Mousetraps

Mousetraps preview image

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Uri_dolphin3 Uri Wilensky (Author)

Tags

mathematics 

Tagged by Reuven M. Lerner about 9 years ago

Model group CCL | Visible to everyone | Changeable by group members (CCL)
Model was written in NetLogo 5.0.4 • Viewed 307 times • Downloaded 28 times • Run 1 time
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WHAT IS IT?

Imagine a gymnasium full of mousetraps. On each mousetrap is a ping pong ball. Now throw a single ping pong ball into the middle of the room. The ball lands on a trap, the trap triggers, and a second ball flies into the air. The first ball also bounces into the air again, so now there are two balls in the air. Each of those two balls triggers another trap, so there's four balls in the air. And so on...

This experiment is a well-known metaphor for nuclear fission. In nuclear fission, atoms of fissionable material such as uranium are the "mousetraps", and neutrons are the ping pong balls.

HOW IT WORKS

Light blue squares represent untriggered mousetraps. Red squares represent triggered mousetraps.

When a ball lands on a light blue square, the square turns red, a new ball appears, and both balls travel a random distance in a random direction.

HOW TO USE IT

Press SETUP to set up all the mousetraps and suspend a single ping pong ball over the center. Press GO to release the ping pong ball.

If you want to see the reaction progress in slow motion, use the GO ONCE button to advance a step at a time.

To vary the maximum distance a ping pong ball can travel when it is released or bounces, use the MAX-DISTANCE slider.

THINGS TO NOTICE

Sometimes the reaction fizzles out almost immediately. Why do you think that happens?

Even if a sustained chain reaction occurs, not every mousetrap gets triggered. Why?

What shape is the "Traps triggered" plot? Why do you think it's shaped that way?

What shape is the "Balls in the air" plot? Why do you think it's shaped that way?

Suppose the gymnasium was infinitely large. What would the two plots look like? What kind of equation would produce such plots?

THINGS TO TRY

Play around with varying the MAX-DISTANCE slider. How big does MAX-DISTANCE need to be in order to get a chain reaction every time? Most of the time?

EXTENDING THE MODEL

There are various ways in which this model could be more physically realistic. For example:

  • Currently both a released ball and a bouncing ball travel the same maximum distance, but in reality the mousetrap would likely send the released ball much farther. Change the model so these different distances are controlled by two different sliders.

  • Currently the balls travel to their new positions instantly --- in reality it would take time proportional to the distance traveled. (Does it make a difference if you take into account that the balls move in a parabola through the air, not a straight line?) Change the model to take this into account.

NETLOGO FEATURES

Note the use of hatch to cause the ping pong balls to "multiply".

When a turtle tries to move off the edge of the world it cannot, it hits the wall, and lands on the same mousetrap it triggered in the last step, it dies.

RELATED MODELS

Rumor Mill is very similar to this model in mechanism and results, even though the domain is completely different (people and rumors instead of mousetraps and ping pong balls). (What other processes in nature or society does this model resemble...?)

Reactor X-Section and Reactor Top Down are two different views of nuclear fission happening inside a nuclear reactor. They both include ways of limiting the rate of fission so the "mousetraps" don't all start triggering uncontrollably.

CREDITS AND REFERENCES

This model is based on the "Mousetrap" demo included with the Swarm agent-based modeling toolkit (http://www.swarm.org/). See http://acoma.santafe.edu/projects/swarm/examples/mousetrap/. Note that this model and that demo differ in various details.

HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:

  • Wilensky, U. (2002). NetLogo Mousetraps model. http://ccl.northwestern.edu/netlogo/models/Mousetraps. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.
  • Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.

COPYRIGHT AND LICENSE

Copyright 2002 Uri Wilensky.

CC BY-NC-SA 3.0

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://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 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.

Comments and Questions

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Click to Run Model

globals [traps-triggered]  ;; how many traps have been sprung?

to setup
  clear-all
  set traps-triggered 0
  ;; an untriggered mousetrap is light blue
  ask patches
    [ set pcolor blue + 3 ]
  set-default-shape turtles "circle"
  ;; make the first ball
  crt 1
    [ set color white
      set size 1.5 ]  ;; easier to see
  reset-ticks
end 

to go
  if not any? turtles
    [ stop ]
  ask turtles
    [ ;; if we hit the wall or land on a triggered mousetrap,
      ;; then stop
      ifelse pcolor = red
        [ die ]
        ;; triggered traps are red
        [ set pcolor red
          set traps-triggered traps-triggered + 1
          ;; send another ball flying off
          hatch 1
            [ move ]
          ;; also bounce ourselves
      move ] ]
  tick
end 

to move  ;; turtle procedure
  rt random-float 360
  fd random-float max-distance
end 


; Copyright 2002 Uri Wilensky.
; See Info tab for full copyright and license.

There are 10 versions of this model.

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Uri Wilensky over 9 years ago Updated to NetLogo 5.0.4 Download this version
Uri Wilensky almost 10 years ago Updated version tag Download this version
Uri Wilensky almost 10 years ago Updated to version from NetLogo 5.0.3 distribution Download this version
Uri Wilensky over 10 years ago Updated to NetLogo 5.0 Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Model from NetLogo distribution Download this version
Uri Wilensky over 12 years ago Mousetraps Download this version

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