Fractal Christmas Tree Paper Craft

I saw one last Christmas themed fractal, as I was sorting through Google images, that I thought would be perfect to turn into a paper, cut and glue, craft for the children.  If you do an Internet search for "Christmas fractals" you'll find an amazing assortment of mesmerizing images, as well as a few of these simple little trees.

We worked on our tree as a group.

D (age 11) made the base (a Sierpinski carpet)  by trimming a sheet of brown construction paper into a square...

...then cutting that square into 9 smaller squares, and removing the center square...

...and cutting the remaining squares into 9 smaller squares...

...and removing the center squares.  Normally we would have left the large square intact, and cut the middle squares out with a pen knife, or razor blade.  Unfortunately, since our move, I haven't been able to locate any of our pen knives, so we just cut the squares apart with scissors, and taped them back into place around the omitted squares.

When the squares got too small for cutting and taping, D switched to coloring in the middle squares, to represent a blank section.

While he worked on that, A (age 13) joined the younger children (after abandoning the fractal snowflake puzzle project that was going on, at the same time, in the basement), in cutting 9 sheets of green construction paper into large equilateral triangles, to be cut apart again, and again, each time removing the center triangle, in preparation for the Sierpinski triangle branches.

Being a middle schooler, I decided to have her cut the triangles one time more than I would have had the younger children cut.  Which, made for enough measuring and cutting of triangles, that the snowflake project was beginning to look better and better to her, but also made for a prettier pattern in the end.

While, their older siblings were measuring and cutting, I gave the younger girls (ages 8 and 10) a sheet of Apollonian gaskets (you can find printable images of them on many different sites), to color in...

...as Christmas ornaments.

I pieced the tree together, incorrectly at first (all those triangles were going to my head)...

...and the younger girls traced, cut out, and pieced together two more equilateral triangles to form the second iteration of the Koch snowflake - or in other words, a star, for the top of the tree.

We decided there were too many triangles to tape back together, and that it would be better to glue them down to a sheet of paper, instead.  After looking around the house for sheets large enough to fit behind the tree (we needed something about 4'x4'), we settled on one of the plastic tablecloths we had used under our toothpick and marshmallow star.

I think a red, or yellow background would have been even better, but we had green (left over from a Lego Friends birthday party) and so it had to do.

After the glue dried, we cut the excess tablecloth away...

...and hung the tree as a replacement for the grid art turkey we'd hung on the wall before Thanksgiving (again, down in the dark, photograph hating basement)...

...where it appears much brighter, and more mathematically festive, in real life.