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Fig. 1.
Snapshots of CA evolution simulating fire propagation in 2D space, borgered
by a two walls
4)The array
Ω
B
(
t
+ 1)is averaged according to (2)for cells whose neighbor-
hood
N
Av
(
i,j
)
∈ M
.Ifin
N
Av
(
i,j
)there are
r
cells out of
M
, then
1
q −r
v
(
i,j
)
=
v
i,j
.
N
A
v
(
i,j
)
The resulting
Ω
R
(
t
+ 1)is the initial averaged array for the next iteration.
In Fig.1 some snapshots are given displaying the CA evolution.
Chemical reaction
. A great number of second order PDE systems modeling
a reaction of Belousov-Zhabotinsky has been proposed and studied. One of them
(a simplified one)[7] is chosen as an example for replacing the PDE system by
a probabilistic CA. Using the notation of the paper the PDEs may be expressed
as follows.
∂t
=
d
∂
2
u
1
∂y
2
+
f
1
(
u
1
,u
2
)
,
∂u
1
+
∂
2
u
1
∂x
2
(19)
du
2
dt
=
f
2
(
u
1
,u
2
)
.
In (20)
d
is a diffusion coe
%
cient,
f
1
(
u
1
,u
2
)=
1
d
(
u
1
(1
−u
1
)
−zu
2
(
u
1
−s
)
/
(
u
1
+
s
))
,
2
(
u
1
,u
2
)=
u
1
−u
2
