Anyone learning topology should already know that not everything in maths is easy, or even possible, to "picture" in a standard way.
A countable connected Hausdorf space is a (topological) space which is Hausdorrf, connected and countable...what else do
you need?! A photo? I don't think there is one, although perhaps there exist somewhere some more "intuitive" descripition of this.
Perhaps in the book "Counterexamples in Topology", by Steen and Seebach, there's something...