## Something for the Season

As I've described and illustrated the fractal nature inherent in natural shapes, such as plants and mountains, I want to share some images that I've discovered while exploring fractals that, on the surface, don't look like natural shapes. The first is the thumbnail image at right, which shows a festive holiday ornament to hang from your tree, or that would make a great element to place at the very top of the tree! Of course, the fact that this fractal image has a suspiciously tree-like outline is no accident, either. In working with variations of the fractal equations, one can generate a host of different ornament types, such as globes and other holiday shapes, each with their own distinctive coloring and patterns.

Well, a tree ornament seems a simple task for fractalic equations, but how about a holiday wreath, complete with an assortment of ornamental decorations, and one you'd be proud to display on your front door? You've got it, right there in the image to left. When I generated this one, I was startled at how festive it was and how amazingly complete it came out. I did not have to do any post processing to make it look the way it does. The fractalic equations computed by the Tiera-zon fractal generating program did all the work. As with the first image, tinkering around with the fractalic equations can yield a variety of images that are equally as attractive. Look at the shape closely and you'll see that it is reminiscent of a snowflake also, so with the right color combinations, you could generate a host of different snowflake shapes to hang as decorations on your tree or to place in other spots for a festive touch. You could call this "mathematics for the holidays"!

Finally, as the holiday draws to a close and night falls, what could bring out more of the holiday spirit than a group of decorated trees in your yard, brilliant against the night sky? No problem, just look at the image to right. If you listen closely, you can almost hear the music of the carolers wafting through the crisp cold night air, with stars sparkling in the sky and the lights on the trees glowing warmly. Another sip of that hot toddy and the thought of fresh-baked pumpkin pie waiting for you when you go back inside, and the joy of the day is complete.

Happy Holidays to You!

Image credit: LariAnn Garner

(Editor's Note: This article was originally published on December 24, 2008. Your comments are welcome, but please be aware that authors of previously published articles may not be able to promptly respond to new questions or comments.)