Information Technology Reference
In-Depth Information
where
P
L
={
p
L1
,
p
L2
,
…,
p
Lc
}
is a set of
c
layer's parameters
that, according to a
transition function and together with other values, concur to the evolution of the
scenario. With the notation
L
(i,t)
.
C
and
L
(i,t)
.P
L
will be indicated the elements of
L
(i,t)
(each layer can contain only cells of one type; it is not excluded more than one layer
containing cells of the same type).
Thus, the configuration CA
(t)
of a specific cellular automaton at the moment
t
is
entirely defined by the pair
P
G
and
L
:
CA
(t)
=(
P
G
,
L
)
(
2
)
where:
•
P
G
={
p
G1
,
p
G2
,
…,
p
Gg
} (also CA
(t)
.P
G
) is a set of
g
global parameters that concur in
regulating the evolution of the CA according to cells' transition functions
•
L
={
L
(1)
,
L
(2)
,
…,
L
(l)
} (also CA
(t)
.
L
) is a set of all
l
layers of cells.
Both the parameters
p
Gk
and the parameters
p
Lk
can assume values in predefined
domains, continuous or discrete, and can vary in time according to assigned laws.
In particular, it is assumed that:
−
for a generic
p
Lk
, the possibility to vary with respect to the moment
t
, with respect
to the values of other parameters of layer
p
Lj
∈
P
Lk
⊂
P
L
where
j
≠
k
, and with respect
to global parameters according to an assigned function
p
Lk
= f
k
(
t,
P
Lk
, P
G
);
−
for a generic
p
Gk
, the possibility to vary with respect to the moment
t
, and with
respect to the values of other global parameters
p
Gj
∈
P
Gk
⊂
P
G
where
j
≠
k
and
according to an assigned function
p
Gk
= f
k
(
t,
P
Gk
);
−
for both types of parameters, the possibility to depend of a generic calculation
model that evolves in parallel with the cellular automaton.
3.3. The Cell
The generic cell of
i
-th layer at the instant
t
is defined as:
c
(i,t)
(
s
,
H, V
,
P
, φ, Σ
, o
)
(
3
)
where the symbols between the parenthesis indicate
attributes
characterising the cell.
As we shall explain later, the form attributes assume determines the type, or better the
class
, of the cell. Being
c
(i,t)
.
X the attribute X of the cell
c
(i,t)
in the instant
t
of the
simulation, in (4) we will have that:
•
s
is the cell's
state
that assumes values from a set of discrete of continuous states
S
(i)
.
•
H
⊆
L
(i)
.
C
is the set of cells constituting the
horizontal neighbourhoods
(cfr. fig. 1).
These are cells that, according to the transition functions φ, can determine a change
of the state
s
of the generic cell belonging to the set
L
(i)
.
C
. The cells of set
H
, that
potentially can change during the evolution of the system, can be defined:
−
as an explicit assignment of specific cells;
−
as a result of a generic
query
on the set of cells
L
(i)
.
C
;
A particular topologies of neighbourhood is comprised implicitly in the latter
possibility.
