Self-organized approach to modeling hydraulic erosion features

Landforms affected by hydraulic erosion exhibit emergent features, such as channels that organize into networks through tributary capture. Our procedural modeling method attempts to simulate these features realistically by using a variant of a principle followed by many physical self-organized systems. The general nature of the approach makes it applicable to modeling river-like channels on top of terrains and cave-like channels inside of volumes of porous rock. AVALANCHING Rodrı́guez-Iturbe et al. have proposed an explanation for the evolution of river networks in terms of self-organized criticality [3], a theory of fractal dynamics in which a physical system approaches a scale-free attractor state. During this process the system undergoes avalanches of change that distribute detail throughout the entire system. We have found that utilizing avalanching separately from its parent theory makes it possible to re-introduce scale into their dynamics. This way the produced objects are not restricted to having a scale-free scaling character. In the following example avalanches transport material based on a slope constraint, smoothing the initial terrain, which is uniformly rough. The scaling character can be judged using spectral density S(f ), which is a way to visualize the distribution of frequencies in a signal. The spectral density of the resulting terrain falls off approximately as 1 fβ , which can be confirmed via a triple-log plot that turns the falloff into a linear one. The 1 fβ falloff corresponds to self-affine scaling, which is appropriate for modeling hydraulic erosion features. For example, rivers have been found to follow several different power laws in respect to drainage area and bifurcation, which make them selfaffine fractals. In general, a terrain dominated by erosion can be expected to be close to a self-affine fractal in shape, because of its unequal scaling behaviour in horizontal and vertical directions. EROSION SIMULATION As an abstraction aid, we discretize each type of the problem setting as a graph with nodes representing locations on a terrain in the 2D case and voxels of a porous rock matrix in the 3D case. A key difference is that a voxel can only contain up to one unit of water, as determined by local porosity.