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3. P = {p 1 ,...,p k } is the amount of each resource produced by the cell at each
update step;
4. T is a flag indicating whether a tree is present in the cell or not;
5. Z T = {z T ,z T ,z l T ,z T } is a vector defining the size of the different parts of
the tree (in our model, roots, trunk, leaves, and fruits);
6. N T = {n T [1] ,...,n T [ k ] } are the amounts of each resource the tree takes
from the cell at each update step (depending on its size);
7. U T = {u T [1] ,...,u T [ k ] } is the vector defining the amount of each resource
needed at each update step by the tree to grow ;
8. U T = {u T [1] ,...,u T [ k ] } is a vector defining the minimum amount of each
resource the tree needs at each update step to survive ; for each i ,1 ≤ i ≤ k ,
we have u T [ i ] <u T [ i ] <n T [ i ];
9. R T = {r T [1] ,...,r T [ k ] } is the amount of each resource stored by the tree at
previous update steps;
10. M T is a vector of threshold values for different parameters defining the
tree, such as maximum size, maximum age, minimum age for reproduction,
maximum number of seeds produced for each mass unity of fruits, and so
on.These threshold values can be fixed or picked at random in a given range
when a new tree is created;
11. G T = {g T ,g T ,g l T ,g T } is a vector defining the growth rate of each of the
parts of the tree, that is, how much each part of the tree grows when enough
resources are available;
12. S = {s 1 ,...,s l } is a vector defining the number of seeds present in the cell
for each of the l species growing in the territory.
2.2
The Update Rule
At each update step of the automaton, the tree present in each cell (if any)
takes the resources it needs from the cell itself and uses them to survive, grow
(if enough resources are available), and produce seeds.If the resources available
in the cell exceed its needs, the tree stores some resources.Conversely, if the
resources available in the cell are not su " cient, the tree uses resources stored
at previous update steps.If also the resources stored are not su " cient for the
tree to survive, the tree dies.A newborn plant can sprout in a vacant cell, if the
latter contains a seed of its species, and again enough resources.
Moreover, we defined the update rule in order to reproduce the increasing
influence that a growing tree can have on neighboring cells.For example, its roots
can extend beyond the limits of the cell hosting it.Or, when it gets taller, it
shades an increasingly wider area around itself, thus having a negative influence
on the growth of other trees in its neighborhood.We modeled the impact of
a tree in a given position on its neighborhood by making resources flow from
richer cells to poorer ones.In other words, a cell hosting a large tree is poor on
resources, since the tree at each update step takes most (or all) of them.If the
neighboring cells are vacant, their resources remain unused, and thus are richer
than the one hosting the tree.Therefore, if we let resources flow from richer cells
to poorer neighbors, the effect is that in practice a large tree starts to collect
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