Compute phi in base x

Hi from /sci/...  There was just a short thread about the digits of pi.  I personally think that phi (golden ratio) is far more interesting and was hoping one of you gentlemen might have some code to compute arbitrary digits of phi in any base chosen by the user.  Hopefully it isn't offensive to ask that it be in C.

Since it's purely random, there's going to be some sort of image in there, eventually.  Just curious to see what the first "significant" finding is.

>>20
There's no algorithm for computing arbitrary digits of a square root that doesn't consume an unbounded amount of memory?

You don't need to keep the entire result in memory, if that helps.  If you're searching for a 32x32 image, for example, you only need to store 1024 bytes of the result at any given time.  So, you should be able to search forever unless the algorithm itself requires unbounded memory.