Spatial modelling

 Equations in drainage1

Variable h : Height array
h = [height]
Where:
[height]=cell/height
Comments:
Outside the cell submodel to provide an array of heights the elements of which are addressable from inside /cell and "/cell/neighbours and self" . (Inside a submodel only values for the current instance is accessible.)

Equations in cell

Variable col
col = index(1)-(row-1)*3

Variable flow direction : Bearing from north to lower neighbour (degrees)
flow direction = if nid_min==1 then 225 elseif nid_min==2 then 180 elseif nid_min==3 then 135 elseif nid_min==4 then 270 elseif nid_min==6 then 90 elseif nid_min==7 then 315 elseif nid_min==8 then 0 elseif nid_min==9 then 45 else-1
Comments:
-1 if no lower neighbour

Variable id
id = index(1)

Variable nid_min : Neighbour ID of the lowest neighbour
nid_min = posleast([h])
Where:
[h]=neighbours and self/h
Comments:
If there is no lower neighbour the value will be the the Neighbour ID of itself, i.e. 5. The Neighbour ID is the index of the "neighbours and self" submodel instances.

Variable row
row = int((index(1)-1)/3)+1

Equations in neighbours and self

Variable col : Column of the cells neighbour's and itself
col = col+element([-1,0,1,-1,0,1,-1,0,1],index(1))
Where:
col=../col
Comments:
If the cell is at the edge of the grid some of the "neighbours" will be outside the grid.

Variable h : Height of the cell's neighbours and itself
h = if col>=1 and col<=3 and row>=1 and row<=3 then element([h],nid)else 1.0E+300
Where:
[h]=../../h
Comments:
Height is assigned the value 1.0E+300 if the "neighbours" will be outside the grid.

Variable nid : ID of the cell's neighbours and itself
nid = 3*(row-1)+col
Comments:
If the cell is at the edge of the grid some of the "neighbours" will be outside the grid

Variable row : Row of the cells neighbour's and itself
row = row+element([-1,-1,-1,0,0,0,1,1,1],index(1))
Where:
row=../row
Comments:
If the cell is at the edge of the grid some of the "neighbours" will be outside the grid.

 Equations in antsworld

Variable n
n = int(sqrt(size(World)))

Variable neighbour offsets a
neighbour offsets a = [0,1,1,0,-1,-1]

Variable neighbour offsets b
neighbour offsets b = [1,0,-1,-1,0,1]

Variable neighbour offsets c
neighbour offsets c = [-1,-1,0,1,1,0]

Equations in Ants

Immigration im1
im1 = 0.1

Variable Pheromone output
Pheromone output = 1

Variable my body size
my body size = 2

Variable my direction
my direction = ceil(rand_var(0,6))

Variable my head size
my head size = 1

Variable my space
my space = infront=element(last([neighbour_spaces]),my_direction),if time()==init_time() then 5102 elseif infront>0 then infront else prev(1)
Where:
my_direction=my direction
[neighbour_spaces]=neighbour spaces

Variable neighbour spaces
neighbour spaces = [neighbours_at]
Where:
[neighbours_at]= ../location/neighbours (to Ants in at)

Variable x
x = x_at
Where:
x_at= ../location/x (to Ants in at)

Variable y
y = y_at
Where:
y_at= ../location/y (to Ants in at)

Equations in location

Condition cond1
cond1 = index(1) is my_space_at
Where:
my_space_at= ../Ants/my space (from Ants in at)

Variable Pheromone
Pheromone = Pheromone_output_at
Where:
Pheromone_output_at= ../Ants/Pheromone output (from Ants in at)

Variable neighbours
neighbours = [their_ids_has]
Where:

[their_ids_has]= ../World/neighbours/their ids (from World in has)

Variable x
x = x_has
Where:
x_has= ../World/x (from World in has)

Variable y
y = y_has
Where:
y_has= ../World/y (from World in has)

Equations in World

Compartment Pheromone
Initial value = 0
Rate of change = + Addition

Flow Addition
Addition = sum({Pheromone_has})
Where:
{Pheromone_has}= ../location/Pheromone (to World in has)

Variable a
a = ceil(index(1)/n)-ceil(n/2)
Where:
n= ../n

Variable b
b = index(1)-n*a-ceil(n*n/2)
Where:
n= ../n

Variable c
c = -a-b

Variable my id
my id = index(1)

Variable x
x = 50+(a-c)* 0.866

Variable y
y = 50+b* 1.5

Equations in borders

Variable x
x = off=sqrt(3/4),x+element([0,off,off,0,-off,-off],index(1))
Where:
x= ../x

Variable y
y = y+element([1, 0.5, -0.5,-1, -0.5, 0.5],index(1))
Where:
y= ../y

Equations in neighbours

Variable a
a = a+element([neighbour_offsets_a],index(1))
Where:
a= ../a
[neighbour_offsets_a]= ../../neighbour offsets a

Variable b
b = b+element([neighbour_offsets_b],index(1))
Where:
b= ../b
[neighbour_offsets_b]= ../../neighbour offsets b

Variable c
c = c+element([neighbour_offsets_c],index(1))
Where:
c= ../c
[neighbour_offsets_c]= ../../neighbour offsets c

Variable their ids
their ids = if all([a,b,c]> - (n/2)) and all([a,b,c]