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- This is a film about
one very simple question:

how did we get here?

These are the elements and compounds

from which all humans are made.

They're incredibly, almost
embarrassingly, common.

In fact, almost 99% of the human body

is a mixture of air,
water, coal, and chalk,

with traces of other
slightly more exotic elements

like iron, zinc, phosphorous, and sulfur.

In fact, I've estimated that
the elements which make up

the average human cost
at most a few pounds.

But somehow trillions of
these very ordinary atoms

conspire miraculously
to organize themselves

into thinking, breathing,
living human beings.

How the wonders of creation are assembled

from such simple building blocks

is surely the most intriguing
question we can ask.

You may think that answering it

is beyond the realm of science.

But that's changing.

For the first time, I believe,

science has pushed past
religion and philosophy

in daring to tackle this most
fundamental of questions.

This film is the story of a series

of bizarre and interconnected discoveries.

It reveals a hidden safe of nature.

That woven into it's
simplest and most basic laws

is a power to be unpredictable.

It's about how inanimate matter
with no purpose or design

can spontaneously create exquisite beauty.

It's about how the same laws that make

the universe chaotic and unpredictable

can turn simple dust into human beings.

It's about the discovery that there is

a strange and unexpected relationship

between order and chaos.

(soft piano music)

The natural world really is one great,

blooming, buzzing confusion.

It's a mess of quirky shapes and blotches.

What patterns there are
are never quite regular,

and never seem to repeat exactly.

The idea that all this
mayhem, all this chaos

is underpinned, indeed
determined, by mathematical rules,

and that we can work out
what those rules might be

run counter to our most
dearly held intuitions.

So not surprisingly,
the first man to really

take on the momentous task of unraveling

nature's mysterious mathematics

had a very special and unusual mind.

He was both a great scientist

and a tragic hero.

He was born in 1912 in London.

His name was Alan Turing.

Alan Turing was a remarkable man;

one of the greatest
mathematicians who ever lived.

He discovered many of
the fundamental ideas

that underpin the modern computer.

Also, during the Second
World War, he worked here

at Bletchley Park just
outside today's Milton Keynes

in what was then a
secret government project

called Station X, which was set up

to crack the German military codes.

The Station X code breakers
proved highly effective,

and Turing's contribution was crucial.

The work he personally did to crack

German naval codes saved
thousands of Allied lives

and was a turning point in the war.

But code breaking was just
one aspect of Turing's genius.

Just one part of his uncanny ability

to see patterns that are
hidden from the rest of us.

For Turing, the natural world
offered up the ultimate codes.

And over the course of his life,

he'd come tantalizingly
close to cracking them.

- Turing was a very original person.

And he had realized that
there was this possibility

that simple mathematical equations

might describe aspects
of the biological world,

and no one had thought of that before.

- [Jim] Of all nature's mysteries,

the one that fascinated Turing most

was the idea that there
might be a mathematical basis

to human intelligence.

Turing had very personal
reasons for believing in this.

- It was the death of this
young man, Christopher Morton,

who Alan Turing, well, he was gay,

and he'd been a great

emotional thing of this
life at that point.

Christopher Morton suddenly died.

And Alan Turing was very,

obviously, he was very
emotionally disturbed by this.

But you can see is he wanted to put this

in a intellectual context,
a scientific context.

And the question he wanted
to put into context was

what happens to the mind?

What is it?

- [Jim] Turing became
convinced that mathematics

could be used to describe
biological systems

and, ultimately, intelligence.

This fascination would give
rise to the modern computer,

and later in Turing's life,
an even more radical idea.

The idea that the simple
mathematical description

could be given for a mysterious process

that takes place in an embryo.

The process is called morphogenesis,

and it's very puzzling.

At first, all the cells in
the embryo are identical.

Then, the cells begin to clump together

and also become different from each other.

How does this happen?

With no thought,

no central coordination,

how do cells that start off identical

know to become, say, skin,

while others become part of an eye.

Morphogenesis is a spectacular example

of something called self organization.

And before Turing,

no one had a clue how it worked.

Then in 1952, Turing published this.

His paper was the world's
first mathematical

explanation for morphogenesis.

The sheer chutzpah of
this paper was staggering.

In it, Turing used a mathematical equation

of the type normally seen
in papers on astronomy

or atomic physics to
describe a living process.

No one had done anything like this.

Crucially, Turing's equations
did, for the first time,

describe how a biological
system could self organize.

They showed that something
smooth and featureless

can develop features.

- One of the astonishing
things about Turing's work

was that starting with the description of

really very simple processes

that were governed by
very simple equations,

by putting these together, suddenly

complexity emerged.

The pattern suddenly came
out as a natural consequence.

And I think in many ways this
was very, very unexpected.

- [Jim] In essence, Turing's equations

described something quite familiar,

but which no one had thought of

in the context of biology before.

Think of the way a steady
wind flowing across sand

creates all kinds of shapes.

The grains self organize into
ripples, waves, and dunes.

This happens even though the
grains are virtually identical

and have no knowledge of the
shape they become part of.

Turing argues that, in a very similar way,

chemicals seeping across an embryo

might cause its cells to self organize

into different organs.

These are Turing's own
very rough scribblings

of how this might work.

They show how a completely
featureless chemical soup

can evolve these strange mods and patches.

In his paper, he refined his sketches

to show how his equations
could spontaneously

create markings similar to those

on the skins of animals.

- Turing went around showing
people pictures, saying,

"Does this look a bit like
the patterns on a cow?"

And everyone sort of,
what is this man on about?

But actually, and he
knew what he was doing,

because yes, indeed, they did
like the patterns on a cow,

and that's one of the reasons have this

sort of duffle pattern order.

So an area where mathematics
have never been used before,

pattern formation in
biology, animal markings,

suddenly the door was
opened and we could see that

mathematics might be useful
in that sort of area.

So even though Turing's exact equations

are not the full story,

they are the first piece

of mathematical work that showed there was

any possibility of doing
this kind of thing.

- [Jim] Of course, we now know

that morphogenesis is
much more complicated

than the process Turing's
equations describe.

In fact, the precise mechanism of how

DNA molecules in our cells

interacts with other chemicals

is still fiercely debated by scientists.

But Turing's idea that whatever is going

is deep down a simple mathematical process

was truly revolutionary.

- I think Alan Turing's paper is

probably the cornerstone in the whole idea

of how morphogenesis works.

What it does is it provides
us with a mechanism,

something that Darwin didn't
for how pattern emerges.

Darwin, of course, tells us
that once you have a pattern

and it is coded for in the genes,

that may or may not be passed on

depending on circumstances.

But what it doesn't do is explain

where that pattern comes
from in the first place.

That's the real mystery.

And so what Turing's had done

was to suddenly provide an accessible

chemical mechanism for doing this.

That was amazing.

- [Jim] Turing was onto
a really big, bold idea.

But sadly, we can only speculate how his

extraordinary mind would
have developed his idea.

Because shortly after
his groundbreaking paper

on morphogenesis, a dreadful

and completely avoidable
tragedy destroyed his life.

After his work breaking
codes at Bletchley Park,

you might all have assumed that Turing

would have been by the country

he did so much to protect.

This couldn't be further from the truth.

What happened to him after the war

was a great tragedy,

and one of the most shameful episodes

in the history of British science.

The same year Turing published
his morphogenesis paper,

he had a brief affair with
a man called Arnold Murray.

The affair went sour,
and Murray was involved

in a burglary at Turing's house.

But when Turing reported
this to the police,

they arrested him as well as Murray.

In court, the prosecution then argued

that Turing, with his
university education,

had led Murray astray.

He was convicted of gross indecency.

The judge then offered
Turing a dreadful choice.

He could either go to prison

or sign up to a regime of
female hormone injections

to cure him of his homosexuality.

He chose the latter,
and it was to send him

into a spiral of depression.

On the 8th of June, 1954,

Turing's body was found by his cleaner.

He died the day before by
taking a bite from an apple

he'd laced with cyanide,
ending his own life.

(somber violin music)

Alan Turing died aged just 41.

The loss to science is incalculable.

Turing would never know that his ideas

would inspire an entirely new

mathematical approach to biology,

and that scientists would
find equations like his

really do explain many of the shapes

that appear on living organisms.

Looking back, we now know Turing

had really grasped the idea that

the wonders of creation are derived

from the simplest of rules.

He had, perhaps unexpectedly,

taken the first step to
a new kind of science.

The next step in this story

was just as unexpected,

and in many ways just
as tragic as Turing's.

In the early 1950s,

around the time of Turing's
seminal paper on morphogenesis,

a brilliant Russian chemist
by the name of Boris Belousov

was beginning his own investigations into

the chemistry of nature.

Deep behind the iron curtain

in a lab at the Soviet Ministry of Health,

he was beginning to
investigate the way our bodies

extract energy from sugars.

Just like Turing, Belousov was
working on a personal project

having just finished
a distinguished career

as a scientist in the military.

In his lab, Belousov had
formulated a mixture of chemicals

to mimic one part of the
process of glucose absorption

in the body.

The mix of chemicals sat on
the lab bench in front of him,

clear and colorless while being shaken.

As he mixed in the final chemical,

the whole solution changed color.

Now this isn't particularly remarkable.

If we mix ink into
water, it changes color.

But then something happened
that made no sense at all.

The mixture began to go clear again.

Belousov was astounded.

Chemicals can mix together and react.

But they shouldn't be able
to go back on themselves

to apparently unmix without intervention.

You can change from a clear
mixture to a colored mixture

fine, but surely not back again.

And it got weirder.

Belousov's chemicals
didn't just spontaneously

go into reverse.

They oscillated.

They switched back and
forth from colored to clear

as if they were being
driven by some sort of

hidden chemical metronome.

With meticulous care, Belousov
repeated his experiment

again and again.

It was the same every time.

His mixture would cycle from clear

to colored and back again repeatedly.

He discovered something
that was almost like magic,

a physical process that seemed to violate

the laws of nature.

Convinced he'd discovered
something of great importance,

Belousov wrote up his findings,

keen to share his discover
with the wider world.

But when he submitted his paper to leading

Russian scientific journal,

he received a wholly unexpected
and damning response.

The editor of the journal told Belousov

that his findings in the lab
were quite simply impossible.

They contravene the
fundamental laws of physics.

The only explanation was that Belousov

had made a mistake in his experiments.

And the work was simply
not fit for publication.

The rejection crushed Belousov.

Deeply insulted by the suggestion his work

had been botched,

he abandoned his experiments.

Soon he gave up science altogether.

The tragic irony was
that, divided as they were

by the iron curtain,

Belousov never encountered Turing's work.

For if he had, he would have
been completely vindicated.

It turns out that Belousov's
oscillating chemicals,

far from contravening the laws of physics,

were actually a real-world example

of precisely the behavior
Turing's equations predicted.

While the connection might not appear

obvious at first sight,

other scientists showed that if you left

a variation of Belousov's chemicals,

unstirred in a Petri dish,

instead of simply oscillating,
they self organized

into shapes.

In fact, they go beyond Turing's
simple blobs and stripes

to create stunningly beautiful
structures and patterns

out of nowhere.

- The amazing and very unexpected thing

about the Bizet Reaction

is that someone had discovered a system

which essentially reproduces
the Turing equations.

And so from what looks like
a very, very bland solution

emerged these astonishing
patterns of waves

and scrolls and spirals.

- [Jim] Now this is emphatically
not abstract science.

The way Belousov's chemicals
move as coordinated waves

is exactly the way our heart cells

are coordinated as they beat.

Animal skins and heart beats.

Self organization seems to operate

all over the natural world.

So why were the scientific community

in Turing and Belousov's day

so uninterested or even hostile

to this astonishing and beautiful idea?

Well the reason was all too human.

Mainstream scientists
simply didn't like it.

To them, it seemed to
run counter to science

and all that it had achieved.

To change that view would require

a truly shocking and completely
unexpected discovery.

In essence, by the beginning
of the 20th century,

scientists saw the universe as a giant

complicated mechanical device,

kind of a super-sized
version of this orrery.

The idea was that the universe is a huge

and intricate machine that obeys
orderly mathematical rules.

If you knew the rules of how the machine

was configured to start with,

as you turn the handle
over and over again,

it will behave in an
entirely predictable way.

- Back in the times of Isaac Newton

when people were discovering the laws

that drove the universe,

they came up with this kind of metaphor

of a clockwork universe.

The universe looked like a machine

which had been set going
at the instant of creation,

and just followed the
rules and ticked along.

And it was a complicated machine,

and therefore complicated things happen.

But once you set it going,
it would only do one thing.

And the message that people drew from this

was that anything describable
by mathematical rules

must actually basically be fairly simple.

- [Jim] Find the mathematics
that describes the system,

and you can then predict
how that system will unfold.

That was the big idea.

It began with Newton's law of gravity,

which can be used to predict how a planet

moves around the Sun.

Scientists soon found many other equations

just like it.

Newtonian physics seemed like
the ultimate crystal ball.

It held up the tantalizing
possibility that the future

could, in principle, be known.

The more careful your
measurements are today,

the better you can predict
what will happen tomorrow.

But Newtonianism had a
dangerous consequence.

If a nice mathematical system

that worked in a similar way to my orrery

did sometimes become unpredictable,

scientists assumed some
malign outside force

was causing it.

Perhaps dirt had got it.

Perhaps the cogs were wearing out.

Or perhaps someone had tampered with it.

- Basically, we used to think if you saw

very irregular behavior in some

problem you're working on,

this must be the result of some sort of

random outside influences.

It couldn't be internally generated.

It wasn't an intrinsic
part of the problem.

It was some other thing impacting on it.

- [Jim] Looked at from this point of view,

the whole idea of self
organization seemed absurd.

The idea that patterns of the kind

Turing and Belousov had found

could appear of their own accord

without any outside influence
was a complete taboo.

- [Man] Six, five, four, three--

- [Jim] The only way for self
organization to be accepted

was for the domineering
Newtonian view to collapse.

But that seemed very unlikely.

After all, by the late 60s,

it had delivered all the
wonders of the modern age.

- [Man On Radio] Beautiful, beautiful

- [Man On Radio] Isn't that something?

(mumbles)

- [Jim] But then at the same
time as the moon mission,

a small group of scientists,
all ardent Newtonians,

quite unexpectedly found
something wasn't right;

not right at all.

During the second half
of the 20th century,

a devil was found in the detail.

A devil that would ultimately
shatter the Newtonian dream,

and plunge us literally into chaos.

(chaotic electrical sounds)

Ironically, the events
that forced scientists

to take self organization seriously

was the discovery of a
phenomenon known as chaos.

Chaos is one of the most
overused words in English.

But in science, has a
very specific meaning.

It says that a system that
is completely described

by mathematical equations

is more than capable
of being unpredictable

without any outside
interference whatsoever.

- There's a widespread misapprehension

that chaos is just somehow saying

the very familiar fact that
everything's complicated.

I mean, the nitwit chaos
assist in Jurassic Park

was under that confusion.

It's something much simpler and yet

much more complicated than that.

It says some very, very
simple rules or equations

with nothing random in them;

they're completely determined;

we know everything about the rule;

can have outcomes that are
entirely unpredictable.

- [Jim] Hail is one of the most unwelcome

discoveries in science.

The man who forced the
scientific community

to confront it was an
American (mumbles) zoologist

called Edward Lorenz.

In the early 1960s, he tried to find

mathematical equations that
could help predict the weather.

Like all his contemporaries,
he believed that, in principle,

the weather system was no
different to my orrery.

A mechanical system
that could be described

and predicted mathematically.

But he was wrong.

When Lorenz wrote down what looked like

perfectly simple mathematical equations

to describe the movement of air currents,

they didn't do what they were supposed to.

They made no useful
predictions whatsoever.

It was as if the lightest
breath of wind one day

could make the difference a month later

between a snow storm and
a perfectly sunny day.

How can a simple system that works

in the regular clockwork
manner of my orrery

become unpredictable?

It's all down to how it's configured,

how the gears are connected.

In essence, under certain circumstances,

the tiniest difference
in the starting positions

of the cogs, differences that
are too small to measure,

can get bigger and bigger
with each turn of the handle.

With each step in the process,

the system then moves
further and further away

from where you thought it was going.

Lorenz captured this radical idea

in an influential talk he gave

called Does the Flap
of a Butterfly's Wings

in Brazil Set Up a Tornado in Texas?

It was a powerful and evocative image,

and within months, a new phrase
had entered our language:

the butterfly effect.

And the butterfly effect,

the hallmark of all chaotic systems,

started turning up everywhere.

In the early '70s, a young
Australian called Robert May

was investigating a mathematical equation

that modeled how animal
populations changed over time.

But here too lurked the
dreaded butterfly effect.

Immeasurably small changes to the rate

at which the animals reproduced

could sometimes have huge consequences

on their overall population.

Numbers could go up and down wildly

for no obvious reason.

The idea that a mathematical equation

gave you the power to predict
how a system will behave

was dead.

- In some sense, this is the
end of the Newtonian dream.

When I was a graduate student,

the belief was

as we got more and more computer power,

we'd be able to solve
ever more complicated

sets of equations.

But this said that's not necessarily true.

You could have the simplest
equations you can think of,

with nothing random in
them, you know everything.

And yet, if they have

behavior that gives you chaotic solutions,

then you can never know the starting point

accurately enough.

- [Jim] Centuries of scientific certainty

dissolved in just a few short years.

The truth of the clockwork universe

turned out to be just an illusion;

something which had
seemed a logical certainty

revealed itself merely as an act of faith.

And what's worse, the
truth had been staring us

in the face all the time,

because chaos is everywhere.

It seemed unpredictability was hardwired

into everywhere aspect
of the world we live in.

The global climate could
dramatically change

in the course of a few short years.

The stock market could
crash without warning.

We could be wiped from the
face of the planet overnight,

and there is nothing
anyone could do about it.

Unfortunately, I have to tell
you that all of this is true.

And yet to be scared
of chaos is pointless.

It's woven into the basic laws of physics.

I mean, really all has to
accept it as a fact of life.

- The idea of chaos really
did have a big impact

over a period of about 20 or 30 years,

because it changed the way everyone

thought about what they
were doing in science.

It changed into the point the point

that they forgot that they'd
ever believed otherwise.

What chaos did was to show us

that the possibilities inherent
in the simple mathematics

are much broader, are much more general

than you might imagine.

And so a clockwork universe

can nonetheless behave
in the rich, complex way

that we experience.

- [Jim] The discovery of chaos was a real

turning point in the history of science.

As it tore down the Newtonian dream,

scientists began to look more favorably

at Turing and Belousov's work

on spontaneous pattern formation.

And perhaps more
importantly, as they did so,

they realized something truly astonishing.

That there was a very
deep and unexpected link,

a truly cosmic connection between nature's

strange power to self organize

and the chaotic consequences
of the butterfly effect.

Between them, Turing, Belousov,

May, and Lorenz had all discovered

different faces of just
one really big idea.

They discovered that the natural world

could be deeply, profoundly unpredictable.

But the very same things
that make it unpredictable

also allow it to create
pattern and structure,

order and chaos.

It seems the two are more deeply linked

than we could have ever imagined.

So how is this possible?

What do phenomena as apparently different

as a pattern in Belousov's chemicals

and the weather have in common?

First, though both systems behave

in very complicated ways,

they are both based on surprisingly simple

mathematical rules.

Secondly, these rules
have a unique property.

A property that's often
referred to as coupling,

or feedback.

To show you what I mean,

to show you both order and
chaos can emerge on their own

from a simple system with feedback,

I'm going to do what seems at first glance

like a rather trivial experiment.

This screen behind me is connected

up to the camera that's filming me.

But the camera in turn is
filming me with the screen.

This creates a loop with
multiple copies of me

appearing on the screen.

This is a classic example
of a feedback loop.

We get a picture in a
picture in a picture.

At first it seems fairly predictable,

but as we zoom the camera in,

some pretty strange
things begin to happen.

The first thing I notice is
that the object I'm filming

stops bearing much resemblance to what

now appears on the screen.

Small changes in the
movements of the match

become rapidly amplified
as they loop around

from the camera to the screen
and back to the camera.

So even though I can describe each step

in the process mathematically,

I still have no way of predicting

how tiny changes in the
flickering of the flame

will end up in the final image.

This is the butterfly effect in action.

But now here comes the spooky bit.

With just a slight tweak to the system,

these strange and rather
beautiful patterns

begin to emerge.

The same system, one that's
based on simple rules

with feedback, produces chaos and order.

- The same mathematics is
generating chaotic behavior

and patterned behavior.

This changes completely how
you think about all of this.

The idea that there are
regularities in nature

and then totally separately
from them are irregularities,

and these are just two different things.

It's just not true.

These are two ends of
the spectrum of behavior

which can be generated by
the same kind of mathematics.

And it's the closest thing
that we have at the moment

to the kind of true mathematics of nature.

- I think one of the
great take-home messages

from Turing's work and
from the discoveries

in chemistry and biology and so on,

is that, ultimately, pattern formation

seems to be woven very, very deeply

into the fabric of the universe.

And it actually takes
some very, very simple

and familiar processes like diffusion,

like the rates of chemical reactions.

And the interplay between
them naturally gives rise

to pattern.

So pattern is everywhere.
It's just waiting to happen.

- [Jim] From the '70s on,

more and more scientists began to embrace

the concept that chaos and pattern

are built into nature's most basic rules.

But one scientist, more than any other,

brought this fundamentally
new understanding

to this astonishing and
often puzzling idea.

He was a colorful character
and something of a maverick.

His name is Benoit Mandelbrot.

Benoit Mandelbrot wasn't
an ordinary child.

He skipped the first two years of school.

And as a Jew in war-torn Europe,

his education was very disrupted.

He was largely self-taught

or tutored by relatives.

He never formally learned the alphabet

or even multiplication
beyond the Five times table.

But like Alan Turing,
Mandelbrot had a gift

for seeing nature's hidden patterns.

He could see rules where
the rest of us see anarchy.

He could see form and structure

where the rest of us just
see a shapeless mess.

And above all, he could see that a strange

new kind of mathematics
underpin the whole of nature.

Mandelbrot's lifelong quest was to find

a simple mathematical basis for the rough

and irregular shapes of the real world.

- Mandelbrot was working for IBM,

and he was not in the
normal academic environment.

And he was working on a
whole pile of different

problems about irregularities in nature,

in the financial markets,
all over the place.

And I think at some point it dawned on him

that everything he was doing seemed to be

really parts of the same big picture.

And he was a sufficiently
original and unusual person

that he'd realized that
pursuing this big picture

was what he really wanted to do.

- [Jim] To Mandelbrot, it seemed perverse

that mathematicians have spent centuries

contemplating idealized
shapes like straight lines

or perfect circles, and yet had no proper

or systematic way of describing the rough

and imperfect shapes that
dominate the real world.

Take this pebble.

Is it a sphere or a cube?

Or maybe a bit of both?

And what about something much bigger?

Look at the arch behind me.

From a distance, it
looks like a semi-circle.

But up close, we'll see
that it's bent and crooked.

So what shape is it?

Mandelbrot asked if
there's something unique

that defines all the
varied shapes in nature.

Do the fluffy surfaces of clouds,

the branches and trees and rivers,

the crinkled edges of shorelines

share a common mathematical feature?

Well, they do.

Underlying nearly all the
shapes in the natural world

is a mathematical principle
known as self similarity.

This describes anything
in which the same shape

is repeated over and over again

at smaller and smaller scales.

A great example are the branches of trees.

They fork and fork again

repeating that simple
process over and over

at smaller and smaller scales.

The same branching principles applied

in the structure of our lungs,

and the way our blood vessels are

distributed throughout our body.

It's even described how rivers

split into ever smaller streams.

And nature can repeat all
sorts of shapes in this way.

Look at this Romanesco Broccoli.

It's overall structure
is made up of a series

of repeating cones at
smaller and smaller scales.

Mandelbrot realized self
similarity was the basis

of an entirely new kind of geometry.

And he even gave it a name:

fractal.

Now that's a pretty neat observation.

But what if you could
represent this property

of nature in mathematics?

What if you could capture its
essence to draw a picture?

What would that picture look like?

Could you use a simple
set of mathematical rules

to draw an image that
didn't look man-made?

The answer would come from Mandelbrot,

who had take a job at
IBM in the late 1950s

to gain access to its
incredible computing power

and pursue his obsession with
the mathematics of nature.

Armed with a new breed of supercomputer,

he began investigating a rather curious

and strangely simple-looking equation

that could be used to
draw a very unusual shape.

What I'm about to show you

is one of the most remarkable
mathematical images

ever discovered.

Epic doesn't really do it justice.

This is the Mandelbrot set.

It's been called the thumbprint of God.

And when we begin to explore it,

you'll understand why.

Just as with the tree or the broccoli,

the closer you study this picture,

the more detail you see.

Each shape within the step contains

an infinite number of smaller shapes,

baby Mandelbrots, that go on forever.

Yet all this complexity stems from

just one incredibly simple equation.

This equation has a
very important property.

It feeds back on itself.

Like a video loop, each output

becomes the input for next set.

This feedback means that
an incredibly simple

mathematical equation can produce

a picture of infinite complexity.

The really fascinating thing

is that the Mandelbrot set

isn't just a bizarre mathematical quirk.

Its fractal property of
being similar at all scales

mirrors fundamental order,
in principle, in nature.

Turing's patterns, Belousov's reactions,

and Mandelbrot's fractals
are all signposts

pointing to a deep
underlying natural principle.

- When we look at complexities in nature,

we tend to ask where did they come from.

There is something in our heads that says

complexity does not
arise out of simplicity;

it must arise from something complicated

with conserved complexity.

But what the mathematics
in this whole area

is telling us is that very simple rules

naturally give rise to
very complex objects.

And so if you look at the
object, it looks complex,

and you think about the
rule that generates it,

it's simple.

So the same thing is
both complex and simple

from two different points of view.

And that means we have
to rethink completely

the relation between
simplicity and complexity.

- [Jim] Complex systems can
be based on simple rules.

That's the big revelation.

And it's an astonishing idea.

It seems to apply all over our world.

Look at the flock of birds.

Each bird obeys very simple rules.

But the flock as a whole

does incredibly complicated things.

Avoiding obstacles, navigating the planet

with no single leader
or even conscious plan.

But amazing though this
flock's behavior is,

it's impossible to predict
how it will behave.

It never repeats exactly what it does,

even in seemingly identical circumstances.

It's just like the Belousov reaction.

Each time you run it,
the patterns produced

are slightly different.

They may look similar but
they are never identical.

The same is true of video
loops and sand dunes.

We know they'll produce a
certain kind of pattern,

but we can't predict the exact shapes.

The big question is can nature's ability

to turn simplicity into complexity

in this mysterious and unpredictable way

explain why life exists?

Can it explain how a
universe full of simple dust

can turn into human beings?

How inanimate matter
can spawn intelligence?

At first you might think that this is

beyond the remit of science.

If nature's rules are
really unpredictable,

should we simply give up?

Absolutely not. In fact,
quite the opposite.

Fittingly, the answer to this problem

lies in the natural world.

All around us there exists a process

that's engineered these
unpredictable complex systems

and hones them to perform
almost miraculous tasks.

The process is called evolution.

- Evolution has built on these patterns,

it's taken them as the raw ingredients.

It's combined them
together in various ways,

experimented to see what
works and what doesn't,

kept the things that do work,

and then built on that.

It's a completely unconscious process,

but basically that's what's happening.

- [Jim] Everywhere you
look, you can see evolution

using nature's self organizing patterns.

Our hearts use the Belousov-type reactions

to regulate how they beat.

Our blood vessels are
organized like fractals.

Even our brain cells interact
according to simple rules.

The way evolution refines
and enriches complex systems

is one of the most intriguing
ideas in recent science.

- My interest in my Ph.D.
research in complex systems

was to see how complex systems
interact with evolution.

So on the one hand, you have systems that

almost organize themselves
as complex systems.

So they exhibit order
that you wouldn't expect.

But on the other hand, you
still have to have evolution

interact with that to create something

that is truly adapted to the environment.

- [Jim] Evolution's
mindless, yet creative, power

to develop and shape complex systems

is indeed incredible.

But it operates on a cosmic time scale.

From the first life on
Earth to us walking about

took in the region of 3 1/2 billion years.

But we now have in our hands

a device that can mimic this process

on a much shorter timescale.

What is the invention I'm talking about?

Well there's a good chance you've been

sitting in front of one all day.

It is, of course, the computer.

Computers today can churn through

trillions of calculations per second.

And that gives them the power
to do something very special.

They can simulate evolution.

More precisely, computers
can use the principles

of evolution to shape and
refine their own program

in the same way the natural
world uses evolution

to shape and refine living organisms.

And today, computer scientists find that

this evolved software can solve problems

that would be beyond
the smartest of humans.

- One thing that we
found, and particularly in

our original research, is how powerful

evolution is as a system, as an algorithm

to create something that is very complex,

and to create something
that is very adaptive.

- [Jim] Swarston and his team's goal

was nothing less than to
use computerized evolution

to create a virtual brain that
would control a virtual body.

To begin with, they
created 100 random brains.

As you can see, they weren't up to much.

Evolution then took over.

The computer selected the brain

that was slightly better
at moving their bodies,

and got them to breed.

- The algorithm then
takes those individuals

that do the best, and then
allows them to create offspring.

- [Jim] The best movers
of the next generation

were then bred together, and so on and on.

Amazingly, after just 10 generations,

although they're still a bit unsteady,

the figures could walk.

- Eventually, miraculously,

you actually end up with
something that works.

The slightly scary thing is you don't know

why it works and how it works.

You look at that brain,

and you have no idea
actually what's going on,

because evolution has
optimized it automatically.

- [Jim] In 20 generations,

evolution had turned this

into this.

But these evolved computer beings

soon went far beyond just walking.

They evolved to do things that really are

impossible to program conventionally.

They react realistically
to unexpected events,

like being hit or falling over.

- Even though we programmed
these algorithms,

what actually then happens
when it unfolds live

we don't control anymore.

And things happen that we never expected.

And it's quite a funny feeling that you

create these algorithms,
but they do their own thing.

- [Jim] An unthinking
process of evolutionary

trial and error had created
these virtual creatures

that can move and react in real time.

What we're seeing here is fantastic

experimental evidence
for the creative power

of systems based on simple rules.

(soft piano music)

Watching how computers can unconsciously

evolve programs to do things that

no human could consciously program

is a fantastic example of the power

of self organization.

It demonstrates that evolution is itself

just like the other
systems we've encountered;

one based on simple rules and feedback,

from which complexity
spontaneously emerges.

Think about it.

The simple rule is that
the organism must replicate

with a few random mutations now and again.

The feedback comes from the environment

which favors the mutations
that are best suited to it.

The result is ever-increasing complexity,

produced without thought or design.

- The interesting thing
is that we can move up

to a higher level of organization.

Once you have organisms that
actually have patterns on them,

these can be selected
for or selected against

by process which are
essentially feedbacks.

And so evolution itself,
the whole Darwinian scheme,

is in sense Turing again

with feedbacks happening
through different processes.

- [Jim] And that's the
essence of this story.

Unthinking, simple rules

have the power to create
amazingly complex systems

without any conscious thought.

In that sense, these computer beings

are self-organized systems

just like the one Belousov observed

happening in his chemicals;

just like the ones in sand dunes

and the Mandelbrot sets,

in our lungs, our hearts,

in weather, and in the
geography of our planet.

Design does not need an
active interfering designer.

It's an inherent part of the universe.

- One of the things that
makes people so uncomfortable

about this idea of, if you will,

spontaneous pattern formation

is that somehow or other
you don't need a creator

but perhaps a really clever designer.

What you would do is to
kind of treat the universe

like a giant simulation,

where you set some initial condition

and just let the whole
thing spontaneously happen

in all of its wonder
and all if its beauty.

- The mathematics of pattern formation

shows that the same kind
of pattern can show up

in an enormous range
of different physical,

chemical, biological systems.

Somewhere deep down inside, it's happening

for the same mathematical reason.

Implicit in those facts

are these beautiful patterns
that we see everywhere.

This, I think, is a mind-blowing thought.

- So what is the ultimate lesson

we can take from all this?

Well, it's that all the
complexity of the universe,

all its infinite richness,

emerges from mindless simple rules

repeated over and over again.

But remember, powerful
though this process is,

it's also inherently unpredictable.

So, although I can confidently tell you

that the future will be amazing,

I can also say with scientific certainty

that I have no idea what it holds.

(soft piano music)