Not to be super anal or anything, but the Nautilus shell is actually a logarithmic spiral, not the golden ratio (http://en.wikipedia.org/wiki/Nautilus#The_shell); although there is a special type of logarithmic spiral called the Golden Spiral, the Nautilus shell ain't it... Still, both are quite common in nature.
However, now that the spiral on the mainframe as resolved a bit more, it doesn't look like either type of spiral. Both (golden or logarithmic) increase their width logarithmically--that is, the distance from the one loop to the next should get significantly bigger with each pass around the center, but it doesn't look to me like that's happening in the mainframe image.
EDIT: Okay, I'm an idiot and can't read, since a bunch of people already said this right above me. Nonetheless, it's not the (current) DEVONThink logo.