River networks around the world exhibit statistical scaling laws,
including the distribution of independent basin sizes in landscapes. The
widespread occurrence of these patterns in various landscapes suggests
that there are fundamental, but not yet fully understood, processes
responsible for these power law distributions. This study investigates
the distribution of independent basin areas across 25 islands worldwide,
revealing a clear adherence to a power law pattern. The research
suggests that the power law exponent is influenced by landscape boundary
characteristics, such as the compactness coefficient and fractal
dimension, with the exponent value increasing with these factors.
Furthermore, the study demonstrates the development of power law
patterns in basin areas using a probabilistic network growth model. This
model, based on a preferential headward growth mechanism, underscores
the significant roles of boundary conditions and headward growth
dynamics in the self-organization of power law patterns in fluvial
landscapes.