We start with a yellow five pointed star.
I add a blue kite into each one of the gaps.
Now, a purple kite and a yellow dart in the new gaps, so that tiles sharing an edge do not share a color. (That was my basic marching order after the very beginning. It's a guideline not a rule.)
Blue kites for the yellow darts.
Yellow darts cap the purple kites.
Purple kites in the gaps.
"Got to have more of that sweet, sweet dart!"
That last caption was for my buddy Abu Scooter. If he didn't read this far, there wasn't much point to that gag.
So now it's growing more or less algorithmically, which is a fancy way of saying "These are the orders architects give to construction workers."
The purple and blue shapes together start to look like M.C. Esher fishies, don't they?
Notice how five straight lines lead out from the middle of the original five pointed star. At this point I thought that was a little too predictable, so I started changing things up.
Once I did that, all chances of tessellating the plane went out the window and I just had fun.
Actually, the whole process was fun for me. I hope my students enjoy it as well this next term.