As a fun challenge, look at the definition of pretty much any fractal. It is a mathematical construct that is almost certainly not equivalent to what most "functional programming" environments let you do. Indeed, most definitions are imperative by nature, that I recall, and yet they work remarkably well.
Really, anything from the book Turtle Geometry would have a challenging time in a lot of functional languages. Which is not that most functional languages are bad. Just they don't usually even try to abstract over the graphical. I hate that folks see how well the abstract over functions and assume that is all programming is.