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I'd like to generate a series of maps, where each map displays graduated colors based on a different variable in the feature's attribute table. The geographic area is the same in each map. I'm using ArcGIS 10.3, and would like to automate this using arcpy.

As an example, see the two maps below, except there will be loads of them:
map1 map2

Manually, I change the Value Field in the Layer Properties to get each map. How can this be done automatically for a high number of different Fields?

Since the underlying data differ for each map, arcpy.ApplySymbologyFromLayer doesn't get me there. Any tips?

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Use GraduatedColorsSymbology.reclassify documented here.

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