I am once again disappointed by Google Search functionality, which has hindered my implementation of proper searching on this site :-(. (See relevant update).
The Google Search API returns a vastly stripped result set compared to using actual Google Search. I have checked and done a bit of research and have not found a good reason for this. And, no, it has nothing to do with local or personalized searches, which has been confirmed by using searches without any kind of cookies or localizations.
My guess is that the Google Search API and normal Google Search itself are just tapping into different result sets from the start :-(.
An example of this problem is as follows: Searching for “Fractal” in the Projects section returns the following results:
At some point I’ll probably have to find another site search solution for this reason, blegh. 
