The challenge then becomes a matter of creating a robust enough technique for randomly generating each location so that you get enough variation to support the experience of an infinite game space. One important concept of creating interesting and realistic randomly generated patterns is self similarity. Raw randomness creates a kind of white noise or gray background of boring uniformity. Things in nature which are close to random, actually have the tendency for adjacent locations to be similar or related, but with abrupt changes as well. So, to get a natural feel or look to things your adajacent locations must be similar a large proportion of the time but often completely different.
Another challenge is the problem of how players change the state of the locations which they visit. This requires that you keep a stack of such changes. In order to keep this stack from growing indefinitely while improving realism rather than losing it, you would use evolution in the random generation of your locations. This way you can drop changes to visited locations from your stack when the locations have evolved. Evolving locations means that the more changable elements of each location depends on the game time as well as its fixed seed.
As an illustration of these concepts see the relativistic physics of spaceflight simulator at www.relspace.astahost.com. You do not need the registered version to see what I am talking about. This program uses a tree like structure for random generation even though everything is located in the same 3 dimensional space. This is because the locations are organized into galactic cluster, galaxies, clusters of stars, star systems with planets and planets with their moons. This fixed seed random generation technique allows me to have hundreds of galaxies, each with hundreds of billions of stars (and most of those with companions and planet) because I do not have to store them or even display them unless they are within range. The concept of self similarity is used in a variety of ways. The average star of a galaxy or star cluster depends on the type or appearance of that galaxy or star cluster. Self similarty is also used in the creation of irregular shaped galaxies and star clusters. But the most important use of self similarity is in the random generation of surface features of the planets and moons (around other stars). The locations are evolving because the locations of the planets and moons in their orbits depend on the time (real time in this case). However I do not have to worry about players changing anything about thei locations they visit. I was led into using this technique for this program by the fact that the data available for what is out there gradually diminishes with distance. Even though this program is not a game at all, I have spent many enjoyable hours exploring its infinite space. Imagine finding interesting views like looking at the Milky Way through the rings of a bright red planet with three suns, in the Smaller Magellanic Cloud.
I noticed on the internet that there is a book available on this idea of infinite game space (http://www.charlesriver.com/Books/BookDetail.aspx?productID=8720), but I haven't read or look at it myself.

