Robert Krulwich for NPR writes about cartographer Harold Fisk’s visualization of the river’s historical paths here.
This is a map of the Lower Mississippi’s evolving floodplains, lifted from cartographer Harold Fisk’s 1944 report, Geological Investigation of the Alluvial Valley of the Lower Mississippi River.
You can download the report in its entirety, including numerous maps like this one, from the U.S. Army Corps of Engineers web site (if you’re looking for maps like the one up top, you want to click the link on the lefthand side of the USACE website that says “Fisk 44 Oversized Plates.” (thanks io9)