Information Technology Reference
In-Depth Information
Ta b l e 2 . 8
An EOL system generating the tri-somatic language
S
→
ABC
A
→
AA'
B
→
BB'
C
→
CC'
A
→
a
B
→
b
C
→
c
A'
→
A'
→
B'
B'
→
C'
C'
A'
→
a
B'
→
b
C'
→
c
a
→
F
b
→
F'
c
→
F
F
→
F
conveying important morphological parameters (e. g., lengths, angles, sizes). The
EOL system of Table 2.8 generates the tri-somatic language.
The first application of L-systems were the developments of some algae (red
alga). In these organisms all cells grow, at each developmental step. This means that,
in symbols, this mechanism corresponds to a parallel rewriting of all the symbols
occurring in a string.
A DOL system (Deterministic OL system) is defined by a triple
(
A
,
μ
,
α
)
where
A
=
{
a
1
,
a
2
,···,
a
n
}
is the
al phabet
,
α
is the
initial word
over the alphabet
A
,and
is a
string morphism
over
A
, that is a function from
A
to
A
∗
which extends to a
function from
A
∗
to
A
∗
by the condition
μ
μ
(
αβ
)=
μ
(
α
)
μ
(
β
)
.
The following is the usual representation of a DOL system, where the morphism is
expressed in a evident arrow notation.
⎛
⎞
a
1
a
2
···
a
n
↓↓ ↓
β
⎝
⎠
μ
=
···
β
β
1
2
n
A
∗
)
→ P
(
When
, we call it a
poly-morphism
, and the system is said to be
an OL system. This means that each symbol can be rewritten with many possible
strings, and, at any (parallel) rewriting step, one of the strings of
μ
:
A
μ
(
)
a
is chosen to
replace the symbol
a
(for any symbol
a
of the rewritten string).
