U.S. House districts are not real geographic boundaries. Particularly since Wesberry v. Sanders (1964), which held that any population difference between House districts at the time of the decennial Census is unconstitutional, state legislatures (and, more recently in many states, specialized commissions) dramatically redraw district lines every ten years. Before Wesberry, it was not uncommon for districts to remain almost unchanged for decades, contributing to massive malapportionment at the expense of cities. The legal and partisan contestation over redistricting also means that there have been over 200 districts that were redrawn between cycles since the 1960s. (The most notorious instance of which, of course, is this one).
This simple web application helps visualize the changes the new constitutional order has wrought on district boundaries. Simply select a state on the U.S. map, select a district on the right hand select box, and an animation will show the evolution of the House district from the 1940s to the present. You can choose to view simply the physical boundaries of districts, or the districts with partisanship or minority racial composition layers. The latter two are useful for spotting gerrymandering; snaking, barely-contiguous districts with high levels of partisanship are classic examples of “packing,” designed to dilute the voting power of constituencies (especially in cities). Partisanship is calculated using the Cook Political Report's Partisan Voter Index (PVI), which is the average difference between the district's two-party presidential vote (over the lifespan of the district) and the national two-party presidential vote.