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In-Depth Information
3. A Generalised Cellular Automata Model
3.1. Aims
In order to allow a realistic modelling of real phenomena, the proposed model aims at
reaching the following objectives:
•
to cope with and to supersede intrinsic rigidities of classical formulation of CA;
−
the
spatial and temporal “stationarity” of neighbourhoods
. In this work, the
neighbourhoods are redefined - in general - as sets of cells whose state can
influence the variation of the current cell's state. The neighbourhood, that can also
modify in time, is hence defined on the basis of not necessarily topological
relations between objects of the simulated reality.
−
the
regularity in “discretisation” of physical system
. The graphical representations
associated to cells are considered attributes whose particular appearance is not
a
priori
subject to constraints of spatial or temporal regularity.
−
the
spatial and temporal
“
stationarity
”
of transition functions
. The transition
function (transition rule) of a cell is defined as a rule depending also on local cell's
parameters as well as on global constants and variables.
−
the
limitations with respect to external events
. By introducing the concept of
variable parameters,
it is possible that global phenomena influence the evolution of
the simulation, even on local level.
•
to design and develop a programmable simulation environment based on CAs with
features permitting the following:
−
to separately model phenomena of different nature interacting within the same
physical scenario: this is obtained with the structuring
in
layers
of the scenario.
Within different layers, various relevant phenomena are simulated according to
assigned rules.
−
to include within a CA-based simulation other calculation models that dynamically
determine values of one or more variable parameters.
−
to obtain an interactive simulation environment capable to import and export
scenarios from and into a GIS in an automatic or a guided manner.
3.2. The Model
The founding element of any CA model is the
cell
. In our CA, on the basis of the
homogeneity of forms assumed by certain attributes,
n
different
types
of cells are
defined.
Let
c
(i,t)
indicate the configuration of a generic cell, of
i-
th type, at the moment
t
of
the simulation.
A set
C
of
c
(i,t)
cells homogenous by type belongs to a
layer of cells
, which will be
indicated as
L
(i,t)
and is defined as follows:
L
(i,t)
(
C
,
P
L
)
(
1
)
