FRACTAL AGGREGATES ON GEOMETRIC GRAPHS

We study the aggregation process on the geometric graph. The geometric graph is composed by sites randomly distributed in space and connected locally. Similar to the regular lattice, the network possesses local connection, but the randomness in the spatial distribution of sites is considered. We show that the correlations within the aggregate patterns fall off with distance with a fractional power law. The numerical simulation results indicate that the aggregate patterns on the geometric graph are fractal. The fractals are robust against the randomness in the structure. A remarkable new feature of the aggregate patterns due to the geometric graph is that the fractal dimension can be adjusted by changing the connection degree of the geometric graph.