# Fractals and Snowflakes

Fractals are fun — and they team up perfectly with a study of snow. To do this activity with your students, you first need to explain what a fractal is:

A fractal is a a curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation. – From Oxford Dictionaries

You can explain this definition to your students by asking them to look at a nearby body of water on a map. It probably looks pretty smooth. Ask them to imagine what the map of the body of water might look like if you only could measure with a yard stick. The edges would not be so smooth.What about a 12-inch ruler? The smaller the measuring tools, the more jagged the map would look. Since all the sides are the same length, this is a fractal.

Ask your students to draw an equilateral triangle on a piece of paper in pencil. Then ask them to divide each side of the triangle in to three equal parts and erase the middle section. Then ask them to draw two lines that are the same distance as the parts removed to create open triangles in the part that was removed. Ask them to do the same thing again. This is called a Koch snowflake.

Ask students what the shape is starting to look like. When they say it looks like a snowflake, share pictures of different snowflakes. You can use this Java applet to show students without asking them to draw the shapes themselves. Ask students to identify snowflakes as fractals or not so they understand what different fractal snowflakes might look like.

Show students different types of snowflakes and discuss whether they are fractals or not. Ask students whether the snowflakes are radially symmetrical or not and whether you can have a non-fractal be symmetrical. Are all fractals symmetrical?

Resources:

Try these other fun, nerdy winter themed activities: