:00:49 > 0:00:53storytellers and composers.
0:00:55 > 0:00:59But their strange beauty is only the start of the story.
0:01:00 > 0:01:04Because these stones tell of a hidden geometric force
0:01:04 > 0:01:08that underpins and pervades all nature.
0:01:14 > 0:01:16And if we can uncover that force,
0:01:16 > 0:01:20it'll help us to explain the shape of everything...
0:01:20 > 0:01:24from the smallest microbe, to the construction of these stones
0:01:24 > 0:01:27and the formation of the world itself.
0:01:59 > 0:02:02As a mathematician, I'm fascinated by the numbers
0:02:02 > 0:02:05and shapes we see all around us...
0:02:14 > 0:02:18..connecting everything, from bees
0:02:18 > 0:02:21to bubbles
0:02:21 > 0:02:26and the handwork of our distant ancestors
0:02:26 > 0:02:29to the imagination of our greatest modern artists.
0:02:42 > 0:02:45These are the hidden connections that make up the Code...
0:02:51 > 0:02:55..an abstract, enigmatic world of numbers that has given us
0:02:55 > 0:02:59the most detailed description of our world we've ever had.
0:03:11 > 0:03:15Ever since they settled here, over 30,000 years ago,
0:03:15 > 0:03:19people have tried to explain these remarkable hexagonal columns
0:03:19 > 0:03:22poking out of the Irish Sea.
0:03:22 > 0:03:26Why are they the shape they are?
0:03:26 > 0:03:29And where did they come from in the first place?
0:03:29 > 0:03:33Legend has it that this peninsula was once home to a giant
0:03:33 > 0:03:34called Fionn mac Cumhaill.
0:03:41 > 0:03:45One day the giant got into an argument with another giant called Benandonner
0:03:45 > 0:03:50who lived 80 miles away across the sea in Scotland.
0:03:55 > 0:03:59The giants hurled insults at each other,
0:03:59 > 0:04:01swiftly followed by a few stones.
0:04:01 > 0:04:04And things soon got out of hand.
0:04:04 > 0:04:07Benandonner swore that if he was a better swimmer,
0:04:07 > 0:04:10he'd come straight over to sort Fionn out.
0:04:10 > 0:04:14Fionn was so enraged that he started picking up huge clumps of earth
0:04:14 > 0:04:16and throwing them across the sea
0:04:16 > 0:04:21so he could create a pathway for the Scottish giant to come and face him.
0:04:21 > 0:04:24And that, legend has it, is what I'm standing on now.
0:04:24 > 0:04:26The handiwork of a giant.
0:04:32 > 0:04:37It's a nice story, but the reality is even more extraordinary.
0:04:37 > 0:04:41Because what's written into these rocks is a fundamental truth
0:04:41 > 0:04:44about the universe.
0:04:49 > 0:04:53A truth that we can find written throughout the natural world.
0:05:09 > 0:05:11These orchards in California,
0:05:11 > 0:05:16are the site of one of the largest animal migrations on the planet.
0:05:20 > 0:05:23Every spring, billions of bees are brought here
0:05:23 > 0:05:25to help pollinate the almond trees.
0:05:33 > 0:05:38Several thousand of these hives belong to Steve Godling.
0:05:45 > 0:05:50- You go ahead and smoke it when we get it open.- Yep.
0:05:50 > 0:05:53- Right there.- That's good.
0:05:56 > 0:06:00Got this glued together very tight.
0:06:00 > 0:06:03You want to try to get an outside one so as not to kill the queen.
0:06:03 > 0:06:09You don't want to kill any of them but you particularly don't want to kill her.
0:06:09 > 0:06:12- If you kill the queen, you've killed the hive.- Wow!
0:06:14 > 0:06:17That's one of the wonders of the natural world.
0:06:17 > 0:06:19It's beautiful.
0:06:21 > 0:06:24'The bees' honeycomb is a marvel of natural engineering.'
0:06:24 > 0:06:28They've got plenty of honey.
0:06:28 > 0:06:30'Everything they need is here.
0:06:30 > 0:06:33'It's a place to raise their young and store their food.
0:06:35 > 0:06:37'And it's all made from wax,
0:06:37 > 0:06:41'a substance so labour intensive that the bees have to fly the equivalent
0:06:41 > 0:06:46'of 12 times round the Earth to produce a single pound of it.'
0:06:48 > 0:06:52- This almost looks man-made, manufactured.- Yeah.
0:06:52 > 0:06:55It doesn't look like something from the natural world.
0:06:55 > 0:07:00- The precision, the fine straight lines that they've created is extraordinary.- Right.
0:07:00 > 0:07:04It's an engineering wonder, for sure.
0:07:04 > 0:07:10- Look at the... It's perfect hexagons here.- Yeah. It's amazing.
0:07:10 > 0:07:15And, er, the hexagon is a very strong structure.
0:07:15 > 0:07:19'The bees have made an identical pattern to the columns
0:07:19 > 0:07:22'on the Giant's Causeway.
0:07:22 > 0:07:25'Each cell is exactly like the others -
0:07:25 > 0:07:29'six walls meeting precisely at 120 degrees.
0:07:29 > 0:07:33'And every honeybee, everywhere in the world,
0:07:33 > 0:07:36'knows how to build these shapes.
0:07:36 > 0:07:40'It's as if the hexagon is built into the bee's DNA.'
0:07:40 > 0:07:43You can see the bees going down inside the cell.
0:07:43 > 0:07:46- It's almost exactly the same size as their bodies.- Right.
0:07:46 > 0:07:49Are they using their body like a ruler in some sense, to do the geometry?
0:07:49 > 0:07:51That's an accurate description.
0:07:51 > 0:07:54I know different races have a smaller body
0:07:54 > 0:07:57and the cell size in their comb is smaller.
0:07:57 > 0:08:02And each of the hexagons, how do they actually make a hexagon rather than some irregular shape?
0:08:02 > 0:08:05They've just done it for thousands of years.
0:08:05 > 0:08:08They were born to do it, they just instinctively know
0:08:08 > 0:08:13that this is the shape of their home.
0:08:15 > 0:08:19But there's more to the bees' behaviour than raw instinct.
0:08:20 > 0:08:25There's another reason why they build in hexagons.
0:08:25 > 0:08:26And to reveal that reason,
0:08:26 > 0:08:30we need to turn to the universal language of all nature.
0:08:30 > 0:08:32Mathematics.
0:08:37 > 0:08:41The bees' primary need is to store as much honey as they can
0:08:41 > 0:08:44while using as little precious wax as possible.
0:08:52 > 0:08:55The bees' honeycomb is an amazing piece of engineering,
0:08:55 > 0:09:00but why have they evolved to produce this hexagonal pattern?
0:09:00 > 0:09:02They don't have too many choices.
0:09:02 > 0:09:07If you try to put pentagons together, for example, they just don't fit together nicely.
0:09:07 > 0:09:10Or circles leave lots of little gaps.
0:09:10 > 0:09:14If they want to produce a network of regular shapes which fit together neatly
0:09:14 > 0:09:18then you've really only got three options.
0:09:18 > 0:09:23You can do equilateral triangles, or you could do squares,
0:09:23 > 0:09:25or you can do the bees' hexagons.
0:09:25 > 0:09:30But why of those three does the bee choose the hexagons?
0:09:30 > 0:09:34Well, it turns out that the triangles actually use
0:09:34 > 0:09:37much more wax than any of the other shapes.
0:09:37 > 0:09:42Squares are a little better, but it's the hexagons which use the least amount of wax.
0:09:42 > 0:09:48'It's a solution that was only mathematically proven a few years ago.
0:09:48 > 0:09:52'The hexagonal array IS the most efficient storage solution
0:09:52 > 0:09:54'the bees could have chosen.
0:09:54 > 0:09:57'Yet with a little help from evolution,
0:09:57 > 0:10:01'they worked it out for themselves millions of years ago.'
0:10:02 > 0:10:05This is nature's Code at work,
0:10:05 > 0:10:08and the bees are in tune with it.
0:10:12 > 0:10:15It's easy to see why efficiency is important to the bees.
0:10:18 > 0:10:22After all, it's hard work making wax.
0:10:22 > 0:10:27But what could be the reason for the same pattern
0:10:27 > 0:10:32being permanently engraved in the rock of the Giant's Causeway?
0:10:33 > 0:10:39The geological processes that form these columns took place over thousands of years.
0:10:39 > 0:10:46But to understand what happened, we need to look at structures that last for only a few seconds.
0:11:03 > 0:11:07Soap films are mostly thinner than wavelengths of light.
0:11:07 > 0:11:12About 20,000 times thinner than a human hair.
0:11:16 > 0:11:18They're almost not here.
0:11:18 > 0:11:21Probably the thinnest thing you've ever looked at
0:11:21 > 0:11:24and got information back from was a soap film.
0:11:25 > 0:11:32Tom Noddy is one of the world's foremost exponents of bubble art.
0:11:36 > 0:11:41The different colours on a bubble are different thickness of soap film.
0:11:43 > 0:11:46So looking over the colours of a bubble,
0:11:46 > 0:11:50you're actually looking at a contour map of the surface of the bubble.
0:11:57 > 0:11:59Bang.
0:12:03 > 0:12:06So, like everything in nature, bubbles are just trying to economise,
0:12:06 > 0:12:10they're trying to get as small as they possibly can.
0:12:10 > 0:12:13But in the case of bubbles, they can do it perfectly.
0:12:13 > 0:12:17A single bubble in the air is always a sphere.
0:12:20 > 0:12:23At first sight, it seems obvious that the bubble should be round.
0:12:24 > 0:12:28But why is the sphere so special?
0:12:36 > 0:12:40The sphere is one surface, no corners, infinitely symmetrical.
0:12:40 > 0:12:43Of all the shapes this bubble could be,
0:12:43 > 0:12:46the sphere is the one with the smallest surface area,
0:12:46 > 0:12:49which makes it the most efficient shape possible.
0:12:53 > 0:12:57And it is because nature loves to use her resources effectively
0:12:57 > 0:13:00that we can see spheres everywhere we look.
0:13:01 > 0:13:03The Earth is round
0:13:03 > 0:13:08because gravity pulls the planet's bulk into a ball around its core.
0:13:10 > 0:13:12Water forms into spherical droplets -
0:13:12 > 0:13:18the shape minimises the amount of surface tension needed to hold the droplet together.
0:13:21 > 0:13:24And a spherical shape gives simple life forms,
0:13:24 > 0:13:26like this Volvox plankton,
0:13:26 > 0:13:29optimal contact with their surrounding environment.
0:13:32 > 0:13:35But not everything is spherical.
0:13:35 > 0:13:38And because bubbles are so thin and flexible
0:13:38 > 0:13:41?we can use them to create other shapes.
0:13:43 > 0:13:46So, a single bubble in the air is always a sphere.
0:13:47 > 0:13:53But if they touch each other, they can save material for both of them by sharing a common wall.
0:13:53 > 0:13:55And so they do.
0:13:55 > 0:14:00If they can save surface area by taking advantage of their environment, they will.
0:14:05 > 0:14:09So when you've got just one bubble, the sphere is the most efficient shape.
0:14:09 > 0:14:13But as we add more bubbles, we see the geometry changing.
0:14:13 > 0:14:14So, in this case,
0:14:14 > 0:14:17we've got four bubbles and you can see them meeting at a point.
0:14:17 > 0:14:21But put a shape in the middle, we don't get a spherical bubble,
0:14:21 > 0:14:25we get, in fact, a little tetrahedron.
0:14:25 > 0:14:29With four faces, they're not exactly flat, they're parts of spheres,
0:14:29 > 0:14:32but each time, the bubbles are trying to find
0:14:32 > 0:14:35the most efficient shape for the arrangement of bubbles.
0:14:35 > 0:14:41So now we've got six bubbles, we've got a little cube appearing in the middle.
0:14:41 > 0:14:43This is nature's laws at work.
0:14:43 > 0:14:48The universe is always trying to find the most efficient solution it can.
0:14:48 > 0:14:51And as we pop them, the bubbles change,
0:14:51 > 0:14:55finding the most efficient, until we're left with a sphere again.
0:14:55 > 0:14:57It has no choice.
0:14:59 > 0:15:03But what's most remarkable is that those solutions
0:15:03 > 0:15:05are so often neat, geometric shapes.
0:15:08 > 0:15:10Wow!
0:15:10 > 0:15:12That's a dodecahedron. That's fantastic.
0:15:12 > 0:15:16And they're almost perfect pentagons. That's really surprising.
0:15:16 > 0:15:19- They're not bulging really very much at all.- That's right.
0:15:19 > 0:15:21So, 12 bubbles around make 12 faces
0:15:21 > 0:15:24and the most economical shape that they can make,
0:15:24 > 0:15:27- the lowest energy, is the dodecahedron.- Yeah.
0:15:30 > 0:15:34The soap bubble reveals something fundamental about nature. It's lazy.
0:15:34 > 0:15:37It tries to find the most efficient shape,
0:15:37 > 0:15:40the one using the least energy, the least amount of space.
0:15:44 > 0:15:48And it appears there ARE fixed rules about how it finds
0:15:48 > 0:15:50these economic solutions.
0:15:58 > 0:16:03The bubbles are incredibly dynamic, but each time one pops,
0:16:03 > 0:16:07they're always trying to assume the most efficient shape,
0:16:07 > 0:16:09the one that uses the least energy.
0:16:09 > 0:16:13And what they're doing is trying to minimise the surface area
0:16:13 > 0:16:15across the whole bubble structure.
0:16:15 > 0:16:20This beautifully illustrates one of the fundamental rules of bubbles,
0:16:20 > 0:16:27which is, three walls of a bubble will meet always at 120 degree angle.
0:16:27 > 0:16:32Wherever you are in the foam, it's the same law.
0:16:34 > 0:16:38But if we, in fact, made each of the bubbles the same size,
0:16:38 > 0:16:40a rather magical shape starts to appear.
0:16:51 > 0:16:53The hexagon.
0:16:54 > 0:16:58'And when you pack lots of hexagons together,
0:16:58 > 0:17:02'the pattern that spontaneously emerges is the familiar sight
0:17:02 > 0:17:04'of a tightly ordered honeycomb.'
0:17:04 > 0:17:10So when we see that pattern at the heart of the beehive,
0:17:10 > 0:17:15it's echoing some of the fundamental geometrical rules of the universe.
0:17:18 > 0:17:24It's the principles we see in bubbles that help explain where all structure comes from.
0:17:24 > 0:17:28And it's those same fundamental laws of shape that played out
0:17:28 > 0:17:32on the Giant's Causeway in the distant geological past.
0:17:33 > 0:17:3750 million years ago, before there was any thought of warring giants,
0:17:37 > 0:17:39this area was very unstable.
0:17:39 > 0:17:42There was a huge amount of volcanic activity.
0:17:42 > 0:17:46The molten rock forces its way through the chalk bed beneath my feet
0:17:46 > 0:17:49and then spread out, forming a huge lava lake.
0:17:54 > 0:17:58As it cooled, the lake contracted, and as it shrunk, it cracked.
0:18:01 > 0:18:05And as the cracks spread, they sought out the most efficient path
0:18:05 > 0:18:07through the lava,
0:18:07 > 0:18:11which turned out to be this neat hexagonal pattern...
0:18:13 > 0:18:17..leaving this monument to the order and economy of nature.
0:18:31 > 0:18:35'It's an engineering wonder, for sure.'
0:18:39 > 0:18:43The Code reveals itself where you would least expect it.
0:18:45 > 0:18:47It defines the shape of honeycomb.
0:18:47 > 0:18:51'They've just done it for thousands of years. They were born to do it.'
0:18:53 > 0:18:55And it forms Ulster's epic coastline.
0:18:55 > 0:18:59'..they just don't seem to fit in to this rugged natural environment.'
0:18:59 > 0:19:01'Fionn mac Cumhaill.'
0:19:04 > 0:19:07And it appears in the lazy efficiency of a soap film.
0:19:09 > 0:19:12'About 20,000 times thinner than a human hair.'
0:19:14 > 0:19:17These natural codes are so fundamental
0:19:17 > 0:19:23that they've been appropriated by artists and architects to shape the modern world.
0:19:23 > 0:19:24CHEERING
0:19:26 > 0:19:31So this is the Olympic stadium that was built in Munich in 1972,
0:19:31 > 0:19:36also scene of a rather famous victory for England.
0:19:36 > 0:19:39A rare one, 5-1 to us against Germany.
0:19:40 > 0:19:42It's really stunning
0:19:42 > 0:19:45but I'm quite surprised at how insubstantial it feels.
0:19:45 > 0:19:49It feels as though it could blow away in the wind.
0:19:50 > 0:19:54It's got those features you expect in nature,
0:19:54 > 0:19:58very elegant, but rather delicate feel to it.
0:19:58 > 0:20:02So it's almost more like a cobweb than a man-made structure.
0:20:09 > 0:20:13In 1972, which you have to remember is pre the computer age,
0:20:13 > 0:20:16it was very difficult to build structures like this.
0:20:16 > 0:20:19The distribution of forces that's going on inside this roof
0:20:19 > 0:20:22are incredibly complicated.
0:20:22 > 0:20:25It would be almost impossible to calculate by hand a shape like this
0:20:25 > 0:20:28that would be both stable and affordable.
0:20:28 > 0:20:32But the revolutionary engineer Frei Otto realised
0:20:32 > 0:20:35that you don't have to do these calculations by hand.
0:20:38 > 0:20:42Otto was desperate to find new shapes and forms to build,
0:20:42 > 0:20:43so he looked to nature,
0:20:43 > 0:20:48and the fundamental principles of the Code, for inspiration.
0:20:49 > 0:20:52What Otto did was to make models like this one here.
0:20:52 > 0:20:55It's constructed out of string, wires and these poles.
0:20:55 > 0:20:57It doesn't look like much
0:20:57 > 0:21:01but when I dip the string inside the soap solution and pull it up,
0:21:01 > 0:21:04something rather surprising happens.
0:21:07 > 0:21:12You start to see these beautiful shapes beginning to emerge
0:21:12 > 0:21:13inside a soap film.
0:21:14 > 0:21:18And you can see that they're not just exact triangles,
0:21:18 > 0:21:21you get wonderful curves and arcs
0:21:21 > 0:21:24that Otto knew were inherently stable.
0:21:26 > 0:21:29Oh, that's lovely, that one there.
0:21:31 > 0:21:34The surface tension pulls the strings
0:21:34 > 0:21:37into the most sparing shape for each arrangement.
0:21:38 > 0:21:41What results is a shape that's not only stable
0:21:41 > 0:21:43but remarkably striking too.
0:21:44 > 0:21:47So he could make copies of these shapes,
0:21:47 > 0:21:50make small little models, which would then be used to construct
0:21:50 > 0:21:54the groundbreaking structures you see behind me.
0:22:03 > 0:22:08Frei Otto started something of a revolution in architecture.
0:22:08 > 0:22:10The sweeping curves of the Munich Stadium
0:22:10 > 0:22:13are echoed in countless modern structures.
0:22:26 > 0:22:28And although Otto discovered
0:22:28 > 0:22:31the mathematical and aesthetic beauty of the Code in the 20th century,
0:22:31 > 0:22:35there's evidence that this obsession with form
0:22:35 > 0:22:38stretches back thousands of years.
0:22:48 > 0:22:51These stone balls were found in Scotland and they date back
0:22:51 > 0:22:55to the Neolithic period, which is over 4,000 years ago.
0:22:55 > 0:22:57They sit very beautifully in the hands.
0:22:57 > 0:23:00They found hundreds of these balls.
0:23:00 > 0:23:03But it's not really clear what they were used for.
0:23:03 > 0:23:04It's a bit of a mystery.
0:23:04 > 0:23:10But imagine the amount of work that's gone into making these shapes.
0:23:10 > 0:23:14For example this one here has got four different faces
0:23:14 > 0:23:17arranged in a beautifully symmetrical manner.
0:23:17 > 0:23:22This one here has six faces, a bit like a cube.
0:23:22 > 0:23:25And you can see some of them are really intricate.
0:23:25 > 0:23:29This ones got... I don't know how many nodules on there.
0:23:29 > 0:23:33Some of them have got up to 160 different nodules.
0:23:33 > 0:23:36But these stones really show an obsession with symmetry
0:23:36 > 0:23:41and regularity, already, thousands of years ago.
0:23:44 > 0:23:49This obsession with shape isn't unique to the ancient Scots.
0:23:49 > 0:23:52We find it in other cultures all over the world.
0:23:53 > 0:23:56The Egyptians had their pyramids, of course.
0:23:56 > 0:24:01But it was the Greeks who first took this innate fascination with shape
0:24:01 > 0:24:04and turned it into a subject of its own.
0:24:04 > 0:24:06They believed that by understanding its principles,
0:24:06 > 0:24:10they could describe the whole world.
0:24:12 > 0:24:14And they gave a name to this new idea.
0:24:14 > 0:24:17One which meant measuring the Earth.
0:24:17 > 0:24:19They called it geometry.
0:24:22 > 0:24:27The mainstay of Greek geometry was a discovery of five perfect shapes,
0:24:27 > 0:24:30now called the Platonic Solids, after the Greek philosopher Plato,
0:24:30 > 0:24:33who believed these were the building blocks of nature.
0:24:33 > 0:24:36So we've got the tetrahedron with its four faces,
0:24:36 > 0:24:38the cube with its six faces,
0:24:38 > 0:24:43the octahedron with its eight faces, the dodecahedron, 12 faces,
0:24:43 > 0:24:45and the most complicated shape of all,
0:24:45 > 0:24:47the icosahedron, with its 20 faces.
0:24:47 > 0:24:50Today these are more commonly known as dice.
0:25:00 > 0:25:04We're all used to the familiar six sided dice,
0:25:04 > 0:25:09but these four other shapes have also been used as dice for centuries.
0:25:13 > 0:25:18What makes them perfect for the job is that they are so regular.
0:25:18 > 0:25:23The faces of each are all the same shape. All meet at the same angles.
0:25:25 > 0:25:29It means that there's no way of telling one end from another,
0:25:29 > 0:25:32and that they are equally likely to land on any face.
0:25:34 > 0:25:36But most surprisingly,
0:25:36 > 0:25:40these are the only five shapes like this that can possibly exist.
0:25:41 > 0:25:44They're the only perfectly symmetrical solids.
0:25:50 > 0:25:53It's this almost magical symmetry which made the Greeks believe
0:25:53 > 0:25:55that these shapes were so important.
0:25:55 > 0:25:58They associated them with the building blocks of nature:
0:25:58 > 0:26:02air, fire, earth, the cosmos and water.
0:26:02 > 0:26:07These five shapes built the natural world.
0:26:09 > 0:26:13It's very easy to dismiss this approach as naive.
0:26:13 > 0:26:15After all, it's clear the world around us
0:26:15 > 0:26:18isn't made out of just five neat geometric shapes.
0:26:21 > 0:26:25But perhaps we should have more faith in this ancient intuition.
0:26:26 > 0:26:29Because by laying out the laws of geometry the Greeks had in fact
0:26:29 > 0:26:33tapped straight into the Code that shapes all nature.
0:26:40 > 0:26:45It turns out that the Greeks were right about their shapes,
0:26:45 > 0:26:48but they couldn't have known it, because the world that's governed
0:26:48 > 0:26:54by their laws of geometry was completely invisible to them.
0:26:54 > 0:26:57We can find traces of it deep underground.
0:26:59 > 0:27:01This is the Merkers potash mine,
0:27:01 > 0:27:05in the heart of what used to be East Germany.
0:27:07 > 0:27:09It has long since stopped production,
0:27:09 > 0:27:13but you can still explore its 3,000 miles of tunnels.
0:27:32 > 0:27:36That's stunning, my God. I've never seen anything like this.
0:27:36 > 0:27:41In fact I think this is the only one like this in the world.
0:27:41 > 0:27:47It's absolutely amazing. Just goes on and on down through the cave.
0:27:50 > 0:27:54The cave is full of perfectly cubic crystals that mirror
0:27:54 > 0:27:57the geometric precision of the Platonic solids.
0:28:01 > 0:28:03These cubes are amazing. Look at that.
0:28:03 > 0:28:04The surface is perfectly flat
0:28:04 > 0:28:08and if you run your finger down the edge here it's so sharp.
0:28:08 > 0:28:10Comes down to this precise right angle.
0:28:10 > 0:28:14An architect would be happy with that kind of precision.
0:28:16 > 0:28:18Doesn't look real.
0:28:22 > 0:28:25Even if you look inside you can see
0:28:25 > 0:28:28all the cracks are right angles and geometric shapes.
0:28:32 > 0:28:34Totally surreal.
0:28:36 > 0:28:39Actually, this isn't anything particularly special.
0:28:39 > 0:28:41This is just sodium chloride
0:28:41 > 0:28:43which we know as salt.
0:28:43 > 0:28:45This is what you stick on your chips.
0:28:46 > 0:28:51But you don't generally see salt as big a cube as this one here.
0:28:54 > 0:28:59How these crystals were able to form with such perfect precision
0:28:59 > 0:29:01was a mystery until just over 100 years ago,
0:29:01 > 0:29:04when X-rays were discovered.
0:29:09 > 0:29:12Our understanding of our biology was transformed
0:29:12 > 0:29:16by being able to see inside the human body.
0:29:17 > 0:29:21And when X-rays were shone through crystals,
0:29:21 > 0:29:24they uncovered another invisible world,
0:29:24 > 0:29:27one that was both mysterious and geometric.
0:29:29 > 0:29:31This was the world of the atom.
0:29:31 > 0:29:34And these neat symmetrical images,
0:29:34 > 0:29:36called diffraction patterns,
0:29:36 > 0:29:39can reveal how individual atoms were put together
0:29:39 > 0:29:42to form the crystals in this cave.
0:29:44 > 0:29:47Essentially you've got to think of these a bit like shadows.
0:29:47 > 0:29:50Just in the same way as an X-ray of my hand
0:29:50 > 0:29:52is a shadow of the bones underneath the skin,
0:29:52 > 0:29:57this is a shadow of the billions of atoms contained inside the crystal.
0:29:57 > 0:30:00It's a little bit more complicated than that, but essentially,
0:30:00 > 0:30:05these are 2D projections of the 3D structure inside this crystal.
0:30:05 > 0:30:07So now we can analyse these patterns
0:30:07 > 0:30:12and work out exactly how the atoms are arranged inside the salt.
0:30:15 > 0:30:18And there is only one possible arrangement of these atoms
0:30:18 > 0:30:21that can produce patterns like these.
0:30:23 > 0:30:26And it too, unsurprisingly, is a cube.
0:30:28 > 0:30:32This is a model of the structure of salt, and these gold balls
0:30:32 > 0:30:36are the sodium atoms, and the green ones are the chlorine atoms.
0:30:38 > 0:30:42And it's this atomic symmetry which explains
0:30:42 > 0:30:45why were seeing such symmetry in these huge crystals.
0:30:46 > 0:30:50But instead of just three atoms lining themselves up in this model,
0:30:50 > 0:30:53we've got billions and billions of sodium and chlorine atoms
0:30:53 > 0:30:57arranging themselves rigidly to create these perfect cubes.
0:31:03 > 0:31:05What makes this cave so special
0:31:05 > 0:31:09is that the perfect geometric arrangement of the atoms has been
0:31:09 > 0:31:12maintained in these huge crystals.
0:31:15 > 0:31:19They're a window into nature, and how it's governed by the laws of geometry
0:31:19 > 0:31:22at the most fundamental atomic level.
0:31:30 > 0:31:34But what's surprising is that we can find the same laws,
0:31:34 > 0:31:38not just in rocks and minerals, but deep inside ourselves.
0:31:40 > 0:31:45I've come to the Department of Chemical and Structural Biology
0:31:45 > 0:31:46at Imperial College in London.
0:31:46 > 0:31:49Steve Matthews studies how individual atoms
0:31:49 > 0:31:54are built up into living systems, like you and me.
0:31:58 > 0:32:01X-rays are obviously very powerful, high energy radiation,
0:32:01 > 0:32:04so proteins are very delicate.
0:32:04 > 0:32:07So we cool it down with a stream of liquid nitrogen gas
0:32:07 > 0:32:09blowing over the crystal.
0:32:11 > 0:32:14In this tiny wire loop is another crystal,
0:32:14 > 0:32:17but this time, it's a crystal of protein,
0:32:17 > 0:32:20part of the machinery of living cells.
0:32:22 > 0:32:25Just as it's possible to work out
0:32:25 > 0:32:26the atomic structure of the salt crystals with X-rays,
0:32:26 > 0:32:31we can deduce the shape of the protein molecules in the same way.
0:32:31 > 0:32:35Though the results aren't quite so easy to interpret.
0:32:36 > 0:32:40I'd be hard pushed to actually give a name to that shape mathematically.
0:32:40 > 0:32:42It looks like a blob.
0:32:42 > 0:32:44It doesn't have a shape but many of these blobs
0:32:44 > 0:32:46come together to form shapes.
0:32:56 > 0:33:00There's a huge amount of structure and symmetry in this protein?
0:33:00 > 0:33:02- Oh yes, definitely.- That's amazing.
0:33:02 > 0:33:04We've got a cylinder now.
0:33:04 > 0:33:09This is a real surprise to see geometry at work inside our bodies.
0:33:09 > 0:33:12But evolution creates a very efficient process,
0:33:12 > 0:33:14so symmetry is a very efficient way
0:33:14 > 0:33:17of building these types of structures.
0:33:17 > 0:33:20So by a process of evolution biology has discovered that...
0:33:20 > 0:33:22Before us, yes.
0:33:22 > 0:33:24..that geometry gives us the best shapes?
0:33:24 > 0:33:27Right. But if you really want symmetry
0:33:27 > 0:33:29we can move over to a virus particle.
0:33:29 > 0:33:33- I recognise that. That's a icosahedron.- That's an icosahedron.
0:33:33 > 0:33:36This is one of the shapes the Greeks were obsessed with.
0:33:36 > 0:33:38- Seems that viruses are too. - That's right.
0:33:38 > 0:33:41It's very striking cos the physical world
0:33:41 > 0:33:44you somehow expect maybe salt crystals to be symmetric,
0:33:44 > 0:33:47but the biological world everyone considers rather a messy one.
0:33:47 > 0:33:50But this is not messy at all. This is beautiful.
0:33:55 > 0:33:58The geometric shapes which you find at the heart of our cells
0:33:58 > 0:34:00are the most efficient that nature can produce.
0:34:02 > 0:34:05It seems like the Greeks could have been right after all.
0:34:05 > 0:34:08It's their shapes that build the word around us
0:34:08 > 0:34:10and produce its inherent beauty.
0:34:17 > 0:34:20'An obsession with symmetry and regulatory.'
0:34:21 > 0:34:25The Code dictates some shapes through efficiency...
0:34:25 > 0:34:28'The building blocks of nature.'
0:34:28 > 0:34:33..and others by providing frameworks for the tiniest particles there are.
0:34:33 > 0:34:36'This is nature's code at work.'
0:34:38 > 0:34:40'It fits beautifully in the hand.'
0:34:41 > 0:34:44What the Greeks discovered in mathematical theory
0:34:44 > 0:34:50is to be found at the heart of nature, from crystals to viruses.
0:34:50 > 0:34:53It all seems very neat.
0:34:53 > 0:34:57'Now I recognise that. That's an icosahedron.'
0:34:57 > 0:35:00'The only one like it in the world.'
0:35:00 > 0:35:03But our world isn't filled with precise geometric shapes.
0:35:06 > 0:35:10It seems random, disordered.
0:35:15 > 0:35:18To find out why we need to look to the sky
0:35:18 > 0:35:20and the crystals that fall from it.
0:35:24 > 0:35:27Snowflakes assemble themselves in the heart of frozen clouds
0:35:27 > 0:35:30and fall to earth in a dazzling display.
0:35:30 > 0:35:32VOICES CHATTER INAUDIBLY
0:35:35 > 0:35:38And if there's one thing we know about snowflakes,
0:35:38 > 0:35:41it's that they're all perfectly symmetrical.
0:35:46 > 0:35:48- Wow.- Here we are. It's the snow lab.
0:35:48 > 0:35:51Physicist Kenneth Libbrecht has created a lab
0:35:51 > 0:35:54for growing and photographing these perfect crystals.
0:36:02 > 0:36:05It's a cold chamber. Its actually cold on the bottom, very cold,
0:36:05 > 0:36:09about minus 40 on the bottom and about plus 40 on top.
0:36:09 > 0:36:10In a sense this machine is trying
0:36:10 > 0:36:13to replicate what happens inside a snow cloud.
0:36:13 > 0:36:16In a sense, that's right. It's not hard to grow ice crystals.
0:36:16 > 0:36:18All you need is cold and water.
0:36:21 > 0:36:23In the freezing conditions of the chamber,
0:36:23 > 0:36:27we should be able to see the inherent geometry of the world
0:36:27 > 0:36:31emerging in front of our eyes, as the crystals start to form.
0:36:33 > 0:36:37Now, with any luck, we'll see some stars growing
0:36:37 > 0:36:39on the ends of those needles.
0:36:41 > 0:36:42As the temperature drops,
0:36:42 > 0:36:46billions of water molecules coalesce out of the vapour,
0:36:46 > 0:36:51spontaneously arranging themselves into these six pointed patterns.
0:36:53 > 0:36:55At least, that's the theory.
0:36:56 > 0:36:59But the reality turns out to be very different.
0:37:02 > 0:37:05As Ken found out, even in laboratory conditions,
0:37:05 > 0:37:09it's almost impossible to grow perfect snowflakes.
0:37:09 > 0:37:15I don't think any of these are symmetrical. Not a single one.
0:37:15 > 0:37:17What's the chance of getting
0:37:17 > 0:37:19a perfectly symmetrical snowflake in here?
0:37:19 > 0:37:20PROFESSOR SIGHS
0:37:20 > 0:37:26The really beautiful snowflakes are about one in a million.
0:37:26 > 0:37:32- Really? Wow.- Sometimes they've got five sides or three sides.
0:37:32 > 0:37:33Five sides? Oh no!
0:37:34 > 0:37:38Or three, or sometimes you get a blob.
0:37:38 > 0:37:40It's a little hard to see
0:37:40 > 0:37:44but this mess here is one funny looking snowflake.
0:37:44 > 0:37:46We do tend to think of the snowflake as something
0:37:46 > 0:37:50beautifully symmetrical, but actually that's just some
0:37:50 > 0:37:53idealised notion and the reality is that they're actually
0:37:53 > 0:37:58much more complex and irregular than we think they are.
0:37:58 > 0:38:02If the molecular scale it's perfect, but as the crystal gets bigger,
0:38:02 > 0:38:05the atoms don't hook on in always exactly the right way,
0:38:05 > 0:38:10so when it grows, or how it grows depends on the environment,
0:38:10 > 0:38:13the temperature and the humidity, so it starts growing one way,
0:38:13 > 0:38:17then moves to a different spot in the cloud and grows a different way
0:38:17 > 0:38:21and then a different way, so by the time the crystal hits the ground,
0:38:21 > 0:38:27it's had a complex growth history, so it ends up as a complex crystal.
0:38:27 > 0:38:29Ah, there it goes.
0:38:38 > 0:38:40It seems you can only come so far
0:38:40 > 0:38:43in trying to describe the world with simple geometry.
0:38:43 > 0:38:47You can see it at work in the salt crystals in the crystal cave.
0:38:47 > 0:38:50But in truth, that's one of the very few places in the world
0:38:50 > 0:38:52where you'll find such crystals.
0:38:52 > 0:38:55The bees use simple geometry to make their honeycomb,
0:38:55 > 0:38:59but they've evolved to perform that task over many thousands of years.
0:38:59 > 0:39:05And it's only occasionally that you'll ever find a purely symmetrical snowflake.
0:39:07 > 0:39:12Because although everything is formed from tidy geometry at the atomic level,
0:39:12 > 0:39:19that underlying order falls apart amid all the competing forces of our chaotic world.
0:39:19 > 0:39:24Even the Giant's Causeway isn't really a neat hexagonal array.
0:39:25 > 0:39:28It's almost there, but amongst the hexagons
0:39:28 > 0:39:32there are pentagons, seven-sided columns, even a few with eight sides.
0:39:32 > 0:39:37That network of perfectly interlocking hexagons just doesn't exist.
0:39:41 > 0:39:45The world clearly isn't just built from simple geometric shapes.
0:39:47 > 0:39:51The movement of the sea and the flow of the waves
0:39:51 > 0:39:54are far too complicated to explain in these terms.
0:39:57 > 0:40:03It's difficult to imagine how we could ever find a code to explain all this complexity.
0:40:09 > 0:40:11But what if there are patterns in the chaos of nature?
0:40:11 > 0:40:16Patterns that we're not aware of, but that we're attuned to on a subconscious level.
0:40:56 > 0:41:00This barn was home to one of the artistic revolutions of the 20th century.
0:41:00 > 0:41:05The painter who worked here had become disillusioned with conventional painting techniques.
0:41:05 > 0:41:08In fact he stopped painting altogether and started splattering.
0:41:12 > 0:41:17He was as controversial as the art he produced.
0:41:17 > 0:41:19An arrogant, self-destructive drunk.
0:41:19 > 0:41:23And perhaps a visionary.
0:41:23 > 0:41:26His name was Jackson Pollock.
0:41:27 > 0:41:30The floor you can still see is covered in paint.
0:41:30 > 0:41:33What Pollock would do is to lay a canvas out on the floor.
0:41:35 > 0:41:40And then - often intoxicated - he would drip and flick the paint all over the surface.
0:41:40 > 0:41:45He'd come back week after week, adding more and more layers, more and more colours.
0:41:52 > 0:41:54The result was extraordinary.
0:41:54 > 0:41:58They're a huge outburst of abstract expressionism.
0:41:58 > 0:42:01Just covered in paint, scattered all over the place.
0:42:05 > 0:42:09Pollock's paintings sent shockwaves through the art world.
0:42:09 > 0:42:12No-one had ever seen anything like this before.
0:42:14 > 0:42:20Life Magazine declared him, artist of the century. Others derided his
0:42:20 > 0:42:25efforts as the substandard dross of a drunken lunatic.
0:42:26 > 0:42:32But though Pollock's paintings courted controversy, they were incredibly influential.
0:42:34 > 0:42:40Not least because the apparent random squiggles are strangely compelling.
0:42:42 > 0:42:45Many people have tried to copy Pollock's techniques.
0:42:45 > 0:42:48Some in homage, others in attempted forgeries.
0:42:48 > 0:42:53But nobody seems to be able to reproduce that magic that Pollock brought to the originals.
0:42:55 > 0:43:01Pollock's paintings seem to have captured something of the wildness of the natural world.
0:43:01 > 0:43:08But for a long time no-one could define exactly what it was that made his work so appealing.
0:43:08 > 0:43:14Until it came to the attention of artist and physicist, Richard Taylor.
0:43:15 > 0:43:22His unique approach was to invent a machine that can mimic Pollock's eccentric painting style.
0:43:30 > 0:43:33It's all based on this apparatus called the Pollockiser.
0:43:33 > 0:43:36The Pollockiser? That's lovely.
0:43:36 > 0:43:42No, what it is essentially though is what's called a kicked pendulum and as you know a basic pendulum
0:43:42 > 0:43:46is very, very regular like a clock, but at the top here what you've got
0:43:46 > 0:43:47is a little device that can actually knock the
0:43:47 > 0:43:54string as it's swinging around and that induces a very different type of motion called "chaotic motion."
0:43:54 > 0:43:57So this would be like Pollock's hand, this would
0:43:57 > 0:44:01be what he'd be trying to achieve with that sort of off balance, um,
0:44:01 > 0:44:06- painting that we do? - Absolutely, so they're very similar processes.- It's very effective.
0:44:08 > 0:44:13By recreating his technique, the Pollockiser is able to mimic
0:44:13 > 0:44:17one particular aspect of the artist's work.
0:44:17 > 0:44:22And that is that it appears more or less the same, no matter how closely you look.
0:44:22 > 0:44:27You keep on seeing these patterns unfolding in front of you.
0:44:27 > 0:44:32And with a Pollock painting, all of those patterns of different size scales look the same.
0:44:33 > 0:44:38This is a property known as fractor.
0:44:38 > 0:44:41So if I took pictures at these different scales and showed them to somebody, in some sense they wouldn't
0:44:41 > 0:44:46be able to tell which one was the close and which one was far away?
0:44:46 > 0:44:51Absolutely. So as long as you can't see that canvas edge, then you have no idea whether you're standing
0:44:51 > 0:44:5730 feet away or 2 feet away, they'll both have exactly the same level of complexity.
0:44:58 > 0:45:04More than any other painter, Jackson Pollock was able to consistently repeat the same
0:45:04 > 0:45:08level of complexity at different scales throughout his paintings.
0:45:10 > 0:45:14The fractor quality of his work appeals to us.
0:45:14 > 0:45:21Because, despite seeming abstract, it actually mirrors the reality of the world around us.
0:45:21 > 0:45:27When we started to actually analyse the buried patterns in there, this amazing thing emerged.
0:45:27 > 0:45:31Deep down hidden in there is this level of mathematical structure.
0:45:31 > 0:45:38So it's this really delicate interplay between something that looks messy and chaotic, but actually
0:45:38 > 0:45:42it has structure and some underlying code hidden inside it?
0:45:42 > 0:45:46Absolutely, and you can see it not only in his paintings, but you see it everywhere.
0:45:46 > 0:45:48You know like a tree outside.
0:45:48 > 0:45:53You look at the tree from far away you see this big trunk with a few branches going off.
0:45:53 > 0:45:57Superficially they look cluttered and they look incredibly complex,
0:45:57 > 0:46:02but your eye can sense that there's a sort of underlying mathematical structure to all it.
0:46:02 > 0:46:06Pollock was the first person to actually
0:46:06 > 0:46:10put it on canvas in a direct fashion that no other artist has ever done.
0:46:10 > 0:46:15It really is the basic fingerprint of nature.
0:46:17 > 0:46:20And that's what's most fascinating about Pollock's art.
0:46:20 > 0:46:24In creating work devoid of conventional meaning,
0:46:24 > 0:46:28he had in fact stumbled across something fundamental.
0:46:28 > 0:46:32Because fractors are how nature builds the world.
0:46:35 > 0:46:40Clouds are fractal, because they display the same quality.
0:46:40 > 0:46:43Giant clouds are identical to tiny ones.
0:46:46 > 0:46:48And it's the same with rocks.
0:46:48 > 0:46:55From appearances you can't tell if you're looking at an enormous mountain, or a humble bolder.
0:46:57 > 0:47:00And then there are living fractors like this tree.
0:47:03 > 0:47:08It's quite easy to see how fractal it is, because if you take one of the branches it looks remarkably like
0:47:08 > 0:47:15a small version of the tree itself. If you look at the twigs coming off the branch, they have the same shape.
0:47:15 > 0:47:20So you see the same pattern appearing again and again at smaller and smaller scales.
0:47:22 > 0:47:27And trees also demonstrate the great powers of fractal systems.
0:47:27 > 0:47:32Their great complexity stems from very simple rules.
0:47:34 > 0:47:39Now the reason the tree makes this shape is because it wants to maximise the amount of sunlight it gets.
0:47:39 > 0:47:44Very clever. But also very simple, because you just need one rule to create this shape.
0:47:44 > 0:47:49What the tree does is to grow, then divide. Grow then divide.
0:47:49 > 0:47:54And by using this one rule, we get this incredibly complex shape we call a tree.
0:47:59 > 0:48:04This is the same pattern repeating itself at a smaller and smaller scale.
0:48:08 > 0:48:11It's a rule that's easy to test.
0:48:11 > 0:48:13Grow a bit, then branch.
0:48:13 > 0:48:16Grow a bit then branch.
0:48:16 > 0:48:20And before our eyes a mathematically perfect tree appears.
0:48:22 > 0:48:28But just as you never get a perfect snowflake, you never get a perfect tree either.
0:48:28 > 0:48:30But allow for some natural variability,
0:48:30 > 0:48:39different growing seasons, the wind, an occasional accident and the result is a very real looking tree.
0:48:39 > 0:48:45And we find the same fractal branching system time and again throughout nature.
0:48:47 > 0:48:52Deep down in there is this level of mathematical structure.
0:48:56 > 0:48:59This idea that the patterns
0:48:59 > 0:49:06of nature may be inherently fractal was pioneered in the 1970s by French mathematician, Benoit Mandelbrot.
0:49:08 > 0:49:10This is his most famous creation.
0:49:10 > 0:49:11The Mandelbrot Set.
0:49:13 > 0:49:20Its systems of circles and swirls repeats itself at smaller and smaller scales forever.
0:49:24 > 0:49:31And this infinite complexity was created from just one very simple mathematical function.
0:49:35 > 0:49:41Mandelbrot's quantum leap was to suggest that similar simple mathematical codes
0:49:41 > 0:49:49could describe not just trees, but many of the seemingly random shapes of much of the natural world.
0:49:49 > 0:49:52INDISTINCT VOICES
0:49:52 > 0:49:58And the most powerful demonstration of that belief comes, not from maths or nature, but from make believe.
0:50:00 > 0:50:02INDISTINCT VOICES
0:50:02 > 0:50:05A smart pencil...
0:50:05 > 0:50:09In the 1980s, a computer scientist working for the aircraft manufacturer Boeing
0:50:09 > 0:50:16was struggling to create computer-generated pictures of planes.
0:50:16 > 0:50:18At Boeing, we discovered a method of making curved surfaces,
0:50:18 > 0:50:22very nice curved surfaces, so I was applying it to airplanes.
0:50:22 > 0:50:25And Boeing publicity photos have mountains behind their planes
0:50:25 > 0:50:28and so I wanted to be able to
0:50:28 > 0:50:32put a mountain behind my airplane, but I had no idea of the mathematics or how to do that, not a clue.
0:50:32 > 0:50:39So you wanted something that however far or near away you were, it would look like something natural?
0:50:39 > 0:50:41Yes, exactly, to show that these mountains were
0:50:41 > 0:50:45real and live, in the sense that you can move around them with a camera.
0:50:45 > 0:50:48So the algorithm needed to be invented
0:50:48 > 0:50:52and so that's what I set my mind to doing was invent the algorithm that would produce the mountain pictures.
0:50:54 > 0:50:57At the time, even creating a virtual cylinder was hard.
0:50:57 > 0:51:03So generating the apparently random jaggedness of a realistic mountain range seemed impossible.
0:51:03 > 0:51:07Then Loren found inspiration.
0:51:07 > 0:51:10Coincidentally at that time, Mandelbrot's book came out.
0:51:10 > 0:51:14He had pictures that showed what fractal mathematics could produce
0:51:14 > 0:51:19and so wow, all I have to do is find a way to implement this mathematics
0:51:19 > 0:51:22on my computer and I can make pictures of mountains.
0:51:24 > 0:51:28Loren set to work to investigate how Mandelbrot's theories about
0:51:28 > 0:51:32the real world could be used to make virtual ones.
0:51:33 > 0:51:36This is a little film I made in 1980.
0:51:36 > 0:51:42- And the landscape is constructed by me, by hand, of about 100 big triangles.- Yeah.
0:51:42 > 0:51:44So that doesn't look very natural.
0:51:44 > 0:51:45No, it's very pyramid-like.
0:51:45 > 0:51:50So what we're going to do is take each of these big triangles and break it up into little triangles
0:51:50 > 0:51:52and break those little triangles up into littler triangles, until
0:51:52 > 0:51:55it gets down to the point where you can't see triangles any more.
0:52:11 > 0:52:15What Loren had realised was that he could use the maths of fractors
0:52:15 > 0:52:20to turn just a handful of triangles into realistic virtual worlds.
0:52:23 > 0:52:26We turn the fractal process loose and instantly it looks natural.
0:52:28 > 0:52:32We went from about 100 triangles to about 5 million.
0:52:34 > 0:52:36And there it is.
0:52:44 > 0:52:46And then we jump off the cliff.
0:52:46 > 0:52:49You feel that it's a real three-dimensional world.
0:52:49 > 0:52:51And we're swooping over the landscape.
0:52:51 > 0:52:56Yeah, we're going from ten miles away to ten feet away
0:52:56 > 0:53:00and all that detail was generated on the fly as we came in.
0:53:02 > 0:53:07- In a few seconds. - And here's that fractal quality, this infinite complexity at work.
0:53:07 > 0:53:09- It's exactly what I wanted.- Yeah.
0:53:12 > 0:53:16By today's standards, this animation does not look like much.
0:53:18 > 0:53:22But in the 1980s, no-one had ever seen anything like it.
0:53:26 > 0:53:30If you did that by hand, to do that frame by frame, it would take you?
0:53:30 > 0:53:34- 100 years. - 100 years and this took to generate?
0:53:34 > 0:53:39It took about 15 minutes per frame on a computer that's about 100 times slower than my phone.
0:53:42 > 0:53:49That one short film changed the face of animation and revolutionised Hollywood.
0:53:50 > 0:53:52Loren went on to co-found Pixar,
0:53:54 > 0:53:59one of the most successful film studios in the world.
0:53:59 > 0:54:06Cars, monsters and, of course, toys owe their existence to the Code.
0:54:06 > 0:54:09An empire built on the power of fractors.
0:54:14 > 0:54:19Did you realise at the time the potential of the discovery you'd made?
0:54:19 > 0:54:21Well, I knew that,
0:54:21 > 0:54:25that within a half a second that it was a major discovery.
0:54:25 > 0:54:30I've seen, you know, all the special effects, all the movies you can imagine, nothing was like that.
0:54:30 > 0:54:32And my heart skipped.
0:54:35 > 0:54:41And the power of fractors is still to be hidden in the fabric of Pixar movies.
0:54:45 > 0:54:52They use the rule of repetition and self-similarity to create the rocks, clouds and forests.
0:54:52 > 0:54:59In fact, the realism and complexity of these virtual worlds is only possible using mathematics.
0:55:08 > 0:55:11Fractals are everywhere in these movies.
0:55:11 > 0:55:15They generate the texture of the rocks.
0:55:17 > 0:55:19And they bring the jungle alive.
0:55:23 > 0:55:26That these pretend worlds are so realistic,
0:55:26 > 0:55:33demonstrates the power of maths to describe the complexity of nature.
0:55:33 > 0:55:38They're evidence that we have glimpsed the Code that governs the shape of the world.
0:55:42 > 0:55:45But that Code is a complicated one.
0:55:45 > 0:55:48If we want to understand the shape of the world, then we need to recognise
0:55:48 > 0:55:52the simple geometry of form at work at the most basic level.
0:55:52 > 0:55:55INDISTINCT VOICES
0:55:55 > 0:55:59We need to understand that the universe is lazy.
0:56:01 > 0:56:05And that it will always seek out the most efficient solution.
0:56:05 > 0:56:09INDISTINCT VOICES
0:56:09 > 0:56:14That at the atomic level, the world is structured around strict geometric laws...
0:56:14 > 0:56:17INDISTINCT VOICES
0:56:17 > 0:56:21..that were first recognised by the Greeks thousands of years ago.
0:56:27 > 0:56:31We also need to appreciate the complexity of that geometry
0:56:31 > 0:56:35playing out against the competing forces of the natural world.
0:56:38 > 0:56:43And that means grasping how even the apparent randomness we see around us
0:56:43 > 0:56:48is underwritten by mathematical rules like fractors.
0:56:50 > 0:56:53Rules that can explain the patterns in everything.
0:56:53 > 0:56:57From the chaos of Jackson Pollock's paintings,
0:56:57 > 0:57:03to the structure of trees and the realism of virtual worlds.
0:57:04 > 0:57:06And that's the beauty of the Code.
0:57:08 > 0:57:12However complex we find our world, it provides a reason,
0:57:12 > 0:57:17an underlying explanation for why things look and behave as they do.
0:57:20 > 0:57:24INDISTINCT VOICES
0:57:24 > 0:57:26This is nature's code of law.
0:57:31 > 0:57:36Go to bbc.co.uk/code to find clues
0:57:36 > 0:57:38to help you solve the Code's treasure hunt.
0:57:38 > 0:57:42Plus, get a free set of mathematical puzzles and a treasure hunt clue
0:57:42 > 0:57:45when you follow the links to the Open University.
0:57:45 > 0:57:52Or call:
0:57:55 > 0:57:58Subtitles by Red Bee Media Ltd
0:57:58 > 0:58:02E-mail subtitling@bbc.co.uk