The Seacow & Plastic in Ocean Currents

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## WHAT IS IT?

This is a mathematical model that demonstrates abstract vector fields and integral curves.

Generally speaking, a field is a "region in which a body experiences a force as the result of the presence of some other body or bodies. A field is thus a method of representing the way in which bodies are able to influence each other. For example, a body that has mass is surrounded by a region in which another body that has mass experiences a force tending to draw the two bodies together.... The strength of any field can be described as the ratio of the force experienced by a small appropriate specimen to the relevant property of that specimen, e.g. force/mass for the gravitational field" (Oxford Minidictionary of Physics).

By 'abstract vector fields' we mean that this model is not committed to any specific type of force, such as gravity or magnetism. Rather, it simulates a general field, in which some focal property of influence affects a "small appropriate specimen", or particle, placed in the field.

Normally, if you look at a field with bare eyes, you will not necessarily see the forces. For instance, if you drop an apple it falls down, even though you cannot see the gravitational force. The apple is an object in the gravitational field. You saw how it behaved so you could guess that there is some force that made it go down. Humans do not perceive (visually) forces of gravitation or electro-magnetic forces. However, in a model, we can use little arrows (vectors) to show where, how forceful, and in which direction there are forces in this field.

## HOW IT WORKS

In this model, the field is plotted using vector graphics: green streaks are individual vectors with yellow turtles serving as arrowheads. The length of each vector is roughly proportional to the magnitude of the vector field at each point. In this model, it is just the distance from the origin: The further away from the origin, the larger the vector. Also, all vectors are aimed clockwise along tangents to circles centered on the origin.

The vectors show you in what direction and how forcefully an appropriate specimen -- here, a 'particle' -- will be "knocked about" once it is placed the field. Once the particle is "knocked" to a new location, it will be knocked yet again by the force there (represented by the vector). Actually, it being "knocked about" continuously, but in this simulation, the "knock" occurs at discrete points in the field. Since the particle does not use up the forces, it will keep being knocked about. The path the particle takes is called its 'trajectory.' You will be able to track this trajectory because the particle will leave a red trail behind it as it moves along its trajectory. Trajectories in vector fields are called 'integral curves.'

Even though behavior of particles can be interesting and possibly unanticipated, owing to forces not being distributed uniformly in the field, or some other factor, we have chosen, for clarity, a vector field with a logical and consistent relation between location in space and size/orientation of the force. The vector field chosen for this particular model is

```text

- y d/dx + x d/dy

```

Ideally, in the particular force field modeled here, the particle trajectories should be concentric circles (that is, the particle should go round and round along the same circular trajectory).

## HOW TO USE IT

SETUP: Clears the world and computes the vector field.

PLACE-PARTICLES: Puts the program into the mode in which you can position red test-particles by clicking anywhere in the View.

GO: Runs the simulation continuously to show the integral curves.

## THINGS TO NOTICE

Notice that the vectors grow in length as you move away from the origin. What effect do short vectors have on a particle? Long vectors?

The way this model is programmed, each particle moves some finite amount before calculating its new heading. Therefore, the particles do not turn as much as they would if their headings were continuously recalculated. This causes their trajectories to spiral slowly outward. (You have to let the model run for a while before this becomes apparent.) We tried to minimize this by having the particles move forward only a very small amount at each time step (the variable `step-size`). We couldn't make this amount too small since the model would then run too slowly. If you want the particles to spiral less, or you want the model to run faster, change this value.

## THINGS TO TRY

Place particles in different parts of the world. Does the particle's position have any effect on the trajectory?

## EXTENDING THE MODEL

Try a different vector field by changing it in the `setup-vector`, `force-x`, and `force-y` procedures. For instance, if you choose

```text

x d/dx - y d/dy

```

the integral curves will be hyperbolas.

## HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

* Wilensky, U. (1998). NetLogo Vector Fields model. http://ccl.northwestern.edu/netlogo/models/VectorFields. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Please cite the NetLogo software as:

* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

Copyright 1998 Uri Wilensky.

![CC BY-NC-SA 3.0](http://ccl.northwestern.edu/images/creativecommons/byncsa.png)

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML). The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612.

This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2002.

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Click to Run Model

breed [ particles particle ]  ;; the things that are affected by the field
breed [ vectors vector ]    ;; the vectors that affect the particles
breed [ seacows seacow ]
breed [ seaelefants seaelefant ]


globals
[
  max-modulus  ;; the maximum modulus of all the vectors
  step-size    ;; the amount a particle moves forward
  zufall-head
  zufall-border
  zufall-himmelsrichtung
  FULL
  OK
  count-caught
  money
  seacow-number
  plastic-total
  A
  caught
]

seacows-own [volume volume-status]
vectors-own [modulus]  ;; the length of the vector
particles-own [weight]
seaelefants-own [elefant-volume]

; ##################### SETUP ########################

to setup
  clear-all
  setup-vectors
  add-initial-plastic
  add-seacow
  add-seaelefants
  add-marks
  set plastic-total 73400000
  set caught 0
  reset-ticks
end 


; ##################### GO ########################

to go
  ;if ticks >= 30000 [ stop ]
  let stop? false

  add-river-plastic
  add-plastic-flow
  move-particles

  seacow-volume-check

  ask seacows [
    if volume-status = "OK"
    [move-seacows
      collect-plastic
    ]
    if volume-status = "FULL"
    [go-seaelefant]
  ]

  ask seacows [ fd 4 / 10 ]

  move-seaelefants
  ask seaelefants [ fd elefant-speed / 10 ]

  tick
  ;; if one of the particles was going to wrap around the world, stop.
  if stop?
  [ stop ]
end 

; ##################### SEACOWS ########################

to add-seacow
  create-seacows seacows-number
  [
    setxy -117 -117
    set size 5
    set heading 0
    set color white
    set volume 0
    set seacow-number seacow-number + 1
  ]
end 

to move-seacows

  if search-algo = "random"
    [
      search-random
  ]

  if search-algo = "circuit seaelefant"
  [
    ifelse distance one-of seaelefants > max-distance-seacow and 2000 >= volume
    [face one-of seaelefants]
    [rt random 10
      lt random 10
    ]
  ]
end 

to search-random
  ifelse distancexy 0 0 > max-distance-seacow and volume-status = "OK"
  [facexy 0 0]
  [rt random 10
    lt random 10]
end 

to with-the-flow
  if zufall-head > 1
    [ set heading (atan force-x force-y) ]
  if patch-ahead 1 != nobody
    [ forward stroemung / 20 ]
end 

to seacow-volume-check
  ask seacows [
    if volume < 2000
      [set volume-status "OK"]
    if volume >= 2000
      [set volume-status "FULL"
        set label-color red ]

    set label precision volume 2
  ]
end 

to collect-plastic
  ask seacows
  [
    let parthere particles-here
    let total-weight-collected 0
    ask parthere
    [
      let weight-loss (weight * 0.0004)
      set weight weight - weight-loss
      if weight < 10 [die]

      set total-weight-collected total-weight-collected  + weight-loss

    ]
    set volume volume + total-weight-collected
  ]
end 

to go-seaelefant
  ask seacows with [volume >= 2000]
  [face one-of seaelefants ]
  if distance one-of seaelefants < 1
    [ set caught caught + volume
      set plastic-total plastic-total - volume
      set volume-status "OK"
      set volume 0
      set label-color white
      facexy 0 0
      output-show one-of ["fuckin' plastic" "ahoi!" "plastic kills!" "love ya all" "anybody out there?" "attention. some big waves comin in" "save the planet!" "I am so lonely out here" "Arrrrgh!!!" "May day, whiskey bottle empty" "Plastic-free zone"]
  ]
end 


; #################### SEAELEFANT ######################

to add-seaelefants
  create-seaelefants 1
  [
    setxy 40 0
    set size 5
    set heading 0
    set label elefant-volume
    set color yellow
    set elefant-volume 0
  ]
end 

to move-seaelefants
  ask seaelefants
    [
      ifelse distancexy 0 0 > max-dist-center-elefant
      [facexy 0 0]
        [rt random 10
        lt random 10]
  ]

  ;set A max-distance-to-center-or-seaelefant * max-distance-to-center-or-seaelefant * 3.14
  ;ifelse (count particles with [distance one-of seacows < max-distance-to-center-or-seaelefant ] < min-conc-before-chance / A)
  ;[move-to patch-left-and-ahead 45 1]
  ;[facexy 0 100]
  ; [set heading (atan force-x force-y)
end 


; ##################### ADD PLASTIC ########################

to add-initial-plastic

  create-particles amount-classI
  [
    let xpos random-normal 0 world-width * 0.12
    let ypos random-normal 0 world-height * 0.12

    set xpos max list (min list xpos max-pxcor) min-pxcor
    set ypos max list (min list ypos max-pycor) min-pycor

    setxy xpos ypos
    set size 0.1
    set color 125
    set weight 310                                                             ;kg pro Agent
  ]

  create-particles amount-classII
  [
    let xpos random-normal 0 world-width * 0.12
    let ypos random-normal 0 world-height * 0.12

    set xpos max list (min list xpos max-pxcor) min-pxcor
    set ypos max list (min list ypos max-pycor) min-pycor

    setxy xpos ypos
    set size 0.3
    set color 115
    set weight 860
  ]


  create-particles amount-classIII
  [
    let xpos random-normal 0 world-width * 0.12
    let ypos random-normal 0 world-height * 0.12

    set xpos max list (min list xpos max-pxcor) min-pxcor
    set ypos max list (min list ypos max-pycor) min-pycor

    setxy xpos ypos
    set size 0.8
    set color 105
    set weight 8250
  ]

  create-particles amount-classIV
  [

    let xpos random-normal 0 world-width * 0.12
    let ypos random-normal 0 world-height * 0.12

    set xpos max list (min list xpos max-pxcor) min-pxcor
    set ypos max list (min list ypos max-pycor) min-pycor

    setxy xpos ypos
    set size 1.2
    set color 95
    set weight 1060
  ]
end 

to add-plastic-flow
  create-particles plastic-flow-random
  [
    set zufall-himmelsrichtung random 4
    if zufall-himmelsrichtung = 0
    [setxy 200 0]
    if zufall-himmelsrichtung = 1
    [setxy -200 -0]
    if zufall-himmelsrichtung = 2
    [setxy -0 200]
    if zufall-himmelsrichtung = 3
    [setxy 0 -200]
    set size 1
    set heading 0
    set color yellow
  ]
end 

to add-river-plastic
  create-particles plastic-flow-river
  [
    setxy -200 0
    set size 1
    set heading 0
    set color yellow
  ]
end 

to move-particles
  ask particles
  [
    set zufall-head random 100

    if zufall-head < pull-effect
      [ face patch 0 0
        forward stroemung / 3 ]

    if zufall-head < move-randomness
      [set heading random 360
        forward stroemung / 10 ]

    set heading (atan force-x force-y)
    forward stroemung / 10
  ]
end 


; ##################### WORLD ########################

;; report true if we will wrap around if we move forward by step-size

to-report going-to-wrap?  ;; turtle procedure
  let next-patch patch-ahead step-size
  report next-patch = nobody
end 

to add-marks
  ask patches at-points [ [50 0] [50 1] [50 2] [50 -1] [50 -2] [100 0] [100 1] [100 2] [100 -1] [100 -2] ]
  [set pcolor white]
  ask patches at-points [ [0 0] [0 1] [0 2] [0 -1] [0 -2] [1 0] [2 0] [-1 0] [-2 0] ]
  [set pcolor white]
  ask patches at-points [ [-119 -119] [-119 -118] [-119 -117] [-118 -118] [-117 -119] [-117 -118] [-117 -117]]
  [set pcolor white]
end 

; ##################### CREATE VECTOR FIELD ########################

;; create vectors at regular intervals to see the effect of the force
;; at a particular place.

to setup-vectors
  ask patches
  [
    if (pxcor mod 13 = 0) and (pycor mod 13 = 0)
    [
      sprout-vectors 1
      [ setup-vector ]
    ]
  ]
  set max-modulus (max [modulus] of vectors)                ;; draw vector field
  ask vectors [ show-vector ]
end 

;; calculate the horizontal force where the turtle is located

to-report force-x  ;; turtle procedure
  report ycor
end 

;; calculate the vertical force where the turtle is located

to-report force-y  ;; turtle procedure
  report (- xcor)
end 

;; draw the vector using a turtle to display strength and direction of field

to show-vector  ;; turtle procedure
  set modulus (10 * modulus / max-modulus)
  forward modulus
  set color yellow
end 

;; make the turtle become a vector and initialize the vector's variables

to setup-vector  ;; turtle procedure
  set color blue
  pen-down
  if (force-x != 0) or (force-y != 0)
    [ set heading atan force-x force-y ]
  set modulus distancexy 0 0
end 

; Copyright 2017 Dominik Huter

There is only one version of this model, created about 1 year ago by Dominik Huter.

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