President Obama was drawing on a common wisdom that had been making the rounds among pundits from David Brooks on the right to Thomas Frank on the left. According to this narrative, the frustration of Americans living in postindustrial heartland towns led them to ignore their economic interests and embrace the cultural conservatism offered by the GOP.

This narrative started with the stark red and blue maps of counties and congressional districts that began to appear every other November since 2000. The maps seemed to reveal “two Americas.” Blue America, according to Brooks, was located “around big cities on the coasts,” while people in Red America “tend to live on farms or in small towns or small cities far away from the coasts.”

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This understanding of the Democrats as the party of metropolitan America and the Republicans as the party of smaller postindustrial cities and towns is deeply ingrained in the American political discourse, and has shaped many analyses of the upcoming presidential election.

It is also completely wrong.

Despite his name, race and untoward comments about small-town America, Obama went on to win large majorities in exactly the small, overwhelmingly white postindustrial cities and towns that, according to mythology, are populated with Republicans.

Let us begin with some examples.

When Sarah Palin excoriated Obama’s “bitter clinging” remarks in her convention speech in 2008, she drew attention to the contrast between San Francisco and Scranton, Pa. Yet Obama’s vote share in Scranton a few months later was well above 70 percent — not much different from his vote share in San Francisco.

As can be seen in the map below, Scranton was not a fluke. Obama also won similar majorities in all of Pennsylvania’s medium-sized industrial agglomerations, including Allentown, Bethlehem, Reading, Lancaster and York. He won smaller industrial towns such as Hazelton, Bloomsburg, Johnstown, Uniontown and Washington, just to name a few. In fact, it is difficult to find a Pennsylvania town with a substantial industrial history where Obama did not win a decisive majority.

When Obama chose a Midwestern industrial town to stage a “damage control” speech after his comments about small-town America, he chose Terre Haute, Ind. He went on to win by a majority approaching 70 percent. Again, Terre Haute is not unusual. The list of small Indiana towns with roots in early 19th-century industrialization is a list of Democratic strongholds: Anderson, Muncie, Richmond, Marion, Fort Wayne, Goshen, Kokomo and Evansville, to name only a few.

The maps reveal that the core downtown neighborhoods of industrial Indiana towns like Terre Haute are the same deep shade of blue as Indianapolis or Chicago.

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The same is true for the industrial towns of Michigan, Ohio, Illinois, Wisconsin and well beyond. Along the shores of the Great Lakes, and along the places where rail lines or canals intersected and gave birth to industrial activity and towns in the late 19th and early 20th centuries, Democrats win majorities today that are as comfortable as their majorities in big cities.

In collaboration with some colleagues, I have assembled a Web map from precinct-level election data that allows users to zoom in and out, focus in on specific towns or neighborhoods and superimpose census data on income and race, allowing readers to examine their own favorite postindustrial towns.

One of the most striking lessons from exploring these maps is that the red nonmetropolitan counties on election-night maps are internally heterogeneous, but always following the same spatial pattern: Democrats are clustered in town centers, along Main Street, and near the courthouses schools, and municipal buildings where workers are often unionized. They live along the old railroad tracks from the 19th century and in the apartment buildings and small houses in proximity to the mills and factories where workers were unionized in an earlier era.

In the graphs above, using the same Indiana towns displayed in the maps above, I plot the Democratic vote share against the distance of each precinct from the town’s city hall. Within two or three miles of the town center in any direction, one finds strong — even overwhelming — Democratic majorities. Only as one moves away from Main Street and downtown does one begin to find majority-Republican precincts in the newer single-family houses on the edge of town.

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Readers can use the Web map to zoom in on any of the Indiana or Pennsylvania towns mentioned above, or pick some postindustrial towns in Illinois, Michigan or Ohio, and see that these towns demonstrate the same pattern. Democrats dominate the 19th- and early 20th-century buildings around Main Street and give way to Republicans in the suburban single-family homes that were built decades later on the outskirts of town, often in proximity to the interstate and suburban-style shopping areas, and in the rural areas that lie beyond.

This pattern is strongest in the towns with the highest levels of early 20th-century industrialization and population growth, such as Terre Haute, Muncie and Fort Wayne, and somewhat weaker in less industrialized towns such as Marion, Ind.

In other words, the same political geography found in big cities is also on display in smaller postindustrial towns. There is a fascinating fractal-like relationship between population density — which is the upshot of early industrial activity — and Democratic voting. As one zooms in to lower and lower levels of geographic aggregation, the relationship only reappears in finer detail.

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Just where did the myth of Republican-dominated industrial towns in the heartland come from? Part of the answer lies in the hopes of Republicans and the corresponding fears of Democrats that small towns in the Midwest will come to resemble many small towns in the Deep South, where elections have come to resemble racial head counts.

But perhaps more important, we have gazed for too long at election-night maps of counties or congressional districts that lacked sufficient granularity to differentiate between towns and their surrounding suburbs and rural peripheries. We also obsess over polls that lead us to assess categories like “low-education nonmetropolitan whites,” blinding us to the difference between deep-blue Johnstown, Pa., for instance, and the red county of Cambria in which it is located.

The distinction between industrial towns and their surrounding rural peripheries is especially important in the 2016 presidential election. The Republican presidential candidate has adopted a nativist, anti-trade platform that seems explicitly tailored not only to white rural voters — who have been voting reliably Republican for years — but also to white voters in postindustrial towns who have been voting overwhelmingly Democratic for decades. This strategy is based on the notion that Obama’s description of “anti-immigrant” and “anti-trade” sentiment among small-town voters was correct.

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Given his difficulties among educated voters — especially women — in large metropolitan areas, victory for the Republican candidate seems to require a major transformation of the maps displayed above, such that deep-blue industrial towns begin to resemble their Republican rural surroundings.

In other words, the best hope for the Republicans in the 2016 presidential election is that Brooks was not so much wrong as prescient when describing a “red America” that includes the cities and towns of the heartland. Only time will tell, but this would require a rather extraordinary electoral transformation.

Jonathan Rodden is professor of political science and senior fellow at the Hoover Institution at Stanford University.