3.4-BasicContactProcess2D.nlogo

;; The MIT License (MIT)
;;
;; Copyright (c) 2011-24 David O'Sullivan and George Perry
;;
;; Permission is hereby granted, free of charge, to any person
;; obtaining a copy of this software and associated documentation
;; files (the "Software"), to deal in the Software without restriction,
;; including without limitation the rights to use, copy, modify, merge,
;; publish, distribute, sublicense, and/or sell copies of the Software,
;; and to  permit persons to whom the Software is furnished to do so,
;; subject to the following conditions:
;;
;; The above copyright notice and this permission notice shall be included
;; in all copies or substantial portions of the Software.
;;
;; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
;; OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
;; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
;; THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
;; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
;; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
;; DEALINGS IN THE SOFTWARE.
;;

globals [
  N  ;; the number of patches in the model
]

to setup
  clear-all
  set N count patches
  ask patches [
    ifelse random-float 1 < initial-proportion
    [ set pcolor black ]
    [ set pcolor white ]
  ]
  reset-ticks
end


to go
  ;; if all sites are dead, then end
  if not any? patches with [pcolor = black] [ stop ]
  ;; otherwise run a 'generation' here equal to a number
  ;; of events equal to the number of sites
  repeat N [
    ask one-of patches [
      ifelse pcolor = black
      [ death-event ]
      [ birth-event ]
    ]
  ]
  tick
end

;; death occurs with the specified probability
to death-event
  if random-float 1 < p-death [
    set pcolor white
  ]
end

;; birth probability occurs dependent on the number
;; of live neighbours - most easily accomplished by picking
;; one at random
to birth-event
  set pcolor [pcolor] of one-of neighbors4
end


to-report get-p-occupied-sites
  report count patches with [pcolor = black] / N
end
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"" ""
PENS
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TEXTBOX
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p-death ~ 0.607 is critical value
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## WHAT IS IT?

This model is a possible implementation of the basic contact process as discussed in

+   Durrett R and Levin SA 1994b Stochastic spatial models: a user’s guide to ecological applications. _Philosophical Transactions of the Royal Society of London. Series B_. *343*, 329-350.

as discussed in Chapter 3 of

+   O'Sullivan D and Perry GLW 2013 _Spatial Simulation: Exploring Pattern and Process_. Wiley, Chichester, England.

You should consult that book for more information and details of the model.

## THINGS TO NOTICE

The most important feature of this model is that although the 'atomic' event in an interacting particle system (IPS) is the random selection of a single particle (i.e., a NetLogo patch) followed by execution of some update rule on that particle, implementation of a `go` procedure in the obvious manner

    to go
      ask one-of patches [
        ;; code
      ]
      tick
    end

leads to very slow model updating, because every single event would lead to a redraw, even though only one location in the system had changed state.  Therefore, in this model (and all the other particle system models in the model zoo) we allow a whole 'generation' of particle updates between NetLogo ticks:

    to go
      repeat N [ ;; the number of patches
        ask one-of patches [
          ;; code
        ]
      ]
      tick
    end

This means that a whole generation of updates, which we consider to be a number of events equal to the number of particles in the system, occurs between display updates, so that the model runs more smoothly.

Unlike the previous models in 3.1 to 3.3, it is also worth noting that this update sequence means that every time a patch updates the effect is immediate, so that there may be effects on neighbouring patches right away.  This type of updating is referred to as _asynchronous_ and is discussed in detail in Chapter 6.

## THINGS TO TRY

As noted in the discussion of this model in Chapter 3, the simple contact process responds sensitively to small changes in the probability of particle death.  You should experiment with this setting to see if you can reproduce the results summarized in Figure 3.12.  In particular with `p-death` set to 0.607 you should be able to observe the _critical_ threshold behaviour where although all particles will die eventually, small numbers can persist for very long periods of time.

## HOW TO CITE

If you mention this model in a publication, please include these citations for the model itself and for NetLogo

+   Durrett R and Levin SA 1994b Stochastic spatial models: a user’s guide to ecological applications. _Philosophical Transactions of the Royal Society of London. Series B_. *343*, 329-350.
+   O'Sullivan D and Perry GLW 2013 _Spatial Simulation: Exploring Pattern and Process_. Wiley, Chichester, England.
+   Wilensky U 1999 NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

The MIT License (MIT)

Copyright &copy; 2011-24 David O'Sullivan and George Perry

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to  permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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