Last year Occupy Math created some Holiday Fractals. This post was moderately popular and so a new edition has been created for this year. Occupy Math has several ornaments for his tree that are based on circular fractals that are printed and then glued to stiff cardboard with a small hook (a bent paper-clip). This year’s holiday fractal post offers a dozen printable ornaments! They are light, difficult to break, safer for small children (be sure to use non-toxic glue) than glass ornaments, and come in a variety of festive colors and patterns. A Comments on the type of fractals these are appear below the fold, as do a few seasonal fractal ornaments. A printable PDF of the ornaments is available at a click.

All twelve of these fractals are Julia Sets, mostly because it is really easy to make these come out as circles, appropriate for ornamentation. Occupy Math has a simple explanation with algorithm for Julia Sets on the fractal taxonomy page. Occupy Math can teach the math used to create these ornamental fractals to young children. It is also easy to develop software that lets people explore the space of fractals, even if they don’t know the math. Occupy Math has published scientific papers on systems for locating Julia Sets. Occupy Math is proud to note that his co-author, Brooke Jamieson, is now a high school math teacher.

Since its is winter, Occupy Math had to shovel some of the white stuff. This triggered a memory about another seasonally appropriate fractal — the generalized Sierpinski fractals of which there are a gallery deep inside the fractal taxonomy web site. Here are four more ornaments. They are on the printable PDF linked near the top of the post.

Last year Occupy Math looked into the possibility that, if Santa was careless with his endless sack of toys you might be able to find evidence he had visited. For the details, click here. Santa is probably clever enough not to get caught, but the post also looks at some interesting fourth dimensional topology.

The year 2016 has been a complex and challenging one. Occupy Math hopes that you can relax with friends and family here at the end of the year. Occupy Math is writing this post as a way of avoiding a large mound of grading, but we seem to be getting near the end of it. It is worth mentioning that Occupy Math does take requests — readers are welcome to suggest other fractal ornaments. Comment or tweet!

**Peace on Earth, Good Will To All**.

I hope to see you here again,

Daniel Ashlock,

University of Guelph,

Department of Mathematics and Statistics