Abstract
An empirical rule (Horton's rule) is known to exist between numbers of branches and lengths of rivers.
A drainage-basin network is simulated based upon a concept of random walk. Simulation is performed for various cases (inland lake, island surrounded by the sea, and alluvial fan). Various effects such as size and form of the area, and location of the outlet are examined. The process of evolution of drainage-basin is also examined.
It is concluded that the simulated results are consistent with the empirical rules. In addition a concept of entropy is introduced to discuss the evolution of drainage-basin system.
