This weeks post is the fifth set of holiday ornaments offered by Occupy Math. If you missed them, here are links to the others.
This year’s ornament were designed with Occupy Math special purpose software for making fractals that draw on multiple different fractal algorithms. A printable version is available as a (large) PDF. To make ornaments, print out the fractals at a fairly high number of dots per inch — this is usually an option in printing software. If you just print the PDF it is at 72 dots per inch and it comes out too large for something to hang on the tree (it might make a nice door decoration). Something near 300 dots per inch should make an appropriate sized ornament. Glue the printout to stiff cardboard, cut it out, and use a paperclip to fashion a hanger. The second ornament, the satin star, might make a good tree-topper. For that you might need to make an aluminum foil cone to hold it (plus the paperclip(s)). Occupy Math would also love to hear from readers that have found a better way to make ornaments from the images supplied. Please tell us all about it in the comments.
An Index of Occupy Math’s Fractal Posts
Each year Occupy Math uses a different type of fractal to make ornaments. Over the last four years, Occupy Math has done a number of articles on fractals. If you are interested is seeing something of the variety of fractals that are out there, beyond those in Occupy Math’s holiday ornaments, here is a list of the posts.
- Summer math shows fractals that look like leaves and adds some flowers.
- NEWT: fractals for everyone is about an Android app for generating Newton’s method fractals.
- Making a Fractal Face is about generalize Sierpinski fractals, which are relatively easy to make whatever shape you want.
- Research on the Mathematical Nature of Beauty is about devising a way for an algorithm to guess if an image will look beautiful.
- The Ghost Mandelbrot Set is about a version of a famous fractal that appears in other fractals.
- The Silent Drum in Your Body is a bout fractals that occur in nature and some of their remarkable physical properties.
- Where are the Beautiful Julia Sets? explains how the Mandelbrot set is like an index to all the Julia sets.
- A fractal garden hidden in engineering tools! explains about Newton’s method fractals.
- The Math of Tie-dye shows a way to generate tie-dye patterns mathematically.
- Newton Biomorphs is about a type of fractal that reminds you of creatures seen through a microscope.
- Infinite Complexity in Finite Space is about the Mandelbrot set, which really is more complex than the entire physical universe.
- Humans and Computers Collaborating on Art is about using fractal algorithms as an artists tool.
In the list of posts there are the names of a lot of types of fractals. If you use something like Google image search those names can be used to locate a whole lot of other fractals, which might be entertaining. There are, of course, added posts coming about other types of fractals. Like this one, whose name does not appear above.
Fractals are a good tool for convincing people that math is not dry and boring. It is a bit of a problem that you need a computer, mostly, to make fractals, unless you are happy with the ones you find on the internet or in nature. That is another thing that is interesting about fractals — like the “tree” above, we often see echoes of natural objects in the images produced by fractal algorithms.
I hope to see you here again,
Daniel Ashlock,
University of Guelph,
Department of Mathematics and Statistics
Occupy Math 