How to apply the four colors theorem in a polygon map in ArcGIS/ArcToolBox automatcally?

Question

I need to apply the four colors theorem in a polygonal shape in a way that I do not need to choose manually each color to put in each region. I wish to knows if there is any extension, plug-in, script or data base that may be used with ArcGIS and ArcToolBox to do it mathematically or programatically, so I could use it for now on with every map I come to create.

Answer 1

First of all, thanks for all answers and comments. Unfortunetaly, the existing tools were not fully compatible with the latest versions of QGIS and ArcGIS. Therefore I made my own solution using the tool indicated by @polygeo, the QGIS plugin from @Alexandre and the name of the algorithm (four color map) from @Jens.

Here is my code for those interested (for ArcGIS but the second part could be used in QGIS as well).

arcpy.MakeFeatureLayer_management(fc, fc[:-4]+ "_lyr" )
try:
    arcpy.AddField_management(fc[:-4] + "_lyr", "color", "SHORT")
except:
    print "field alread exists"   
arcpy.CalculateField_management(fc[:-4] + "_lyr", "color",  "10" , "PYTHON")

arcpy.PolygonNeighbors_analysis(fc[:-4] + "_lyr", fc[:-4] + "_tb.dbf" )
graph = []
cursor=arcpy.da.SearchCursor( fc[:-4] + "_tb.dbf" , ("src_FID","nbr_FID") )
for row in cursor:
    graph.append(row)


pols = arcpy.da.UpdateCursor(fc[:-4] + "_lyr", ("OID@","color"))
colored = []
for pol in pols:
    nbrs = [ second for first, second in graph if first == pol[0]]
    usedcolors = []
    for nbr in nbrs:
        usedcolors += [second for first, second in colored if first == nbr]
    pol[1]=[color for color in range(10) if color not in usedcolors][0]
    colored.append(pol)
    pols.updateRow(pol)

Note that the algorithm does not guarantee that only 4 colors are used: though it has been proven that the solution exists, the "brute force" is necessary to achieve it. In my case, I got 7 colors which is small enough. The script could have an additional loop until the solution is found, but I need to do it for hundreds of maps and 7 colors is OK.

Answer 2

There is a VB6 developer sample and an ArcGIS 9.x geoprocessing tool but from the comments on this ArcGIS Idea they don't work at 10.0+.

Perhaps someone would be interested in porting it.

A QGIS solution called TopoColour is given in the comments of this related question: Color polygons so each is distinct from its neighbors

Answer 3

If you are using QGIS, I believe that what you need is the Coloring a map plugin.

Unfortunatly, the plugin is only available for QGIS 1.8 version, but you can always download and see how the code works!

Answer 4

This is an adaptation of @radouxju's answer into a function. It will add a color field to the input feature layer and calculate. It should work regardless of the field name endings of PolygonNeighbors (they seem to be different for different users/inputs/arcgis versions (?))

def color_me(feature_layer):
    import arcpy
    try:
        arcpy.AddField_management(feature_layer, 'color', 'SHORT')
    except:
        print 'Could not add color field. Maybe it already exists?'   

    arcpy.CalculateField_management(feature_layer, 'color',  '10' , 'PYTHON')

    arcpy.PolygonNeighbors_analysis(feature_layer, r'in_memory\neighbor_table' )
    graph = []
    neighbor_fields = [f.name for f in arcpy.ListFields(r'in_memory\neighbor_table') if f.name.startswith(('src', 'nbr'))]
    cursor=arcpy.da.SearchCursor(r'in_memory\neighbor_table' , neighbor_fields)
    for row in cursor:
        graph.append(row)

    pols = arcpy.da.UpdateCursor(feature_layer, ('OID@','color'))
    colored = []

    for pol in pols:
        nbrs = [ second for first, second in graph if first == pol[0]]
        usedcolors = []
        for nbr in nbrs:
            usedcolors += [second for first, second in colored if first == nbr]
        pol[1]=[color for color in range(10) if color not in usedcolors][0]
        colored.append(pol)
        pols.updateRow(pol)
    arcpy.Delete_management(r'in_memory\neighbor_table')