eCollegeFinder, a service linking students with online colleges that has an apparently busy side gig in making maps, has created this fascinating GIF of the growth of four-year colleges in the US. You can watch Harvard University start as a lonely dot in 1636, joined by the College of William and Mary in 1693, and eventually 2,066 other four-year colleges:
Colleges marched west as the US did. And you can see the effects of the Morrill Land-Grant Act of 1862, which created state colleges and universities in many states, and especially the second Morrill Act in 1890, aimed at the former Confederate states. In 1890 and 1891 alone, 59 colleges were founded that are still around today.
Other years of growth were more recent. Thirty four-year colleges that still exist today were founded in 1946, as returning members of the military from World War II began to take advantage of GI Bill benefits. And another 30 four-year colleges were founded in 1965, as the Higher Education Act began to open up need-based grants and lower-cost student loans to all Americans.
This doesn't include the many colleges that once existed and have since closed, either.