Procedural Worlds

• A collection of notes and insights on how to procedurally generate a world (i.e., how Minecraft and Dwarf Fortress do it)

Noise Based Generation §

• Consider how we store map data.
  • All methods of storage revolve around discretizing the representation in some form and generating data based on this representation ¹
  • Some options for discretizing include using Voronoi maps (hard to manipulate but smoother) and Tiled Arrays (easier to manipulate but may look artificial)

• With regards to generating map data, we require some form of noise function.

  • Complexity is achieved by stacking layers of noise on top of each other.
  • Noise has a few parameters:
    • Frequency - controls the level of “zoom” that the noise function exhibits. More specifically, it bounds the gradient at each point in the map. Higher frequency means a finer level of detail
    • Wavelength - inversely proportional to frequency. Dictates the distance between seemingly repeating patterns in the map / noise function used.
    • Octaves - the number of frequencies we stack on top of each other. Each generated frequency is weighted with a corresponding amplitude. For example
      can be normalized to be between and .
  • One thing to be wary of is any visual artifact due to the noise function used
    • Each term in an octave may overlap with each other and produce artifacts.
  • Note: Perlin Noise is not uniformly distributed. It roughly follows a Gaussian Distribution.

• More Noise Functions. These are typically build off of Perlin Noise

• For maps, we can make use of curves (i.e., exponentiation curves) to exaggerate differences between troughs and crests.

• Generate biomes and climates using multiple maps that are related to each other.

  • Some examples of maps to use:
    • Temperature
    • Atmospheric Pressure
    • Moisture
    • Level of insolation, including seasonal effects
    • Latitude / Longitude.
  • We use some form of thresholding to differentiate biomes based on the values of the different maps and our rules for what biome corresponds to each combination of condition.

• Map generation can be viewed algorithmically as a pipeline for transforming or interpreting noise map data. Each transformation in this pipeline is some function

• Islands on the map can be generated by using a shaping function. It takes the distance between a center point. The output of the shaping function is then used to weight the value of the map.

• We can also apply redistribution functions which act on the value in the map and remaps them to a new value. Some examples:

  • Create ridges by accentuating the middle.
  • Make the map more discretized (using a staircase function).

• If we want to have the map wrap around, in such a way that the map remains continuous at the wrap around points, we can generate the map with a cylindrical, toroidal, or spherical projection in mind.

  • One approach is to generate the map one dimension higher, create a loop in this high dimensional space, and then project down to our desired dimension.

Key Algorithms §

• Perlin Noise
• Wavelet Noise

Simulation Based Approaches §

Links §

• Undiscovered Worlds - Guidelines for Procedurally generated worlds
• Red Blob Games Making Maps with Noise functions
• Azgaar’s Blog on Procedural Worlds

Footnotes §

1. Analogous to Computer Graphics which makes use of vertices. In fact, we may think of terrain as a mesh and the vertices as our sample points ↩