Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
maximize

Fractal Landscape Classification

Description

These worlds have been created by a very simple fractal generator. The base mesh is constructed starting with an octahedron which is recursively refined by triangle bisection. Height values at refinement vertices are computed by adding a normally distributed random variable to the interpolated height from hierarchical neighbors. The variance of the random variable depends negative exponentially on the level of the current vertex (which is in fact the Brownian bridge construction for Brownian motion). By changing the exponential factor, terrains with different roughness characteristics can be created. For a more thorough explanation see the literature below.

The more scientific question behind all this is fractal classification of real landscapes. By computing the fractal exponential factor from topographical data it is possible to classify the world around us depending on scale and location.

Examples

Click on the pictures to see an enlarged version.

Each of these worlds is uniquely defined by one single number: the initial seed of the (here linear congruential) random number generator. By simply using different seeds, a great variety of worlds can be generated. By right clicking on the worlds you can view the images at full resolution. You can theoretically zoom into the terrain infinitely, although you need to create and store a lot of random numbers for this.

The images have been computed and rendered (using OpenGL) on an SGI O2 in a few seconds. Color just depends on the height value, while oceans are simply constructed by thresholding. On some worlds you can see some artifacts from the initial (octahedral) mesh. These could be circumvented by choosing a finer initial mesh, although in the long run they cannot be avoided once you zoom in. Dominant structures will always generally align with a coarser triangulation.

References

Related Projects


Thomas Gerstner