Quad Cycle
For some reason I got thinking about line art today with quadrilaterals instead of lines. Thick lines, I guess.
You might want to download this to play, as the canvas is just the largest integer rectangle that can fit in the window. On the tube you'll be able to zoom in and out, but not change proportions.
There are some things about which you can wonder:
What do you notice about the controls? What makes for different patterns? Which ones are aesthetically pleasing? How is the sketch determining maximum n and N? What does k do?
More GeoGebra at bit.ly/mh-ggb