First - argh - looks like I got a link wrong - here's the correct link to the first Loom screenshot.
The patent is US Patent 6,031,537: Method and apparatus for displaying a thought network from a thought's perspective, owned by TheBrain. Depending on the interpretation, it can be read to basically claim showing a thing and also showing some of the other things connected to it, and when you click on one of the latter, it shows that thing and the things connected to that. (Of course that's just one of the claims, but it's what we're most worried about.)
The patent affects the Loom visualization and similar views, which are at the heart of the Fenfire vision.
We're working in Java plus Jython, plus some C++ for the OpenGL bindings.
As for the different directions, we're kind of implementing the philosophy of ZigZag but with RDF as the structure, instead of zzStructure, which is used in ZigZag. The fundamental idea of a desktop environment based on items was proposed by Ted Nelson (the link may not be stable, if it's broken try googling 'ted nelson item-storm modularities and overlaps more'). Our visualizations and UI are inspired by those developed for zzStructure.
RDF is actually similar to zzStructure in some pretty important ways: connections are typed and bidirectional; everybody can create a new type of connection and add information orthogonally about existing 'objects' in the system, not interfering with others' connections. This means that you're never locked in by someone else's idea of what data you should be able to store about a person or video or appointment or whatever - you can always add your own kinds of connections. Plus the structure isn't hierarchical; you can connect anything to anything.
(But as you're an old RDFie, of course I don't need to explain those benefits to you ;-))