The Ben Paul Thurston Blog
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Wednesday, May 6, 2015
Algebraically coloring a map
I noticed you can take an uncolored map like:
You can set up a set of equations to solve for, as follows... if region X is next to regions Y, Z,... one equation is X=Y*Z*...
For the above:
Note that C is not considered adjacent to D...
And there are a few solutions to the above, but we can add extra conditions such as A!=B, because A and B are adjacent and so on until we get down to one solution...
Now we can use a map of these complex numbers to color values by putting a color wheel on the complex plane:
And use that as a key to fill in the colors:
In this case it gave 5 colors not 4 as for the famous 4 color theorem, but I still think it's an interesting process...
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