Procedural Terrain Heightmap Generation using DLA (Diffusion Limited Aggregation)

In the past days I have worked on improving the terrain generation function. The basic 3D perlin noise works well to generate a generic terrain, but to get more appealing mountains, different approaches are necessary. For height maps, perlin noise can be used too, but does not look as appealing as erosion based terrain.

To achieve similar looking structures, Diffusion-limited_aggregation (DLA) is the solution. The initial result looks as the upper left image. Using gaussian smoothing, the final height image, lower right, can be obtained. The final rendering of the 3D image follows on the lower left.

The algorithm requires three steps:

• Create the DLA image. When attaching a new point, draw a line to the referring point and add random midpoint displacement to the line to make it more interesting.
• Create multiple copies of the DLA image and apply gaussian smoothing. The smoothing radius is increased exponentially from one image to the next.
• Sum up all copies weighted and normalize the result.

DLA cannot easily create an infinite procedural heightmap, but using a sparse set of points, its possible to cover a quite large area and refine the DLA once you get closer. Due to the smoothing radius of 1..256 here, one pixel is influenced by an area of 512x512 pixels around the target pixel.

I have searched to find a reference for this algorithm, but so far I could not find one yet. If you find a good reference, you can post it in the comments.

The uppermost Heightmap can be downloaded as OBJ format here. (viewable with MeshLab e.g.)

Below more examples. The corresponding heighmaps are:
Heightmap1 Heightmap2 Heightmap3
You can use the GeoGen Studio to view the results.

The original heightmap data is float, but the images are limited to 256 steps.
The computation time is about 1min for 1024x1024.