Modeling Real-World Terrain

Ian Parberry, "Modeling Real-World Terrain with Exponentially Distributed Noise", Journal of Computer Graphics Techniques, Vol. 4, No. 2, pp. 1-9, 2015. [Manuscript and BibTex at JCGT]

Abstract

A statistical analysis of elevation data from a 160,000 square kilometer region finds that terrain gradients appear to be exponentially distributed at all horizontal resolutions. Simple modifications to the Perlin noise algorithm and the amortized noise algorithm change the gradient distribution in each octave to an exponential distribution, resulting in varied and interesting procedurally generated terrain.

This paper was mentioned by Sean Murray in his GDC 2017 talk "Building Worlds Using Math(s)" as influencing the design of the procedural terrain generator in the Hello Games title No Man's Sky. The following video starts at 22:56.

The source code for this paper is available for free download from https://github.com/Ian-Parberry/Tobler. It has been released under the GNU All-Permissive License and contains the following notice. If these conditions are unacceptable to you, then do not download them.

The source code is written in C++ and includes project files for Windows Visual Studio 2012 and a Unix makefile using g++.

Documentation

• Generate with Perlin Noise (to generate terrain using exponentially distributed Perlin noise)
• Generate with Amortized Noise (to generate terrain using exponentially distributed amortized noise)
• Pack (to pack DEM files into a single binary file)
• Analyze (to perform a gradient analysis of a packed DEM file)
• Exponential Distribution (to experiment with exponentially distributed pseudorandom numbers)

A preliminary (and much longer) version of this paper was published under the title "Tobler's First Law of Geography, Self Similarity, and Perlin Noise: A Large Scale Analysis of Gradient Distribution in Southern Utah with Application to Procedural Terrain Generation", LARC Technical Report LARC-2014-04, Laboratory for Recreational Computing, University of North Texas, June 2014. [manuscript, BibTeX]