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Fractals for Fun: Teaching Kids Patterns in Nature

Fractals are patterns that repeat at different scales: If you zoom in on a picture of a fractal, you will still see the same pattern repeated. These patterns can be found in math equations, and they can also be found in the world all around us, from snowflakes to the leaves on trees.

Fractals can also be useful in things that we make and do. For instance, some antennae used for TV and radio broadcasting or reception are made using fractal patterns, which allows for a larger range of frequencies to be transmitted without making an antenna bulkier than it has to be. Doctors can also look closely at fractal patterns in blood vessels inside of cancerous tumors to learn about how the tumors grow.

Jackson Pollock and Max Ernst are two artists who use fractal patterns in their art. You can also see fractal shapes in African art and in the designs of some buildings. The special effects in movies like the popular Star Wars and Star Trek films sometimes use fractal patterns, too: Fractals can help make computer-generated things like mountains, stars, and lava look more realistic.

History and Math in Fractals

Benoit Mandelbrot, a mathematician, is the one who first studied and named fractals. He's famous for coming up with the idea that some shapes found in nature are roughly textured at all scales: For instance, whether you look at the coastline of a country from space or examine a tiny bit of where the land meets the water using a magnifying glass, you'll see the same jagged texture. He created a mathematical formula that could measure the level of roughness found in these structures, and he was also one of the first to use computers to make fractal images. One famous fractal pattern is named after him, called the Mandelbrot set. Other commonly known fractal shapes that mathematicians have created include the Koch curve, Koch snowflake, and Sierpinski triangle.

The Mandelbrot set and other shapes like it are made by graphing an iterative equation. This is an equation that's repeated over and over again to create a shape that repeats at smaller and smaller scales. The pattern is virtually infinite, even though it doesn't seem that way when you first look at the image. As you zoom in on it, you'll notice that the pattern repeats at a smaller scale, smaller and smaller, over and over again.

Fractals Found in Nature

Fractals are not only found in mathematicians' designs. You can also find them in many places in nature. Branching is one type of fractal design we see everywhere, from the branches of trees that grow out from the trunk, smaller and smaller, to the branching of your own blood vessels. Both blood vessels and trees use the larger surfaces created by this pattern to exchange more oxygen and carbon dioxide. The vein patterns in leaves look like this, too.

Another type of fractal pattern we see in nature is the spiral. You can see biological spirals in some types of mollusk shells. You can also find spirals in star formations and the shapes of galaxies, and hurricanes are spiral-shaped, too.

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