We watched Frozen at Grandpa's house a couple weeks ago, and my boys are just loving the music, particularly Let It Go. Which works for me; it's outstanding music that's fun to sing along with. And it just happens to have a fun math tie-in, so we'll be playing around with fractals, in between re-watching the raising of the castle.
About 2 years ago, we played with fractals once before. We made some Sierpinski Triangles, but he doesn't remember, at least, not by the name, so I think we'll start out with doing those again. Happily, you can print graph paper from the web - we'll be using this site's Isometric Graph Paper. Which is fun. I mean, what's not to love about triangle graph paper? I bet we can find some fraction work in these triangles too, since that's what we were supposed to be focusing on right now. And coloring. Math + Art is pretty much always good. So much more fun than the worksheets we were going to do tomorrow, though we'll probably do those as well. It'd be fun if we had enough finished triangles to put a composite up on the wall or something, though that's probably pushing our luck for a single day.
But, cool as they are, Sierpinski Triangles just don't look much like the stuff in Elsa's ice castle. That one looks much more like this Koch Snowflake. There's directions for making it; looks like more triangle paper is going to be in order. We won't look at the equations they have on this page, but they have some lovely pictures of these Koch Snowflakes and some variations. Here's some historical background. And some more. I wonder why it is that Koch Snowflakes were discovered by a Wilson Bentley? I might put something about this in my Book of Centuries, whatever the reason for the name. This book is tempting, but I don't know if we'll get that into this project. Our local library has this one. Makes me wonder if our used book shop has it. That's tempting, though the baby's sick, so it won't happen fast either way.
Of course, we'll also have to have a look at some of the fractal zoom clips on Youtube. This looks like a likely starting point.
That should do for a start. we'll see if there's more interest after that.