I suppose one heuristic would be to find a shortest tour through uniformly distributed points on a sphere.  The following image applies Mathematica's FindShortestTour command to $10000$ points generated by your own sphere command from Computational Geometry in C.



We could also use more regularly distributed points to obtain a path that (I suspect) has better local properties.  This image uses 5000 points generated by the algorithm described here.



I don't know that I quite follow your $\gamma(L)$ function, but it might be something like an inverse of the function obtained by plotting the length $L$ as a function of the number of points input to this procedure.



Equitably distributed curve on a sphere
I am looking for a wiki or wiki-like system for writing and managing specification and documentation for a software project. 

I know there are lots of wiki-implementations available, but are there some that are especially well-suited for this kind of task?

Actually it doesn't have to be a wiki, just a system that makes it easy to write and navigate specs and documentation, and which support change tracing.
