Information Technology Reference
In-Depth Information
Based on equation 8 and 9, the state of cell
j
at time
t+1
can be determined as fol-
lows:
1 if P
j
(t) =P
j'
(t) and j'∈ [1 ∼ ∆L(t)]
(10)
S
j
(t+1)=
0 if not
Simply, totally ∆
L(t)
cells will be selected at time
t
for the transition from develop-
able land (0) to urban (1) according to their development potential values
P
j'
(t). L(t)
is
to be determined as below.
Another advantage of project-based CA modelling is able to control the temporal
development pattern of each project. Previous studies suggest that urban development
process (
L(t
) in eq.4) follows a logistic curve over time
[17]
.
The logistic curve is
illustrated as eq. 11.
L(t)=1/(a+b*e
(-c*t)
)
(11)
Assuming that
L(0)=L
0
=1/(a+b)=1, L(n)=L
n
=1/(a+be
(-cn)
)=L
d
,
the parameters
a
and
b
can be calculated as the functions of parameter
c
(eq.12):
1
−
l
(12)
n
a
= 1
−
b
b
=
−
cn
l
(
e
−
1
)
n
The shape of logistic curve usually represents the speed of urban development over
time, which is controlled by the parameter
c
and
n
. Here, in simplicity, temporal con-
trol is classified as three types: slow growth, normal or basic growth and quick
growth, which indicates three distinguishing scenarios (eq.13). Of course, you can
define more classes or even use fuzzy logic.
Quick growth:
c
*n
> 25
Basic growth:
c* n
<25 and >15
Slow growth:
c
* n < 15
(13)
The selection of temporal control pattern is a top-down process of decision-making
as shown in equation 14. Where
y
denotes the real time-year (
1
∼
m
) such as 1993
(
y
=0) and 2000 (
y
=7), which is different from iteration number
t
(
1
∼
n
) in simulation.
G(y)= L
d
(y) y
≤
m
(14)
