Peano network

The bias of the transport through the network can be defined as — out in — 2P(jut We focus on an oriented Peano network at the first level of construction. Figure 6.6 shows this network, where the segment AB is the backbone direction. 

Great efforts have been undertaken to describe the intricate geometry of river networks [363]. In Chap. 6 we illustrated some models, such as the Peano network, which resembles fractal river basins. Another well-known structure that was proposed to describe better the evolution and formation of river basins and that agrees with most of the observations is the Optimal Channels Network (OCN) model, based on some optimization principles that minimize the energy expenditure by the net-... 

Figure 7.11 summarizes the results obtained from (7.42) (lines) and compares it with random walk simulations on the Peano basin up to order Q = 10 (open circles) and OCNs (full circles). In the simulations, all the walkers were initially on the left side of the lattice and the front advanced to the right. A logistic growth rp(l — p) was introduced at every site at every time step to simulate the reaction process. For the OCNs, we averaged over 10 different 200 x 200 networks. 

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