To make these maps, we'll say that each city projects power (population, wealth, etc) over distance, and that power decays according to some equation as it gets farther away. As a first stab, let's just say that power decays according to 1/distance. Here's how that looks:
Suppose, however, that power is more difficult to project in the future. Perhaps transportation networks have shut down, or social communities have become more clannish. Now, power is projected according to: P = population/d^t
The land under the rule of large cities quickly deteriorates as small and medium-sized cities. Then, as t get very high, some of the medium-sized cities begin losing land at their periphery. Watch Denver (purple) as it expands until t=4.5, then begins to lose lands to cities like Boise and Spokane.
At t=6, the dominant cities are those in sparsely populated areas, while cities in dense-populated urban conglomerates (NC Piedmont, NYC, San Francisco Bay) continue to do badly. Look at the fragmentation of the Northeast:
At our final state where t=6, the eastern half of the US is split into similarly-size chunks of land, while city-states like Denver and Sale Lake rule over vast stretches of emptiness. Living in this version of the future would be wholly different from what we know - traveling would require constant crossing of borders, and power struggles between many nations who are roughly at parity could get ugly.
...Here's to an interesting future.
To see how your city fares under each equation, check here: https://docs.google.com/file/d/0B-g8I7dAEkRuNURfNlBPd1UzSFE/edit?usp=sharing
To anyone interested in playing around with these scripts, they're available here: http://ge.tt/7y5sVTv/v/0