Transcript of YouTube Video: Why trees look like rivers and also blood vessels and also lightning…

- Hey, smart people, Joe here.

Ever notice how if you look at part of a tree,

it looks a lot like an entire tree?

And why does this underground part of a tree

look so much like the rest of the tree?

That's pretty weird.

This isn't a tree, but it sort of looks like one.

And so does this, hmm.

And these branches, sure look an awful lot

like these branches, except those are blood vessels

and so are these, which also kind of look like a tree,

although this part reminds me of a river

or maybe every river?

Lightning, lungs, cracks in the ceiling,

what's going on here?

Why do all these things look so similar?

Once you start seeing it, you see it everywhere.

It haunts your dreams!

It's like there's some spooky connection

between rivers and lightning bolts and broccoli and trees

and all sorts of living and non-living things.

Well, all these objects have one thing in common,

zoom in or out, and we see the same branching pattern

repeat itself over and over at different scales.

These are fractals, a special kind of self-similar shape

that mathematicians, and the rest of us, go extra crazy for.

And this video is about why we see them everywhere.

(pensive music)

I don't know if you've ever looked at a tree

as deeply as I have, but that weird thing

where part of the tree also looks like a tree,

that's called self similarity.

It's like one of those triangles

with an infinite number of smaller triangles inside it

or whatever this thing is.

And unlike the self-similar shapes we see in nature,

these perfectly self-similar shapes are infinite.

We could zoom in or out

and continue to see those patterns repeat forever!

Mathematician Benoit Mandelbrot

named these self repeating shapes, fractals,

because they exist sort of in between dimensions

or in fractured dimensions.

What the heck does that mean?

Let's take a quick sidebar

to talk about how the way that mathematicians use a word,

it isn't always the same

as how you and I use a word.

(upbeat music)

You and I think of dimensions as the three that we live in

or the two that exist on paper

or even the one dimension of a line,

because that's what we learned in geometry class.

What Mandelbrot meant by, "Dimension,"

has to do with how different shapes fill space

as they get bigger or smaller

and this is kind of the key thing for us

as we explore fractals in nature.

You can 2X the length of this line

and you get twice as much line.

Another way of saying that is you scale it up

by two to the power of one.

If we do the same to a square,

2X its length and width, you get four times as much square,

or you scale it up by two to the two.

Do it to a cube, 2X length, width, and height

and we get eight times as much cube or two to the three.

This power right here

is the dimension Mandelbrot was talking about

and for simple shapes,

it matches with our usual idea of dimension.

But what's interesting about a fractal like this one

is when you scale it up by 2X,

you get three times as much fractal.

(fractal reverberating)

That exponent isn't one or two, you get 1.585 dimensions.

Even though the fractal sits in a two dimensional plane,

just like a regular triangle does,

when you scale it up, it doesn't fill space

quite the same as a two dimensional object.

The same thing is true for fractals with volume, like this.

To a mathematicianologist or whatever,

it's more than two dimensional,

but not quite three dimensional.

Fractals exist in this weird in-between space

and that's part

of what Mandelbrot found so fascinating about 'em.

By the way,

you know what Benoit B. Mandelbrot's middle name is?

Benoit B. Mandelbrot.

Nerdiest joke I know right there.

Anyway, Mandelbrot pointed out

that fractals are not just a toy

for mathematicians to make psychedelic art

for your dorm room wall.

They can help us understand nature better,

because they're everywhere.

To start off, why do trees even look like trees?

Well, the thing is, biologically speaking,

there's no such thing as a tree.

Sure, there are things you and I call, "Trees,"

because of the way they look.

(buoyant music)

But if you look at a tree like this one,

many of the plants we call, "Trees,"

are more closely related to things that aren't trees

and more distantly related to other things

that do look like trees.

So, "Tree," is just a way of describing plants

that look kind of tree-like.

It's almost as if growing fractal-like branches

that look similar at different scales

was the solution to some problem

that all these different plants faced

and that problem is soaking up a bunch of sun and CO2.

Growing tall is one solution to that problem

or maybe growing just a few gigantic leaves

on top of a trunk or even a canopy the size of a city block

with all the leaves on the very tip.

But all of these options require spending a bunch of energy

to grow for not that much gain,

basically, you gotta make a whole lot of wood

for not that much sun.

Luckily there's a better way to do it

and that's where being a fractal is really useful.

A perfect fractal lets you put infinite surface area

in a finite amount of space.

This snowflake isn't getting any bigger,

but you can keep zooming in

then you'll keep finding another smaller layer

just like the first.

And you can keep doing this forever,

meaning its outer edge,

the line you need to draw this shape,

is infinitely long.

Trees do something similar,

by growing out each level as a smaller version

of the previous level

a tree can pack a bunch of surface area in its volume,

not an infinite amount,

like a mathematically perfect fractal,

but it's a pretty cool way of soaking up more sun

without wasting energy by getting all bulky.

And it's no coincidence

that trees roots grow in a similar way,

they need lots of surface area

to soak up water and nutrients

and fractal branching is the best bang for their buck,

maximizing the volume that the tree can draw from

without wasting unneeded energy

building plumbing that's too big.

Meanwhile, inside our bodies, we have our own little trees.

A lung's job is to take in oxygen

and an adult body needs around 15 liters of O2 every hour.

If our lungs were just two balloons, they'd never keep up.

Fractal branching means our lungs can hold half the area

of a tennis court while staying packed up

nicely inside our chest.

(graphics whirring)

(crowd clapping)

And our lungs aren't the only trees we have inside us.

Our entire circulatory system

looks kind of like a bunch of fractal branches too.

We have almost a 100,000 kilometers of blood vessels

in our bodies delivering oxygen and nutrients

and removing wastes.

Fractal branching lets our circulatory system

pack in as many blood vessels as we need

to protect every point A with every point B,

while also spending the least possible energy

building our body's plumbing

and manufacturing all the blood that runs through it.

In a way, it's like each of these living systems has a goal.

A tree wants to soak up a bunch of light and CO2,

a lung wants to take in a bunch of air,

a blood vessel wants to exchange nutrients

with every cell in the body.

In all these cases,

fractal branches are the most efficient way

to scale up while staying basically the same size.

This secret pattern shows up in non-living things too.

All around the world, from their sources to their ends,

rivers arrange themselves into branching shapes.

And by now you can probably guess why,

at their source, fractal branching is the most efficient way

to drain water from a given area of land.

And at their mouths we see fractal branching

as sediment piles up and splits a river

into smaller and smaller strands.

Cracks and lightning bolts are both ways

of dissipating energy and it shouldn't surprise you

that fractal branches are the most efficient way to do that

inside of a given space.

And when scientists model all these ways of growing,

it turns out that, like perfect mathematical fractals,

these branching shapes are best described

as in between dimensions.

At this point, it might be tempting to think

there's one universal rule

that underlies every branching fractal pattern

that we see around us,

but as usual, nature isn't so predictable.

We also see fractal branches in crystals,

the shapes of snowflakes, even strange mineral deposits

people sometimes mistake for ancient plant fossils.

Similar fractals, but a different reason.

Here, things like temperature, humidity,

and the concentration of different chemicals

act as a set of rules for building the thing.

And as these structures grow,

those rules repeat themselves at multiple scales

giving us self-similar fractal shapes.

What's amazing is that as much

as these fractal shapes pop up in nature,

there isn't a single gene or law of physics or brain

making all these things grow fractal branches.

But one by one, as each of these systems evolved

to be as efficient as possible,

they all landed on the same solution

to their individual problems,

letting us look at things in an interestingly new dimension

and making them infinitely interesting.

Stay curious.

Hey guys, just jumping in here with a quick announcement.

Look, it's an undisputed fact that everything looks cooler

when you film it with a drone, right?

I don't make the rules, it's just how it is.

And I think there are some stories

that, well, you can only tell

from that perspective, the overview perspective.

Which is why I have a whole other show called, "Overview,"

about stories just like that.

And we are back with new videos,

it's over on the PBS Terra channel.

You're gonna love this,

We've won like real life science journalism awards

for the stuff we make over there.

It's really cool.

Go check it out, there's a link down the description

or you can click, you know, up there,

wherever it's gonna be and I'll see you on, "Overview."

Now, back to your regularly scheduled end-card.

You know what else is infinitely complex and interesting?

All of you lovely people who support the show on Patreon.

Thank you, every one of you.

You are the reason that we can research questions like this

and bring you interesting answers,

like the one that you just filled your brain with.

If you would like to join our community,

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there's a link down to the description

where you can learn more.

See you in the next video.

By the way,

you know what Benoit B. Mandelbrot's middle name is?

"Ben Watt," did I just call him, "Ben Watt?"

- [Crew Member] Yeah!

That's not how we say that...

Ben-oit!