I’ve come across a couple blogs where people are working on slither link variations. The first set comes from a blog a called *Insert Clever Title Here*. Here the puzzles are called loop-de-loop (which is also sometimes used for slither link.) At certain points in these puzzles there are symbols which place limits on the path through that point. For example, a symbol might indicate that the path must turn at that point or must not turn at that point. To really get the idea, click over and try them out.
The other set comes from zotmeister where the puzzles are called “The One Ring”. The variation here is similar, with the added twist that the dots have clever names. Dots where the path can’t bend are called angel dots. Dots where the path must bend are called devil dots.

