There are many "strange" functions to choose from and the deeper you get involved with math the more you encounter. I consciously don't mention any for reasons of bias. I am just curious what you consider strange and especially like.
Please also give a reason why you find this function strange and why you like it. Perhaps you could also give some kind of reference where to find further information.
As usually: Please only mention one function per post - and let the votes decide :-)