A batrachion is a special class of mathematical curve which is actually defined only for the integers - in other words, it's domain is identical to N. There are any number of examples of this function, although typical ones include the highly-unpredictable Hofstadter's Q-sequence and the similarly erratic blancmange function.
A consequence of this 'jumpy' behaviour is that many batrachions are fractals.
As something of a curiosity, this class of curves gets it name from the Greek βατραχιον (bat-rak-ee-on), meaning "small frog". The analogy is between the batrochion's 'leaping' from one integer to the next and the leaping of the small frog. Creative mathematical naming? Whatever next?