Viral growth actually can be explained with a formula for the viral factor (aka viral coefficient or k-factor). You can see the basic formula for Send Hotness's viral factor here: http://www.slideshare.net/StanFan/send-hotness-stanford-face.... When your viral factor is above 1.0, you will see exponential growth. In the case of Send Hotness, our viral factor was approximately 1.4, which allowed us to grow to 5 million users in 5 weeks. We spent much of our time in the Stanford Facebook class measuring and tuning the viral factor.
While it was easier back in the early days of 2007-08 to build viral apps on Facebook (hence the "gold rush" that is referred to in the article), it is still possible to do so today, albeit with quite a bit more effort. As you can see here, we have recently been growing virally at friend.ly, to the tune of 5 million users in the past couple of months: http://www.appdata.com/apps/facebook/5569318595-friend-ly
One other thing I should point out is that viral growth alone is not enough. Without engagement/retention, you will likely "jump the shark", as you can see Andrew Chen has discussed in the following blog post: http://andrewchenblog.com/2008/03/05/facebook-viral-marketin... This is one of the reasons why we have spent the past 18 months at friend.ly focusing on engagement and retention before trying to grow virally.
By way of full disclosure, I am Ed Baker, who Aaron refers to above. Aaron, good to hear from you. Glad to hear that you've been able to put some of the old Qubescape code to use at FaceCash!