Map coloring
Map coloring is the act of assigning different colors to different features on a map. There are two very different uses of this term. The first is in cartography, choosing the colors to be used when producing a map. The second is in mathematics, where the problem is to determine the minimum number of colors needed to color a map so that no two adjacent features have the same color.
Cartography
Color is a very useful attribute to depict different features on a map.[1] Typical uses of color include displaying different political divisions, different elevations, or different kinds of roads. A choropleth map is a thematic map in which areas are colored differently to show the measurement of a statistical variable being displayed on the map. The choropleth map provides an easy way to visualize how a measurement varies across a geographic area or it shows the level of variability within a region.
Displaying the data in different hues can greatly affect the understanding or feel of the map.[2] Also, the cartographer must take into account that many people have impaired color vision, and use colors that are easily distinguishable by these readers.[3]
Colors can also be used to produce three-dimensional effects from two-dimensional maps, either by explicit color-coding of the two images intended for different eyes, or by using the characteristics of the human visual system to make the map look three-dimensional.[4]
Mathematics
In mathematics there is a very strong link between map coloring and graph coloring, since every map showing different areas has a corresponding graph. By far the most famous result in this area is the four color theorem, which states that any planar map can be colored with at most four colors.