(Describer) An animated ball becomes an amoeba and a rocket. Title:

(singers)
♪ Science ♪

♪ Out Loud ♪♪

(Describer) Outside, in the snow...

What do snowflakes
and cell phones have in common?
The answer is never-ending
patterns called fractals.

(Describer) Inside...

Let me draw a snowflake.
I'll start with
an equilateral triangle.
Then I'll draw
another equilateral triangle
on the middle of each side.
We'll remove the middle
and repeat the process,
this time with 1, 2, 3,
4 times 3, which is 12 sides.
By doing this over and over,
the shape will look like this.

(Describer) A snowflake.

This is a Koch snowflake.
It has a special property.
No matter where I look,
I'll see the same pattern
over and over.
Never-ending patterns
like this
that on any scale look roughly
the same are called fractals.

(Describer) Outside...

We can draw a Koch snowflake
on the computer
by having it repeatedly graph
a mathematical equation.

(Describer) Inside...

Each time we add a triangle,
one side of the snowflake
becomes four.
After the first repetition,
we'll get 3 times 4
to the first, or 12 sides.
After the second repetition,
we'll get 3 times 4
to the second, or 48 sides.
After repetition number n,
we'll have 3 times 4
to the n sides.
Doing this
an infinite number of times
produces
infinitely many sides.
The snowflake's perimeter
will be infinite.
But the area of the Koch
snowflake wouldn't be infinite.
If I draw a circle with a finite
area around the snowflake,
it will fit inside
no matter how many times
we increase the number of sides.
So the Koch fractal
has an infinite perimeter
but a finite area.

(Describer) In an elevator...

In the 1990s,
a radio astronomer
named Nathan Cohen
used the fractal antenna to
rethink wireless communications.

(Describer) On top of a building...

At the time,
Cohen's landlord
wouldn't let him put
a radio antenna on his roof.
So Cohen made a more compact,
fractal-like radio antenna.

(Describer) She stands by a pole.

Not only could he hide
this antenna from his landlord,
but it worked better.

(Describer) Inside...

Regular antennas are cut
for one type of signal.
They work best
when their lengths
are certain multiples
of their signal's wavelengths.
So FM radio antennas can only
receive FM radio stations,
and TV antennas
can only receive TV channels.
But fractal antennas
are different.
As the fractal
repeats itself,
the fractal antenna can pick up
more and more signals.
Because the perimeter
of the Koch snowflake
grows faster than its area,
the fractal antenna
takes up less space.
Then Cohen designed
a new antenna
using a fractal
called the Menger sponge.

(Describer) Cubes with square holes.

The Menger sponge
is like a 3D-version
of the Koch snowflake.
It has infinite surface area
but finite volume.
The Menger sponge is sometimes
used in cell phone antennas,
and it takes up even less area
than a Koch snowflake.
These antennas aren't perfect.
They're smaller,
but they're also intricate,
so they're harder
and more expensive to make.
And although fractal antennas
can receive
many types of signals,
they can't always
receive each signal
as well as an antenna
that was cut for it.

(Describer) Outside...

Cohen's invention was not the
first application of fractals.
Nature has been
doing it forever.
You see fractals
in river systems,
lightning bolts, seashells,
and even whole galaxies.
Many natural systems
previously thought off-limits
to mathematicians
can now be explained
in terms of fractals,
and by applying
nature's best practices,
we can solve
real world problems.
Fractal research is
changing fields such as biology.
For example, MIT scientists
discovered that chromatin
is a fractal,
and that keeps DNA
from getting tangled.

(Describer) ...looking like ball of worms.

Look around you.
What beautiful patterns
do you see?

(Describer) Title: Made with love at MIT.

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