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Fig. 1.
Relations s between cells and layers in the proposed model
3.4. “Ingredients” of a Cellular Automaton
The generalisation proposed by our model requires, for each application to a concrete
case-study, a preliminary structuring-programming and initialisation. The design of an
cellular automaton requires in fact two subsequent phases:
1.
Design of the structure and rules
. This is done through the definition of the
number and types of the following elements::
•
the number of global parameters
g
:
P
G
={
p
G1
,
p
G2
,
…,
p
Gg
} and their respective
domains of definition
P
G1
,
P
G2
,
…,
P
Gg
;
•
the eventual functions of variation of parameters
p
Gk
= f
k
(
t,
P
Gk
);
•
the number of cell types
n
and the number of layers
l
;
•
for each layer:
−
the number of layer's parameters
c
:
P
L
={
p
L1
,
p
L2
,
…,
p
Lc
} and their respective
domains of definition
P
L1
,
P
L2
,
…,
P
Lc
;
−
the eventual functions of variation of parameters:
p
Lk
= f
k
(
t,
P
Lk
, P
G
);
−
the domain of definition of cell states
S
(i)
;
−
the rules for the definition of sets
H
⊆
L
(i)
.
C
of cells constituting the
horizontal
neighbourhood
;
−
the number of local parameters
m
:
P
={
p
1
,
p
2
,
…,
p
m
}
and their respective domains
of definition
P
1
,
P
2
,...,
P
m
.
−
the eventual functions of variation of parameters:
p
k
= f
k
(
t,
P
k
,
P
L
, P
G
);
−
the eventual rules for the definition of cell's
vertical neighbourhood
V
={
V
1
,
V
2
,…,
V
q
} and their respective sets Σ of
transferring functions
σ
k
;
−
the eventual definition of graphical object type characterising cells.
2.
Scenario Initialisation
. This comprises the definition of initial values of global
and layer parameters, the definition of initial values of cells' states and the
initialisation of graphical objects associated to cells.
