Map (tree) of citations/references
If you're serious about such a project, I think what you need to do is recognize that this task naturally separates into two parts. It will be very easy to find a good, general purpose and freely available program that suits your taste for visualizing/analyzing/discovering networks in general. I think cytoscape is pretty good, although I've only played around with it a little and many others exist.

Now, the second (well, first) part is to fetch and prepare the input data for the citation relationships of interest to you. You need to be very specific about exactly where you want to get this from and for what subset of articles, since it may not be possible (due to license restrictions) or technically feasible (as noted, the size of the network grows exponentially).