We are getting more milage out of the fractals than I ever imagined we might. The pictures in this post actually represent at least 3 days of playing with the patterns.
We started with reviewing the Sierpinski Triangles. All three of us made at least one because that first day was one of the days Dragon wanted in on school. Hero made several. By the end of the day we had gone to taping them together on the fridge because we outgrew our papers. Later, we moved them to the ceiling in Hero's bedroom because we couldn't find wall space big enough.
As we got into it, Hero started to branch out. He wanted to experiment with making his own "fractals." I suggested that the Sierpinski Triangles have a rule: leave the center empty. So, if he wanted to try and find another shape, perhaps he should try a slightly different rule. The first time, he drew this.
Another day, we did these. With this batch he was starting to understand better, I think, what I was trying to suggest with the idea of a "rule." He made the center shape, and wanted me to copy it.
We ended up with several stacks of the same shape, colored according to different "coloring rules", but drawn with the same "shape rules", and I was very surprised at how different that could make them look.