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I need to create a map where states have different colors depending on a piece of data about that state. I found an example of a US map in the cartopy gallery, but it didn't demonstrate how to refer to the states and access their attributes, and there little else out there:

From the example, I've simplified their code to the following, and would appreciate any help with modifying this to get the face colors of the states to be set according to the magnitude of popdensity for the state.

import matplotlib.pyplot as plt
import cartopy.crs as ccrs
import cartopy.io.shapereader as shpreader

fig = plt.figure()
ax = fig.add_axes([0, 0, 1, 1], projection=ccrs.LambertConformal())

ax.set_extent([-125, -66.5, 20, 50], ccrs.Geodetic())

shapename = 'admin_1_states_provinces_lakes_shp'
states_shp = shpreader.natural_earth(resolution='110m',
 category='cultural', name=shapename)

popdensity = 
 'New Jersey': 438.00,
 'Rhode Island': 387.35,
 'Massachusetts': 312.68,
 'Connecticut': 271.40,
 'Maryland': 209.23,
 'New York': 155.18,
 'Delaware': 154.87,
 'Florida': 114.43,
 'Ohio': 107.05,
 'Pennsylvania': 105.80,
 'Illinois': 86.27,
 'California': 83.85,
 'Virginia': 69.03,
 'Michigan': 67.55,
 'Indiana': 65.46,
 'North Carolina': 63.80,
 'Georgia': 54.59,
 'Tennessee': 53.29,
 'New Hampshire': 53.20,
 'South Carolina': 51.45,
 'Louisiana': 39.61,
 'Kentucky': 39.28,
 'Wisconsin': 38.13,
 'Washington': 34.20,
 'Alabama': 33.84,
 'Missouri': 31.36,
 'Texas': 30.75,
 'West Virginia': 29.00,
 'Vermont': 25.41,
 'Minnesota': 23.86,
 'Mississippi': 23.42,
 'Iowa': 20.22,
 'Arkansas': 19.82,
 'Oklahoma': 19.40,
 'Arizona': 17.43,
 'Colorado': 16.01,
 'Maine': 15.95,
 'Oregon': 13.76,
 'Kansas': 12.69,
 'Utah': 10.50,
 'Nebraska': 8.60,
 'Nevada': 7.03,
 'Idaho': 6.04,
 'New Mexico': 5.79,
 'South Dakota': 3.84,
 'North Dakota': 3.59,
 'Montana': 2.39,
 'Wyoming': 1.96

ax.background_patch.set_visible(False)
ax.outline_patch.set_visible(False)

ax.set_title('State Population Density')

for state in shpreader.Reader(states_shp).geometries():

 ### I need to replace the following code with code that sets the
 ### facecolor as a gradient based on the population density above
 facecolor = [0.9375, 0.9375, 0.859375]
 edgecolor = 'black'

 ax.add_geometries([state], ccrs.PlateCarree(),
 facecolor=facecolor, edgecolor=edgecolor)

plt.show()

To have access to states' attributes, you need to iterate through .records() rather than .geometries(). Here is a working code based on yours. Read comments in the code's portions that I add / modified for clarification.

import matplotlib.pyplot as plt
import cartopy.crs as ccrs
import cartopy.io.shapereader as shpreader

fig = plt.figure()
ax = fig.add_axes([0, 0, 1, 1], projection=ccrs.LambertConformal())

ax.set_extent([-125, -66.5, 20, 50], ccrs.Geodetic())

shapename = 'admin_1_states_provinces_lakes_shp'
states_shp = shpreader.natural_earth(resolution='110m',
 category='cultural', name=shapename)

popdensity = 
 'New Jersey': 438.00,
 'Rhode Island': 387.35,
 'Massachusetts': 312.68,
 'Connecticut': 271.40,
 'Maryland': 209.23,
 'New York': 155.18,
 'Delaware': 154.87,
 'Florida': 114.43,
 'Ohio': 107.05,
 'Pennsylvania': 105.80,
 'Illinois': 86.27,
 'California': 83.85,
 'Virginia': 69.03,
 'Michigan': 67.55,
 'Indiana': 65.46,
 'North Carolina': 63.80,
 'Georgia': 54.59,
 'Tennessee': 53.29,
 'New Hampshire': 53.20,
 'South Carolina': 51.45,
 'Louisiana': 39.61,
 'Kentucky': 39.28,
 'Wisconsin': 38.13,
 'Washington': 34.20,
 'Alabama': 33.84,
 'Missouri': 31.36,
 'Texas': 30.75,
 'West Virginia': 29.00,
 'Vermont': 25.41,
 'Minnesota': 23.86,
 'Mississippi': 23.42,
 'Iowa': 20.22,
 'Arkansas': 19.82,
 'Oklahoma': 19.40,
 'Arizona': 17.43,
 'Colorado': 16.01,
 'Maine': 15.95,
 'Oregon': 13.76,
 'Kansas': 12.69,
 'Utah': 10.50,
 'Nebraska': 8.60,
 'Nevada': 7.03,
 'Idaho': 6.04,
 'New Mexico': 5.79,
 'South Dakota': 3.84,
 'North Dakota': 3.59,
 'Montana': 2.39,
 'Wyoming': 1.96

ax.background_patch.set_visible(False)
ax.outline_patch.set_visible(False)

ax.set_title('State Population Density')

#for state in shpreader.Reader(states_shp).geometries():
for astate in shpreader.Reader(states_shp).records():

 ### You want to replace the following code with code that sets the
 ### facecolor as a gradient based on the population density above
 #facecolor = [0.9375, 0.9375, 0.859375]

 edgecolor = 'black'

 try:
 # use the name of this state to get pop_density
 state_dens = popdensity[ astate.attributes['name'] ]
 except:
 state_dens = 0

 # simple scheme to assign color to each state
 if state_dens < 40:
 facecolor = "lightyellow"
 elif state_dens > 200:
 facecolor = "red"
 else:
 facecolor = "pink"

 # `astate.geometry` is the polygon to plot
 ax.add_geometries([astate.geometry], ccrs.PlateCarree(),
 facecolor=facecolor, edgecolor=edgecolor)

plt.show()

The resulting plot: