Gumdrop and Toothpick Sierpinski Christmas Trees

Having the marshmallows, and toothpicks out for our Koch snowflake lesson, reminded the children of the fun we've had in the past building marshmallow, and toothpick Sierpinski tetrahedrons.

Just to jog your memory, a Sierpinski tetrahedron is a tetrahedron with the middle section removed, leaving four smaller tetrahedrons from which the middles are removed, leaving each smaller tetrahedron with four even smaller tetrahedrons from which the middles are removed...on into infinity.

I figured they might want to make a few, and was prepared with gumdrops (in place of marshmallows which we had pretty well used up) and green colored toothpicks, so we could turn them from fractals into tetrahedonish Christmas trees.

Of course, I should have known they wouldn't want to stop with the tiny trees I had planned.  They very quickly used up all our green toothpicks...

...and moved on to a multicolored Christmas creation...

...that was terribly festive, but much less tree-like, and not nearly as stable as I had originally planned.  It turns out stale marshmallows make for better building material than fresh gumdrops.  We've gone a lot taller with marshmallow our marshmallow tetrahedrons.

But then, the gumdrops were pretty, and tastier than old marshmallows when it came to disposing of the leftovers.