life-rule-switching.nlogo

patches-own [
  next-pcolor ;; the next state is calculated using current pcolor
]

globals [
  living1k
]

;; clear the board and create some life
to setup
  ;; standard setup
  clear-all
  reset-ticks

  ;; data collected during the game
  set living1k []

  ;; make the world with custom size
  resize-world 0 (world-size - 1) 0 (world-size - 1)

  ;; heuristic scaling of the patch size
  set-patch-size floor ( 50 / (sqrt world-size) )

  ;; use next-pcolor to initialize pcolor
  ask patches [
    ifelse random 100 < init-life [
      set next-pcolor black
    ][
      set next-pcolor white
    ]
    set pcolor next-pcolor
  ]
end

;;
;; main function
;;
to go

  ifelse synchronous [
    ask patches [
      simulate-life
    ]
    ask patches [
      update-state
    ]
  ][
    ask patches [
      simulate-life
      update-state
    ]
  ]

  update-living1k
  tick
end

;;
;; calculate the updating rule
;;
to  simulate-life
  ifelse deterministic [ ;; deterministic rule switching
    ifelse ticks mod deterministic-period = 0 [
      update-rule-modified
    ][ ;; ticks mod deterministic-period \= 0
      update-rule-std
    ]
  ][ ;; random rule switching
    ifelse random-float 1 > rule-switch-prob [
      update-rule-std
    ][
      update-rule-modified
    ]
  ]
end

;;
;; standard update rule for the Game of Life
;;
to update-rule-std
  let x (count neighbors with [ pcolor = black] )

  ifelse pcolor = black [
    ifelse x < 2 or x >= 4 [ ;; x>=4 (weak inequality) - standard rule
      set next-pcolor white ;; ie. die
    ][
      set next-pcolor black ;; ie. stay alive
    ]
  ][ ;; pcolor = white
    if x >= 3 and x < 4 [ ;; modified rule if second-threshold != 4
          set next-pcolor black ;; ie. birth
    ]
  ]
end

;;
;; update rule with the altered treshold for the overpopulation
;;
to update-rule-modified
  let x (count neighbors with [ pcolor = black] )

  ifelse pcolor = black [
    ifelse x < 2 or x >= second-threshold [ ;; modified rule if second-threshold != 4
      set next-pcolor white ;; ie. die
    ][
      set next-pcolor black ;; ie. stay alive
    ]
  ][ ;; pcolor = white
    if x >= 3 and x < second-threshold [ ;; modified rule if second-threshold != 4
          set next-pcolor black ;; ie. birth
    ]
  ]
end

;;
;; update the state
;;
to update-state
  set pcolor next-pcolor
end

;;
;; reporters
;;

;;
;; percentage of living cells
;;
to-report %living
  report 100 * ( count patches with [ pcolor = black] ) / ( count patches )
end

;;
;; fraction of living cells
;;
to-report living-fraction
  report ( count patches with [ pcolor = black] ) / ( count patches )
end

;;
;;
;;
to update-living1k
  ;; add current vale of cooperators-fraction to the list cooperators1k
  set living1k fput living-fraction living1k
end

;;
;;
;;
to-report mean-living1k
  ifelse ticks >= 1000 [
    report mean ( sublist living1k 0 1000 )
  ][
    report -1
  ]
end
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@#$#@#$#@
## WHAT IS IT?

This model implements a version of Game of Life cellular 2D automaton extended with the ability to alter the rules utilized by the cell during the evolution. Simple versions of random and deterministic mechanisms of rules selection are implemented. In both case, at each step, the cell can be updated according to one of the rules - the standard one and the alternative one. The standard rule is identical to the rule for dying due to overpopulation (Any live cell with four or more live neighbors dies, because of the  overpopulation). The alternative rule for threshold _r_ is: Any live cell with _r_ of more live neighbors dies, because of the  overpopulation.

Additionally, one can switch between synchronous and asynchronous state updating policy. In the synchronous update policy, corresponding to the standard version of GoL, the state of the lattice is updated globally at the end of each simulation step. In the asynchronous policy, the state of each agent is calculated and updated immediately. Thus, each simulation steps consists of the calculation of next state of the cell, and the update of the cell state. The order of cells is chosen randomly

## HOW IT WORKS

Game of Live is a 2D cellular automaton. Black color marks living cells, white cells are dead. In the basic version of the game - synchronous stat updating and single evolution rule - cells can become live or dead according to threshold on the number of living cells in their neighborhood.

The following parameters of the model are available through the controls:

* _world-size_ - size of the lattice used to run the simulation;
* _init-life_ - percentage of living cells at the beginning of the simulation;
* _synchronous_ - toggle between synchronous and asynchronous updating policy;
* _deterministic_ - toggle between deterministic and random rule selection mechanism;
* _deterministic-period_ - the number of iteration between the utilization of the alternative rule in the deterministic rule switching mechanism;
* _rule-switch-prob_ - set the probability of utilizing an alternative rule in the random rule switching mechanism;
* _second-threshold_ - threshold used in the second (alternative) rule used in the game;

## HOW TO USE IT

After setting the required parameters, use _Setup world_ button to initialize the simulation. To run the model ones, use _Play life_ button. _Loop_ button runs the game in a loop, and _Play 50 times_ runs 50 simulation cycles.

## THINGS TO NOTICE

The formation of patterns and the stability of the evolution depends on the selection of parameters. 

Some popular formation could occur in the case of synchronous or asynchronous updating. It is possible to switch between synchronous and asynchronous updating during the game to observe the changes in the behavior.

Similarly, in the case of random mechanism for selecting rules, it is possible to change the probability of switching between the base rule and the alternative rule.

## THINGS TO TRY

The most important element to try is to modify the threshold for dying due to the underpopulation.

## EXTENDING THE MODEL

Currently, all patches are updated during each step. To explore the transition between synchronous and asynchronous policy, only a fraction of the cell should update its state synchronously. This could be achieved by introducing a new parameter defining the probability of synchronous updating.

## RELATED MODELS
Conway’s Game of Life, http://www.modelingcommons.org/browse/one_model/6948

## CREDITS AND REFERENCES

Conway's Game of Life, https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
Asynchronous cellular automaton, https://en.wikipedia.org/wiki/Asynchronous_cellular_automaton

A model of the Game of Life with asynchronous updating was introduced in 
H.J. Blok, B. Bergersen, "Synchronous versus asynchronous updating in the “game of Life”", Phys. Rev. E 59, 3876 (1999), https://doi.org/10.1103/PhysRevE.59.3876

1D cellular automata with random updating due to the noise were studied in 

Louis, P.-Y., &#38; Nardi, F. R. (Eds.). (2018). Probabilistic Cellular Automata (Vol. 27). Springer International Publishing. https://doi.org/10.1007/978-3-319-65558-1
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