Apparently, either nobody who read this thread is familiar with anything like this or they did not want to bother to reply.
Anyway, I have since found a partial
solution to what I'm looking for. I have since remembered that the category of software I was thinking about is called "flowchart" or "mind mapping" or "concept mapping". A very useful list of mind mapping and concept mapping software can be found on Wikipedia, here: http://en.wikipedia.org/wiki/List_of_mind_mapping_software
Surprisingly, quite a few of these are free and/or open source. But none
of these are exactly
what I was looking for. Unfortunately, I think I will have to settle for one of these. (Right now I don't feel up to re-learn how to program software and then write my own program.)
The only one I found that allows a 3D representation of concepts or data is 3D Topicscape
. Sadly, the 3D part is limited to 3D pyramid representations of the 2D data. It is considered a "commercial" product, but there is a "Lite" edition that is free for personal use.
FreeMind is one of the most popular and which I've read a recommendation for in the past. But I think I might try VUE first because, from the screenshots, it appears like it has a few more features that I would find useful.