In math terms an extrema, the plural of extremum, are the high and low points (either locally or globally) of a function. This translates into maps as the high and low points of various features. Elevation is an obvious application, but they can also denote any number of other things.

The procedure to make an Extrema drop map is simple:

  • Pick a feature: elevation, water, vegetation, population, danger level, etc…
  • Drop a bunch of d20s on a piece of paper
  • Interpret results:
    • One option: X lowest dice are minima, rest are maxima. This fixes the number of maxima and minima and just randomizes magnitude and location.
    • Another option: Roll of X or lower is a minima, higher is a maxima. This randomizes the number of minima and maxima, though it will tend to be in a proportion matching your split value.
    • Another option: Certain dice are minima, others are maxima regardless of roll. This method may tend to create odd features like craters in mountain ranges and oases in the middle of desserts, but the results will be interesting.
    • Across all options, the more extreme the roll, the more extreme the extremum, either from the min or max roll, or from the value that splits your minima and maxima, depending on the roll method you’re using.

Here’s an example map using this method. It features some complex topography, a few towns (including a small dwarf hold in the northern cave and an aquatic elf city, a few spots of heavy vegetation and some barren spots, a few water features, and a particularly deadly area mid map.

Extrema Map Sample