If your child is all about getting ready for Halloween, then this can be a terrific idea to introduce some beautiful math. I saw this idea on Almost Unschoolers and immediately bookmarked it!
The idea is to turn Apollonian and Sierpiensky fractals into fun arts projects. To start, you can learn more about these fractals and download the printouts from the Apollonian gasket wiki page and this page about Sierpinski triangle. And if you don’t have a printer readily available, you can just free-hand it (here’s Vi Hart’s video to get inspired by).
I showed Apollonian gasket to my 4-year old earlier today and told him that it’s a mathematical pumpkin patch (again, thanks to Almost Unschoolers for the inspiration). He’s really into Halloween decor, but it has to be scary, not cute. So I told him that if he colors the print, he can make it as scary as he wants it to be. It worked! My otherwise coloring-books-are-boring son could hardly wait for the pattern to be printed out.
Some of the questions that we discussed as he started working were:
As you can see from the picture, he didn’t make it to the green crayon although he worked really-really hard on getting the red and blue ones just perfect. But he seemed quite content with the results and so was I.
I still have the Sierpinski printout saved for later and another Apollonian gasket for myself to doodle on.