It works like this: Normally, when you roll Fudge Dice, you're only concerned with the total, from -4 to +4. What makes the Triangle work is that it cares about the actual results of those dice, not their total. So 0000 is not the same as ++--, and 00-- is a different result than +---. This gives you 15 possible results and a bell curve with more variation than what Fudge Dice normally deliver.
I'll let Mr. Goodwin explain it a little more:
I've had two insights into this table concept since I wrote it up.
The first is that the main difference between it and a regular 2-dimensional range of results (from -4 to +4) is that it opens up the middle of the bell curve. That is, on a normal 4dF, you roll a 0 about a quarter of the time (or something like that). On this table, you expand that single result into three results (0000, 00+-, and ++--). Which is handy, and adds variation, even though it only actually adds 6 new results (15 total, instead of 9).
The other interesting thing about this tale is that it's actually an equilateral triangle - the three corners being ++++, ----, and 0000. I didn't realize that at first because of how I laid it out, and because FATE trains us to ignore blank side of the die - but it means we've got a chart with three different axis. There are probably a lot of triads you could use that would give you a neat table: crown, church, and guild; social, mental, and physical; heaven, hell, and mundane...Here's an example he did to illustrate how he intends to use it:
But it doesn't stop there. In that same RPG.net thread, he shows how you can use this to establish elements of a character's background, intra-party relationships, or the politics of a setting. It's a campaign-in-a-box, basically. It's also awesome.
As I said in that thread, if you combine this with the Random Adventure Generator in the Legends of Anglerre Companion, you can throw a pretty cool game together in no time. Which is probably exactly what I'll do when the Companion comes out, if not sooner.
Or match it up with Diaspora's cluster creation and figure out some more stuff with those clusters. Really, the possibilities are fairly limitless. Thanks, David S. Goodwin!
(My enthusiasm for random tables is in an especially high gear these days; I just bought the original three Traveller LBBs at DiceHouse the other day, and I've rolled up a dozen or so characters since then, many of whom survived the character generation process.)
PS: Sorry about the weird formatting on this post. It's Blogspot's fault.