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Ta b l e 2 . 9 A string theory associated to a Chomsky grammar G
Derive ( S )
Terminal ( a )
for every a T
Rule ( α , β )
for every α β R
x (( Terminal ( x ) Terminal ( y )) Terminal ( xy ))
x , y , z (( Derive ( xyz ) Rule ( y , w )) Derive ( xwz ))
x (( Derive ( x ) Terminal ( x )) Generate ( x ))
Cells of this organism are indicated by the symbol F , cells inside brackets are
“branches”, inclined (alternatively in opposite verses) with respect to a main grow-
ing axis. For n
called a basal part
and an apical part. Every second cell in the basal part carries a non-branching fila-
ment. These filaments develop linearly in time, they add at each stage one new cell.
At stage 6 the lengths of these filaments are 3, 2, 1, respectively. The apical part
at stage 6 consists of four cells without any branches. In the following stages, the
apical part is a repeat of the apical part at the previous stage, together with two new
cells at the end of the apical part. The second of these new cells carries a branch,
identical to the whole organism six stages before.
>
5 we distinguish in R
(
n
)
two parts B
(
n
) ,
A
(
n
)
R
(
0
)=
F
R
(
1
)=
FF
R
(
2
)=
FFFF
R
(
3
)=
FF
[
F
]
FF
R
(
4
)=
FF
[
FF
]
FF
[
F
]
FF
R
(
5
)=
FF
[
FFF
]
FF
[
FF
]
FF
[
F
]
FFFF
R
(
x
+
6
)=
B
(
x
+
6
)
A
(
x
+
6
)
A
(
5
)=
FF
A
(
x
+
6
)=
FF
[
R
(
x
)]
A
(
x
+
5
)
B
(
x
+
6
)=
FF
[
L
(
x
+
3
)]
FF
[
L
(
x
+
2
)]
FF
[
L
(
x
+
1
)]
L
(
0
)= λ
L
(
x
+
1
)=
FL
(
x
)
.
The following derivation is based on the equations defining Red Algae structure:
R
(
10
)=
B
(
10
)
A
(
10
)
A
(
10
)=
FF
[
R
(
4
)]
A
(
5
)=
FF
[
R
(
4
)]
FF
=
FF
[
FF
[
FF
]
FF
[
F
]]
FF
B
(
10
)=
FF
[
L
(
7
)]
FF
[
L
(
6
)]
FFL
(
5
)=
FF
[
FL
(
6
)]
FF
[
FL
(
5
)]
FFL
(
5
)=
F 7
F 6
FFF 5
FF
[
]
FF
[
]
F 7
F 6
FFF 5 .
R
(
10
)=
FF
[
FF
[
FF
]
FF
[
F
]]
FFFF
[
]
FF
[
]
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