Association submodel

Equations in top level Variable magic magic = sqrt(3) Variable offa_even offa_even = [ 0.5, -0.5,-1, -0.5, 0.5,1] Variable offa_odd offa_odd = cos(theta)*[offa_even]-sin(theta)*[offb_even] Variable offb_even offb_even = [ 0.866, 0.866,0, -0.866, -0.866,0] Variable offb_odd offb_odd = sin(theta)*[offa_even]+cos(theta)*[offb_even] Variable theta theta = atan(3*sqrt(3)) Equations in hexagon Variable centre x centre x = if posn_in_parent==0 then hi_cx_lower else hi_cx_lower+magic*element(element([[offb]],my_level),int(posn_in_parent)) Where: my_level=my level posn_in_parent=posn in parent [[offb]]= ../level info/offb {hi_cx_higher}= ../hierarchy/hi_cx (to hexagon in higher) hi_cx_lower= ../hierarchy/hi_cx (to hexagon in lower) magic= ../magic Variable centre y centre y = if posn_in_parent==0 then hi_cy_lower else hi_cy_lower-magic*element(element([[offa]],my_level),int(posn_in_parent)) Where: my_level=my level posn_in_parent=posn in parent [[offa]]= ../level info/offa {hi_cy_higher}= ../hierarchy/hi_cy (to hexagon in higher) hi_cy_lower= ../hierarchy/hi_cy (to hexagon in lower) magic= ../magic Variable my level my level = hi_level_lower+1 Where: {hi_level_higher}= ../hierarchy/hi_level (to hexagon in higher) hi_level_lower= ../hierarchy/hi_level (to hexagon in lower) Variable my parent my parent = if index(1)==1 then 1 else int((index(1)+5)/7) Variable posn in parent posn in parent = if index(1)==1 then 0 else int(fmod(index(1)-2,7)) Equations in hierarchy Condition cond1 cond1 = index(1) is my_parent_lower Where: my_parent_lower= ../hexagon/my parent (from hexagon in lower) my_parent_higher= ../hexagon/my parent (from hexagon in higher) Variable dummy dummy = index(2)==1 Variable hi_cx hi_cx = if dummy then 0 else centre_x_higher Where: centre_x_lower= ../hexagon/centre x (from hexagon in lower) centre_x_higher= ../hexagon/centre x (from hexagon in higher) Variable hi_cy hi_cy = if dummy then 0 else centre_y_higher Where: centre_y_lower= ../hexagon/centre y (from hexagon in lower) centre_y_higher= ../hexagon/centre y (from hexagon in higher) Variable hi_level hi_level = if dummy then 0 else my_level_higher Where: my_level_lower= ../hexagon/my level (from hexagon in lower) my_level_higher= ../hexagon/my level (from hexagon in higher) Equations in level info Variable even level even level = fmod(index(1),2)== 1.0 Variable offa offa = side*(if even_level then [offa_even] else [offa_odd]) Where: even_level=even level [offa_even]= ../offa_even [offa_odd]= ../offa_odd Variable offb offb = side*(if even_level then [offb_even] else [offb_odd]) Where: even_level=even level [offb_even]= ../offb_even [offb_odd]= ../offb_odd Variable side side = 50/7^((index(1)-1)/2) Equations in for display Condition cond1 cond1 = my_level==6 Where: my_level= ../my level Variable colour colour = index(1) Variable xpts xpts = centre_x+element([[offa]],my_level) Where: centre_x= ../centre x [[offa]]= ../../level info/offa my_level= ../my level Variable ypts ypts = centre_y+element([[offb]],my_level) Where: centre_y= ../centre y [[offb]]= ../../level info/offb my_level= ../my level

Contained submodel(s)
others  
balls  

Submodel others

Submodel others is a relation submodel for a relation between balls and itself.

Condition for existence of submodel

effect
Units: boolean
effect = hypots<bounce_distance and rightway
Where:
bounce_distance is the variable bounce distance in this submodel.
hypots is the variable hypots in this submodel.
rightway is the variable rightway in this submodel.

Variable(s)

comps
Units: array(1,2)
comps = forces*[distances]/hypots
Where:
forces is the variable forces in this submodel.
hypots is the variable hypots in this submodel.
[distances] is the variable distances in this submodel.

bounce distance
Units: 1
bounce distance = sizes_b1+sizes_b2
Where:
sizes_b1 is the variable sizes in balls
sizes_b2 is the variable sizes in balls

distances
Units: array(1,2)
distances = [posns_b1]-[posns_b2]
Where:
[posns_b1] is the variable posns in balls
[posns_b2] is the variable posns in balls

hypots
Units: 1
hypots = hypot(element([distances],1),element([distances],2))
Where:
[distances] is the variable distances in this submodel.

forces
Units: 1
forces = pow(bounce_distance/hypots,4)
Where:
bounce_distance is the variable bounce distance in this submodel.
hypots is the variable hypots in this submodel.

rightway
Units: boolean
rightway = index(1)<index(2)

Submodel balls

Submodel balls is a fixed membership submodel with 32 members.

Variable(s)

Actions
Units: array(1,2)
Actions = sum({[comps_b1]})-sum({[comps_b2]})
Where:
{[comps_b1]} is the variable comps in others
{[comps_b2]} is the variable comps in others

green?
any(index(1)==[2,3,4,5,7,8,9])
Units: boolean
green? = any(index(1)==[2,3,4,5,7,8,9,12,13,14,17,18,22,23,27,32])

posns
Units: array(1,2)
posns = [p]
Where:
[p] is the compartment p in balls/dims

x
Units: 1
x = element([p],1)
Where:
[p] is the compartment p in balls/dims

y
Units: 1
y = element([p],2)
Where:
[p] is the compartment p in balls/dims

sizes
Units: 1
sizes = 15

wees
Units: 1
wees = sizes/10
Where:
sizes is the variable sizes in this submodel.

weex
Units: 1
weex = x/10+45
Where:
x is the variable x in this submodel.

weey
Units: 1
weey = y/10+45
Where:
y is the variable y in this submodel.

Contained submodel(s)
green  
dims  
orange  

Submodel balls/green

Submodel green is a conditional submodel.

Condition for existence of submodel

cond1
Units: boolean
cond1 = green_
Where:
green_ is the variable green? in balls

Variable(s)

size
Units: 1
size = sizes
Where:
sizes is the variable sizes in balls

x
Units: 1
x = x
Where:
x is the variable x in balls

y
Units: 1
y = y
Where:
y is the variable y in balls

Submodel balls/dims

Submodel dims is a fixed membership submodel with 2 members.

Compartment(s)

p
Units: 1
    Initial value: if index(1)==1 then fmod(25*(index(2)-1),112.5) else 16.66*int((index(2)-1)/4.5)
    Inflows: move

v
Units: 1
    Initial value: 0
    Inflows: flow1

Flow(s)

move
Units: 1
move = v
Where:
v is the compartment v in this submodel.

flow1
Units: 1
flow1 = force/mass
Where:
force is the variable force in this submodel.
mass is the variable mass in this submodel.

Variable(s)

gravity
Units: 1
gravity = 10*mass*if p<0 then 0-p elseif p>100 then 100-p else 0
Where:
mass is the variable mass in this submodel.
p is the compartment p in this submodel.

force
Units: 1
force = a+element([Actions],index(1))+rand_var(-10,10)

mass
Units: 1
mass = sizes*sizes/100
Where:
sizes is the variable sizes in balls

Submodel balls/orange

Submodel orange is a conditional submodel.

Condition for existence of submodel

cond1
Units: 
cond1 = missing

Variable(s)

size
Units: 1
size = sizes
Where:
sizes is the variable sizes in balls

x
Units: 1
x = x
Where:
x is the variable x in balls

y
Units: 1
y = y
Where:

 Equations in submodel Bank

creation: initial number = 2
compartment: money = 100000
flow: revenue = 0.1*money
flow: allocation = 0
variable: bank ID = index(1)

Equations in submodel Consumer
creation: initial number = 4
compartment: money = 0
flow: allocation = 0
flow: expenditure = 100
variable: consumer ID = index(1)
variable: request = (if rand_var(0,1)<0.2 then 1 else 0)
variable: mediator chosen = greatest({mediator})
variable: bank = sum({bank})

Equations in submodel Mediator
variable: mediator ID = index(1)
variable: bank = -1*floor(rand(1,2.9999))

Equations in submodel CM
condition: condition = (rand_const(0,1)<0.5)
variable: request = (if mediator==mediator_chosen then request else 0)
variable: mediator = mediator_id
variable: mediator chosen = mediator_chosen [in submodel Consumer]
variable: bank = (if mediator==mediator_chosen then bank else 0)

Equations in submodel MB
condition: condition = (bank==bank_id)

Equations in submodel CB request
condition: condition = (bank==bank_id&&request>0)

Equations in submodel CB account
compartment: money = 0 

 Equations in ../Desktop

IDa = [1,2,3]
IDb = [2,3,4]

Equations in Node
ID = index(1)

Equations in Arc
cond1 = (any(ID == [IDa]and ID_0 == [IDb])or any(ID == [IDb]and ID_0 == [IDa]))
where
ID = ../Node/ID (from Node in role1)
ID_0 = ../Node/ID (from Node in role2)
[IDa] = ../IDa 

 Equations in ../Desktop

hs = [1,1,2]
fs = [3,4,4]
Comment: This two arrays together specify that household 1 owns fields
3 and 4, while household 2 owns field 4 (part ownership allowed!)

Equations in Household
h = index(1)

Equations in Owns
cond1 = any(var1 == [hs]and f == [fs])
where:
var1 = ../Household/h (from Household in owner)
f = ../Field/f (from Field in owned)
[hs] = ../hs
[fs] = ../fs

Equations in Field
variable:f = index(1)

 Variable: n_total = sum({n}) 

Where: {n} = Cohort/n

Variable: population_total_size = sum({cohort_total_size})
Where: {cohort_total_size} = Cohort/cohort_total_size

--------------------------------------------------------------
Submodel Bigger

Submodel "Bigger" is an association submodel between "Cohort" and itself with roles "other" and "me".

Condition: condition = other_size>me_size
Where:
me_size = Value(s) of ../Cohort/size from submodel "Cohort" in role "me"
other_size = Value(s) of ../Cohort/size from submodel "Cohort" in role "other"

Variable: total_size_of_bigger_cohort = other_cohort_total_size
Where:
me_cohort_total_size = Value(s) of ../Cohort/cohort_total_size from submodel "Cohort" in role "me"
other_cohort_total_size = Value(s) of ../Cohort/cohort_total_size from submodel "Cohort" in role "other"

-------------------------------------------------------------------------
Submodel Cohort

Submodel "Cohort" is a population submodel.

Compartment: n
Initial value = 100
Rate of change = - loss

Compartment: size
Initial value = 0
Rate of change = + growth

Flow: growth = gr*(1-size/max_size)

Flow: loss = 5

Immigration: create_new_cohort = 1

Loss: remove_cohort = n<=0

Variable: cohort_total_size = n*size

Variable: gr = 1.5

Variable: max_size = 10

Variable: total_size_of_all_bigger_cohorts = sum({cohort_total_size_of_bigger_me})
Where:
{cohort_total_size_of_bigger_me} = ../Bigger/total_size_of_bigger_cohort for submodel "Cohort" in role "me"