Square String Functions

This sketch makes a rectangular frame with M pegs on each side. It then connects the points as given by a function. For example, g(x)=2x+1 connects point f(1) to f(2) to f(3)... up to f(N). (The second slider.) That would connect 3 to 5 to 7 to 9 etc. What patterns can you make? Some of my patterns are at: http://mathhombre.tumblr.com/post/115784495364/square-string-functions This GeoGebra was inspired by some art by Carol Bove, but I can't figure out a function to make her pattern! Can you? Here's her drawing: http://mathhombre.tumblr.com/post/115662135024/vjeranski-carol-bove-via-wcydwt
More GeoGebra at bit.ly/mh-ggb