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This model represent the urban development as a process of settlement of agents (random walkers) randomly looking for a place where to settle. Two possibilities are available to a random walker for settling: everywhere at random with a low probability, or nearby already settled random walkers. More than one agent can settle in a patch, and once settled an agent stops moving. This model is able to represents the scattered shape of the urban agglomeration as resulting from sprawl and leapfrogging dynamics of urban evolution.


At the beginning two agents are put in the center of the surface. In each step, two main phases are performed: the generation of new agents and the location of that not yet located. Because the place of settlement depend from where the settlers are initially located, this aspect plays a crucial role in the model. Roughly speaking, candidates as birth place of settlers are the patches where many settlers are located. It is for this reason that patches are sorted by the number of settlers plus a random factor Gumbel distributed, and the new settlers are located, as birth place, beginning from the first sorted patch. After that, each new agent begins a random walk. In each visited patch the agent evaluates if stay or not. With a low probability the agent may stay everywhere. Otherwise, the agent decide to locate where other settlers are or close to a road, in case it exists. In this second case the density of agent which influences the decision is calculated after a diffusion of the number of settled agents.


The model allows one to observe the self-organized growth of the urban fabric. You can establish the spatial context, including the roads network and the most important parameters of the simulation.
These are:
a) probability to settle. The probability that a random walker settles at random. The greater this parameter is, the more punctuated and scattered is the resulting urban pattern
b) variability: the random factor for choosing the place from where to start the random walk. When zero, one only cluster grows in the center. Increasing the value one obtain a more polinucleated urban fabric
c) diffusion-factor. It regulates the intensity of diffusion of the value of the population. Because it is utilized for locating random walkers, the greater is the value of this parameter the grater is the possibility the urban fabric expands as in a diffusion process, generated fro the existing clusters
d)road-factor. In case you hae designed a roads network, this factor influences the location of a random walker in relationship with a road. The greater the value the greater the influence of roads in settling random walkers.

First click on setup-clear, and the surface, green colored, will appear. To draw the roads network click on draw-roads, and later pushing the right button of the mouse you can draw the roads network that will appear yellow colored. You are free to draw the network you like. Note that the connectivity of the roads network is not checked. Roads are not considered in fact as a network but only as cell crossed by roads. It is your concern to draw a roads network which resemble the most the characteristics of a true roads network.

Then click on GO and the growth will start.

To repeat the simulation without changing the roads network, select settlers-only in the chooser clear, and later click on setup-clear. The built cell will be canceled, but the road network remain unchanged. You are thus able to change the rule and to repeat the simulation.


The number of settlers in each patch is represented with red tone : light represents the highest value, dark the lowest. In the right side the average density in relation with the distance is represented, as well as the density along a horizontal (H) and vertical (V) transects, passing through the center of the surface. Watching at these two curves one appreciates the distribution of picks of density along the transects


Comments are welcome, as well as suggestions to upgrade the model. Please send you comments and suggestions to semboloniATunifi.it

Copyright 2011 Ferdinando Semboloni. All rights reserved.