SCALING PROPERTIES OF TOPOLOGICALLY RANDOM CHANNEL NETWORKS

The analysis deals with the scaling properties of infinite topological ly random channel networks (ITRNs) first introduced by Shreve (1967, J . Geol., 75: 179-186) to model the branching structure of rivers as a random process. The expected configuration of ITRNs displays scaling b ehaviour only asymptotically, when the ruler (or 'yardstick') length i s reduced to a very small extent. The random model can also reproduce scaling behaviour at larger ruler lengths if network magnitude and dia meter are functionally related according to a reported deterministic r ule. This indicates that subsets of ITRNs can be scaling and, although ITRNs are asymptotically plane-filling due to the law of large number s, scaling ITRNs can also display fractional dimension.