ModelId:

landuse1

SimileVersion:

3.1+

This model illustrates one approach to modeling land-use dynamics. In this case, individal units of land ("patches") can be in one of two states: forest or crop. Each patch can switch from one state to the other, depending on various factors including the current state of the forest or crop in the patch.

Results:

The following sequence of screen shots shows how the cropping area on the left (yellow) gradually encroaches into the forest. It is then replaced by young forest (light green), until eventually it in turn is cut down and the cycle continues.

ModelId:

hexagon

SimileVersion:

3.1+

This model shows how it is possible with Simile to disaggregate a land area into a grid of hexagons instead of the squares normally used, and display results using a polygon diagram. Hexagons have many advantages, including being better able to model lateral diffusion because all the neighbours of a cell are at the same proximity. This model has an inter-cell flow in one direction only, representing the movement of biomass in a situation where seed dispersal happens only in one direction.

Results:

ModelId:

gridspread1

SimileVersion:

3.1+

This simulates diffusion over a grid of cells. We use a multiple-instance submodel to represent the set of cells. Each cell has a unique (row,column) attribute.

ModelId:

drainage1

SimileVersion:

4.0

A classic spatial problem is calculating the drainage pattern for a given land area. If the land is divided in to cells in a grid with the altitude of the land in each cell being known the law the drainage direction for each cell can be found by finding the neighbour with the lowest altitude.

Equations:

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.

Results:

ModelId:

country_links1

SimileVersion:

3.1+

This model is an example of setting up an association between objects using a data file. The file consists of pairs of IDs, with each pair specifying one instnace of the association. In this case, we specify which countries share a trading association (i.e. which country can export to another country). The data file which specifies the country trading pairs also contains information on the volume of trade between each country pair. This is totalled for both the exporting country and the importing country.

ModelId:

antsworld

SimileVersion:

5.9

In this model, a population of animals (called ants) is created and the individuals move around at random. The area in which they move is represented by a grid of hexagons.

An association model is created to relate each individual to the hexagon it currently occupies. The technique of one-sided enumeration is used to make this association; it is vital that it happens efficiently, because it changes each time step. In this case the position of each ant is used to determine the index of the submodel instance for the hexagon containing it.

Equations:

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]

Results:

This image shows the distribution of pheromone over the grid are after 3000 time units: