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What Is a Fractal (and What Are They Good for)?

5 minutes

(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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Fractals are complex, never-ending patterns created by repeating mathematical equations. A math student at MIT delves into their mysterious properties and how they can be found in technology and nature. Part of the "Science Out Loud" series.

Media Details

Runtime: 5 minutes

Science Out Loud
Episode 1
4 minutes
Grade Level: 9 - 12
Science Out Loud
Episode 2
6 minutes
Grade Level: 10 - 12
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Episode 3
5 minutes
Grade Level: 10 - 12
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Episode 4
4 minutes
Grade Level: 10 - 12
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Episode 5
4 minutes
Grade Level: 8 - 12
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Episode 6
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Episode 7
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Episode 8
5 minutes
Grade Level: 10 - 12
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Episode 8
4 minutes
Grade Level: 8 - 12
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Episode 10
4 minutes
Grade Level: 10 - 12