Information Technology Reference
In-Depth Information
Using simple probabilistic reasoning, it is easy to show that for each cell
k
in
the next state, the probability
p
of being in the “1” state is a linear combination
of the bits representing the ID of the cell. For semi-totalistic cells with five inputs,
as defined in Chap. 3, the binary representation of ID is a vector
>
!
with
y
representing the less significant bit. The value
q
of
the quiescent state (0 or 1) also influences the formulae of
p
.
As seen in Fig. 7.5. for each of the nine cells considered in the 1s5 case the de-
tailed formulae for each of the cells involved are:
Yyy y
,
,
@
98
0
Quiescent state
p
1
1
1
1
(7.4)
p
FP ID
,1,1,1,1, 0.5
y
y
,
9
8
2
1
1
2
(7.5)
p
FP ID
,1,1,1, 0.5, 0.5
y
2
y
y
,
9
8
7
4
1
1
3
(7.6)
p
FP
ID
,
y
2
y
y
y
2
y
y
9
8
7
4
3
2
8
,
(7.7)
1
1
4
p
PID
,1, 0.5, 0.5, 0.5, 0.5
y y yyy y yy
3
3
3
3
,
9
8
7
6
4
3
2
1
16
1
(7.8)
1
5
p
PID
, 0.5, 0.5, 0.5, 0.5, 0.5
y y y yyy y y yy
4
6
4
4
6
4
.
9
8
7
6
5
4
3
2
1
0
32
Quiescent state
p
0
1
1
(7.9)
p
FP
ID
,
y
y
1
0
2
1
1
2
(7.10)
p
FP ID
,0,0,0,0.5,0.5
y
2
y
y
,
2
1
0
4
1
1
3
(7.11)
p
FP ID
, 0, 0, 0.5, 0.5, 0.5
y
2
y
y
y
2
y
y
,
7
6
5
2
1
0
8
1
1
4
(7.12)
p
PID
, 0, 0.5, 0.5, 0.5, 0.5
y
3
y
3
y
y
y
3
y
3
y
y
,
8
7
6
5
3
2
1
0
16
5
is computed according to (7.8)
p
u
to
u
, forming the
next state
uncertainty profile
, are then computed by simply applying (7.3) to the above prob-
abilities. In the following we will denote
The corresponding values of the uncertainties
k
the uncertainty computed in the case
u
u
in the case of “1” quiescent state.
of “0”-quiescent state (
) and
q
0
The same uncertainty profile may be used to compute exponents of growth the
both “1s5” and “2s5” cases since the same input combinations occur in the
“2s5”
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