You have likely made or come across many political maps in atlases or wall maps of the world. Or perhaps you have created your own maps of administrative regions, states, counties, or plot boundaries, or made other polygonal reference maps.
In these applications, polygons themselves are the subject. There is no thematic field or choropleth value to color by. Instead, the creator wants to add a fill to make it easier to see the different shapes—where one ends and another one begins.
According to Megan Johnson at the National Center for Supercomputing Applications (NCSA), “For a world map to be useful, each country must be easily distinguishable from the next.” Conversely, if we color in every country differently, it becomes visually overwhelming and similar colors start to look thematic or of the same group.
To address this issue, the Calculate Color Theorem Field tool in ArcGIS Pro can help you color map polygons while ensuring that any two adjacent polygons will not have the same color.
The idea that a contiguous set of two-dimensional polygons can be colored with no more than four or five colors (while still ensuring that any two adjacent polygons will not have the same color) has been around since the 1800s, but debate around this idea continued until 2005. Since then, developer samples and solutions both from Esri and from users in various GIS ecosystems have emerged, but generally, most cartographers have chosen to color these polygons manually.
While there is still a case for cartographers’ manually improving certain decisions, this tool automates as much of the process as possible.
Welcome the Calculate Color Theorem Field Tool
With most solutions until now, data needed to be contiguous (have no gaps), have no overlaps, and be composed of only single-part features. But GIS data and use cases are often not quite that simple! Also, Esri developers were very keen that none of these solutions should be prohibitive. So, rather than enforce four or even five colors, this tool works out both neighbors and proximity using graph theory, and respects and retains multipart polygons. Doing this keeps the number of colors used low while ensuring that the color of every neighboring, overlapping, or very near feature is different.
Rather than dictate colors, the tool provides an integer field that you can use with the Unique Values renderer to effectively color by number with a palette of your own choosing. Some data providers already provide color index fields with their datasets in a similar fashion.
To get started using the tool in ArcGIS Pro, follow these steps:
- Search for the tool or find it in the Cartographic Refinement toolbox (Cartography Tools).
- Select the input features you wish to color and the name of the field (existing or new) that will contain the new values.
- Run the tool to populate the chosen field with an integer value (e.g., 1 through 5).
- Now, open the Symbology options, then choose Unique Values. Choose the updated integer field and a suitable color scheme. That’s it!
If the resultant field has many unique values, it is likely that this is caused by a lot of overlaps in your data or by duplicate geometries. You may want to consider some data cleansing before running the tool again.
To ensure that certain polygons are assigned the same color value—a mainland extent with a chain of islands under the same sovereign rule, for example, or a country and its enclaves—then make them a multipart feature and the tool will treat them as one.
The tool is designed to use as few colors as possible and to use them evenly. However, under some circumstances, our tool does not use the minimum number of colors. This is usually when the data is noncontiguous, overlapping, or multipart. Solutions that enforce minimum colors often won’t run on such scenarios.
If you wish to reduce the number of colors, you can edit the field for manual fine-tuning after running the tool, or run the tool several times on different geographic extents. To set the processing extent, go to the Analysis ribbon and, under Geoprocessing, choose Environments.
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