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]


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.

Application in the Game Industry

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.


Videos rendered with Terragen 3.

Source Code

The source code for this paper is available for free download from 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.

Copyright Ian Parberry, (date).

This file is made available under the GNU All-Permissive License.

Copying and distribution of this file, with or without
modification, are permitted in any medium without royalty
provided the copyright notice and this notice are preserved.
This file is offered as-is, without any warranty.

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


Preliminary Version

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]

Created June 2, 2014. Last updated August 3, 2019.