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a
H
=sin(
B
max
)
∗
max(
H
c
,H
mean
)
a
S
=
H
mean
/
0
.
455
a
B
=
1
2
(min(
H
p
,H
c
)+
rand
+
B
min
)
a
dir
=min(
rand,B
min
)
−
sin(
d
p
)
Fig. 3.
An example GP-tree for the four outputs
a
H
,
a
S
,
a
B
,and
a
dir
3. Color the current pixel according to the output variables.
For a pixel, each agent will probabilistically decide whether to paint it or
not. The color to paint for the current pixel is determined by (
a
H
,a
S
,a
B
)
from step 2.
4. Move to the next pixel in the direction given by output.
Each agent will move to the next pixel according to direction
a
dir
, no matter
the current pixel is colored or not. This study develops two strategies for
the moving direction, i.e., deterministic and uncertain direction. The first
strategy moves the agent to the pixel in the direction of
a
dir
deterministically.
In the second strategy, the nine directions can be selected for the agent to
move, where the
a
dir
direction has a high probability 1
/
2 while each of the
remaining eight directions has a low probability 1
/
16 to be selected as the
moving direction. This uncertainty in the moving direction is expected to
diversify the generated patterns.
3.2 Genetic Operators
The genetic operators of GA include parent selection, crossover, mutation, and
survival selection. In this study, we employ the
k
-tournament selection in view
of its recognized performance. The proposed GA uses a 5-tournament selection,
which selects the best of 5 randomly picked chromosomes as a parent. Performing
this selection twice gains a pair of parents for subsequent crossover and mutation.
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