Seems like you are on your way: modulo arithmetic, and/or feeding ascending/descending ramps to trig functions.
I would carry it beyond pyrochild’s running down a straight line. That’s fourteen year old thinking; you’ve got a lot more chops than that. Trace along constant contours, laying down spots of the current modulo function as you go. Could be some interesting Moiré patterns to come of it.
Have fun, whatever you do.