First I got tapers (truncated cones) working:
Then I started working on turtle strings, rendering them using cylinders:
As you can see, there's a problem with the cylinders not being the correct length:
Then I started using tapers. The following is a rendering of this turtle string:
F[F[+F][-F][^F][&F]][+F[+F][-F][^F][&F]][-F[+F][-F][^F][&F]][^F[+F][-F][^F][&F]][&F[+F][-F][^F][&F]]
I'm not using any automated productions to create the turtle string just because I wanted to get the basic system working first. It's far from finished, but it's a start! Check back later for updates.