I've been loving some Tássia Bianchini line art lately, like http://tssbnchn.tumblr.com/post/168857610380, and wanted to play in GeoGebra. So...
Not sure if they should be rays or segments. Or if there should be multiple. But it's a start! Very interested in your ideas here.
If you need some famous curves with which to start: http://www-history.mcs.st-and.ac.uk/Curves/Curves.html