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Why trees look like rivers and also blood vessels and also lightning…

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

And why does this
underground part of a tree

This isn&amp;#39;t a tree, but it
sort of looks like one.

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,

Once you start seeing it,
you see it everywhere.

It&amp;#39;s like there&amp;#39;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.

I don&amp;#39;t know if you&amp;#39;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,

with an infinite number of
smaller triangles inside it

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

these perfectly self-similar
shapes are infinite.

and continue to see those
patterns repeat forever!

named these self repeating
shapes, fractals,

because they exist sort
of in between dimensions

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

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

because that&amp;#39;s what we
learned in geometry class.

What Mandelbrot meant
by, &amp;quot;Dimension,&amp;quot;

has to do with how
different shapes fill space

Another way of saying
that is you scale it up

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

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

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

is the dimension Mandelbrot
was talking about

it matches with our
usual idea of dimension.

But what&amp;#39;s interesting about
a fractal like this one

That exponent isn&amp;#39;t one or
two, you get 1.585 dimensions.

Even though the fractal sits
in a two dimensional plane,

when you scale it up,
it doesn&amp;#39;t fill space

quite the same as a
two dimensional object.

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

Fractals exist in this
weird in-between space

of what Mandelbrot found
so fascinating about &amp;#39;em.

you know what Benoit B.
Mandelbrot&amp;#39;s middle name is?

for mathematicians to
make psychedelic art

They can help us
understand nature better,

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

Well, the thing is,
biologically speaking,

Article by AI based on youtube video transcript: Why trees look like rivers and also blood vessels and also lightning…

Summary by AI based on youtube video transcript

Article by AI based on youtube video transcript

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