Information Technology Reference
In-Depth Information
•
P
={
p
1
,
p
2
,
…,
p
m
}
is a set of
m
local cell's parameters
that, together with layer's
parameters
L
(i,t)
.P
L
and global parameters
P
G
, determines the transition from one
state of the cell to another. The generic
p
k
∈
P
k
, where
P
k
is the domain of variation
of parameter, can be calculated:
−
with respect to the time
t
, with respect to values of other parameters
p
j
∈
P
k
⊂
P
(where
j
≠
k
) and to global and layer's parameters, according to a function
p
k
= f
k
(
t,
P
k
,
P
L
, P
G
), assigned analytically of in a tabular form;
−
according to a generic calculation model evolving parallel with the CA;
−
according to a
transferring function
σ
k
∈Σ (cfr. fig. 1), starting from states
s
of a
defined subset of cells
V
k
={
c
1
(j)
,
c
2
(j)
,…,
c
v
(j)
} belonging to a layer
L
(
j
)
where
j
≠
i
:
p
k
=σ
k
(
c
1
(j)
.
s,
c
2
(j
)
.
s,…,
c
v
(j)
.
s)
(
4
)
The subset of cells
V
k
can be defined analogously as with the definition of
horizontal neighbourhoods. If
q
≤
m
is the number of parameters depending on the state
of groups of cells belonging to layers different than
L
(i)
, the
vertical neighbourhoods
of cells
is defined as the set:
V
={
V
1
,
V
2
,…,
V
q
}
(
5
)
where:
•
φ is the
transition rule
of the cell: the state
c
(i, t+1)
.
s
is obtained from the current state
c
(
t
)
.
s
following the relation:
c
(i,t+1)
.
s
= φ(
c
(i,t)
.
s
,
c
1
(i,t)
.
s
,
c
2
(i,t)
.
s
,…,
c
h
(i,t)
.
s
; AC
(t)
.P
G
,
L
(i,t)
.P
L
,
c
(i,t)
.P
)
(
6
)
where {
c
1
(i, t)
,
c
2
(i, t)
,…,
c
h
(i, t)
}=
c
(i, t)
.H
⊆
L
(i)
.
C
is the horizontal neighbourhood at the
moment
t
. The global and layer variable parameters are updated (in this order) before
the application of the rule φ.
•
o
is a graphical object, eventually geo-referenced, that can be chosen from a finite
set
O
of objects each characterised by an adequate vectorial graphical description.
Any relevant entity of the simulated phenomenon can be represented by one or, if
necessary, can be “discretised” and represented by more than one graphical objects
In the exposed definition of cells, we have implicitly abandoned the classical
“discretisation” of space in regular grid: in fact, potentially, different cells belonging
to the same layer can be represented by different graphical objects. Furthermore, it is
not necessary that the entirety of graphical objects representing cells of a layer
constitutes a complete and exhaustive partitioning of the space.
In particular, a cell belonging to a layer can be seen as an
object
-instance of a
class
(the class of
that
layer's cells) characterised by common
properties
: the domain of
state variation
S
(i)
, the number
m
of parameters with respective domains of definition
and variation
P
1
,
P
2
,...,
P
m
, the form of transition rules, the form of horizontal and
vertical neighbourhoods determination rules, the form of parameters evolution rules,
the transferring functions Σ and connection with other simulation models.
