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[MUSIC PLAYING]

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[SINGING] Science out loud.

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What do snowflakes and
cellphones have in common?

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The answer is never ending
patterns called fractals.

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Let me draw a snowflake.

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I'll start with an
equilateral triangle.

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Then I'll draw another
equilateral triangle

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on the middle of each side.

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Pull out the middle and repeat
the process, this time with 1,

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2, 3, 4 times 3,
which is 12 sides.

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If I do this over
and over, the shape

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will look something like this.

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This is called a Koch snowflake,
and it has a special property.

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No matter where I look
or how much I zoom in,

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I will see the same
pattern over and over.

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Never ending patterns like
this that on any scale,

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on any level of zoom
look roughly the same

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are called fractals.

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We can actually draw a Koch
snowflake on the computer

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by having it repeatedly graph
a mathematical equation.

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Each time we add a triangle,
one side of the Koch snowflake

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will turn into four.

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After the first repetition,
we'll get three times four

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to the first, or 12 sides.

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After the second repetition,
we'll get three times four

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to the second, or 48 sides.

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After repetition number n,
we'll have three times four

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to the n sides.

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If we do this an
infinite number of times,

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we'll get infinitely many sides.

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So the perimeter of the Koch
snowflake will be infinite.

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But the area of the Koch
snowflake wouldn't be infinite.

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If I draw a circle with a finite
area around the snowflake,

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it will fit completely inside
no matter how many times we

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increase the number of sides.

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So the Koch fractal has
an infinite perimeter,

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but a finite area.

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In the 1990s, a radio
astronomer named

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Nathan Cohen used the
fractal antenna to rethink

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wireless communications.

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At the time, Cohen's
landlord wouldn't

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let him put a radio
antenna on his roof,

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so Cohen decided to make a more
compact, fractal like radio

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antenna instead.

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But it didn't just hide the
antenna from the landlord.

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It also seemed to work
better than the regular ones.

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Regular antennas have to be
cut for one type of signal,

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and they usually work
best when their lengths

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are certain multiples of
their signals' wavelengths.

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So FM radio antennas can only
pick up FM radio stations,

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TV antennas can only pick
up TV channels, and so on.

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But fractal antennas
are different.

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As the fractal repeats
itself more and more,

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the fractal antenna can pick up
more and more signals, not just

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one.

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And because the perimeter
of the Koch snowflake

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grows way faster than its
area, the fractal antenna

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only takes up a quarter
of the usual space.

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But Cohen didn't stop there.

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He designed a new antenna, this
time using a fractal called

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the Menger sponge.

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The Menger sponge is kind of
like a 3D version of the Koch

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snowflake and has infinite
surface area but finite volume.

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The Menger sponge is sometimes
used in cellphone antennas.

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It can receive all
kinds of signals

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while taking up even less
area than a Koch snowflake.

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Now, these antennas
aren't perfect.

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They're smaller, but
they're also very intricate,

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so they're harder and
more expensive to make.

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And though low
fractal antennas can

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receive many different
types of signals,

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they can't always receive
each signal as well as

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an antenna that was cut for it.

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Cohen's invention was not the
first application of fractals.

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Nature has been doing
it forever, and not

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just with snowflakes.

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You can see fractals in river
systems, lightning bolts,

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seashells, and even
whole galaxies.

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So many natural systems
previously thought off limits

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to mathematicians can now be
explained in terms of fractals,

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and by applying
nature's best practices,

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we can then solve
real world problems.

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Fractal research is changing
fields such as biology.

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For example, MIT
scientists discovered

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that chromatin is
a fractal, and that

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keeps DNA from getting tangled.

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Look around you.

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What beautiful
patterns do you see?

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Hi.

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I'm Yulia.

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Thanks for watching
"Science Out Loud."

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Check out these other awesome
videos, and visit our website.

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Good.

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Now wait for it.

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OK.

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That's it.

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