PSA: check out Anna Weltman’s new book, This Is Not A Math Book. Looks great.
Also check out Dan Meyer’s fall contest (ends 10/6/15) that asks the students to be creative in making their own Loop-de-loop mathematical art.
Programming connection: have the students make their loop-de-loop with python and turtles, here is a 3-5-2 loop-de-loop:
or with Scratch, here is a 2-4-5: 
Enjoy!
Thank you for this simple demo! I am so wanting to introduce coding into my mathematics teaching but don’t know the best sources or methods! I’m a bit of an old dog trying to learn some new tricks!
Here are some ideas for a programming progression related to loop-de-loops:
1) basic program to draw a static loop-de-loop
2) program that generates a random loop-de-loop (maybe within some constrained family)
3) draw a user-input loop-de-loop
4) draw a non-rectangular l-d-l (interesting to think about what constraints you keep)
5) draw l-d-l based on some well-known sequence (for example, digits of e, pi)
6) draw l-d-l families based on well known sequence
7) drawl loop-de-loop on a sphere (maybe show a projection back to the plane as an easier graphics challenge?)
8) automate the coloring of the regions of the l-d-l