### Christmas Fractal Lesson

Over the years I have shared my love for fractals with you. I began with my introduction to frozen fractals after Elsa sings about them in "Let It Go" in Disney's Frozen. A fractal is an object that has self-similarity, or each part looks like the whole. It introduces new ideas of symmetry, dimensionality, and more. Fractal geometry often explains some of the irregularities of our world. It can be a very complex topic to understand, but it is an important one. Fractals are making advances in our medical world, entertainment (movies, computer games and more) as well as science. There are some topics that kids even young kids can understand. Since they were introduced in Frozen, many kids have now heard of them. I feel it is important to teach kids about them and give them a true idea of what they are.

In November I read somewhere (perhaps the National Council of Teachers of Mathematics forum) that we can easily "create" fractals with three glass ball ornaments. I wanted to try it. However, I did not have shiny glass ball ornaments. I found some mini ones at Michaels and then got bigger ones at the Dollar Tree. Then it was midterm time at school, so I didn't take the time to check it out. Now on Boxing Day I decided to try it and share it with you.

Where the balls meet we see the reflection of the other balls, which include reflections of the reflections. This creates a fractal.

I played around with different colors--silver and gold worked the best--as well as the different sizes. The ornaments need to be the shiny ones and not glitter or frosted. Personally, I find the light reflections the most interesting. I even tried more than three ornaments.

I added some of the larger balls around the smaller balls in the one below.

I find the images so fun to play with and suggest as you take your tree down to play with them and have your kids see the fractals. Or if you are like me, go pick up some shiny glass ornaments up in the post-Christmas clearance sale and give it a try. Then look for some of the fractals you can find in nature--a fern, broccoli or cauliflower, the actual coastline.

After playing with the ornaments, you can also try creating some of the simple handdrawn fractals that I have shared previously. Or a fractal tree or dragon (which I haven't shared yet).