Information Technology Reference
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of animals in the area, and so on.The effect of the presence of a tree in a cell
on the neighboring ones has been modeled by making resources flow from richer
cells to poorer ones (that possess less resources since a part of them is consumed
by the tree).The resources we explicitly included in the model are water, light,
nitrogen, and potassium.Both von Neumann and Moore neighborhoods have
been considered in the simulations.
The CA can be thus defined as:
CA
=
R, N, Q, f, I
where:
1.
R
=
{
(
i, j
)
|
1
≤ i ≤ N,
1
≤ j ≤ M}
is a two-dimensional
N ×M
lattice;
2.
H
is the neighborhood, that can be either the von Neumann or Moore neigh-
borhood;
3.
Q
is the finite set of cell state values;
4.
f
:
Q × Q
|H|
→ Q
is the state transition function;
5.
I
:
R → Q
is the initialization function.
2.1
The Cells
Each cell of the automaton reproduces a square portion of terrain with a side
ranging from three to five meters.As mentioned before, each cell contains some
resources, and can host a tree.Thus, the possible states of a cell must define:
1.The type of terrain the cell reproduces;
2.The resources present in the cell;
3.The amount of resources the cell produces at each update step, and the
maximum amount of resources it can contain, according to its type;
4.Whether a tree is present in the cell, or not;
5.If a tree is present:
a) the size of the tree;
b) the amount of each resource it needs at each update step to survive and
grow;
c) the amount of each resource stored by the tree at previous update steps;
6.Seeds scattered by trees living in the area.
If we assume that
k
types of resource and
l
different tree species are present
in the area, the finite set of states
Q
can be defined as follows:
Q
=
{
R
,
M
,
P
,T,
Z
T
,
N
T
,
U
T
,
U
T
,
R
T
,
M
T
,
G
T
,
S
}
where:
1.
R
=
{r
1
,...,r
k
}
is a vector defining the amount of each resource present in
the cell;
2.
M
=
{m
1
,...,m
k
}
is the maximum amount of each resource that can be
contained by the cell;
