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3. Urban Cellular Automata and Inverse Problem
As far as an Urban Cellular Automaton is concerned, the challenge is trying to
reproduce the behavior of the system “city”; so, the core of this research is to
determine the transition rules of an Urban CA. The data we need are maps displaying
cells' characteristics, i.e. land use in our case studies; maps are like pictures of the
city taken in different years, and their sequence displays the changes that affected the
city. What we are looking for are the rules that governed these changes, and they
should be derived by the comparison of couples of successive maps, trying to extract
the rules that directed the transitions happened between the maps. It is the same
situation that faces a chess player who compares two configurations on a chessboard
and tries to extract the moves that were made.
The most important issues are data availability and their quality. The first is
relevant because we are dealing with a system that cannot be reproduced in
laboratory, so we are not able to gain more data easily. Two important factors
regarding data quality are the span of time covered by data and the frequency they are
collected with; both these issues do affect greatly the precision we may obtain in
structuring the model with a given data-set. In fact, it is worth reminding the reader
that data are the starting point of the procedure and, of course, different data do lead
the observer on different paths.
Even if the purpose of this approach is to extract as more as possible information
from data, the observer has often to choose, because there are some critical points
where data cannot help him anymore; of course every choice must be tested against
the evolution of the city. The first choice that is necessary is the category of models in
which looking for the best fitting for our case studies; evidently, we have chosen CA.
This implies that we will use a kind of “if...and…then” rules; but rules are only one of
the elements of a CA, so a choice must be made for grid, neighborhood, states and
time. Because of these elements are strictly connected each other, the setting of each
element influences the result we obtain in structuring the transition rules.
We are free to decide which kind of grid is the best, its dimensions, the function
that gives the neighborhood, the number of land uses to consider and the span of a
time step ∆t. We choose to adopt a regular grid, made of 100m X 100m square cells;
the neighborhood is a Moore one, considering only the first eight cells around, and its
class is the prevalent among its cells; there are 12 land uses: residential continuous
urban fabric, residential discontinuous urban fabric, industrial areas, commercial
areas, public and private services, roads and railways, abandoned land, construction
sites, green urban areas, crops, forests, canals and rivers. The calibration of time step,
actually, is a different kind of freedom, because the frequency data are collected with
inevitably forces the choice of the time step and, in the end, the precision we get in
predictions made using the model. In fact, rules derived from the comparison of maps
N years far in time can be applied to make predictions on N years time intervals; you
cannot hope to get more precise results with that set of rules.
Moreover, the issue about asynchronous transition is not faced in this paper, and all
transitions will be assumed as synchronous.
