The pictures below came from an idea a friend of mine had…. Looking at a grid of squares, imagine drawing diagonal lines across the squares. If the line hits a wall, bounce off at a 45º angle. If it hits a corner, stop drawing the line.

You can play around with the game on the NCTM Illuminations site.

Here are some of the patterns we drew. What do you notice about them? What do you wonder? Leave a comment to tell us!