Vacancy Chains

;; These are global variables:
globals [
  ;; The following two boolean variables take the values 0 and 1 instead of true and false because they must be able
  ;; to generate error messages even if they have not been initialized.
  positions-made?  ;; positions must be made before vacancies can be made;
  vacancies-made?  ;; vacancies must be made before vacancy chains can be made;
  wall-length  ;; is the length of walls;
  meter  ;; measures the length of walls;
  direction  ;; tells where walls are expanded;
  x-target  ;; the x-coordinate of a position to be reached;
  y-target  ;; the y-coordinate of a position to be reached;
  reachable?  ;; whether the target position can be actually reached;
  x y  ;; scan the screen in search for patches where new turtles can be posed;
  cum-num-chains-by-length-list  ;; a list for the cumulative number of chains, where each element refers to a different chain length
  max-chain-length-attained  ;; the maximum length vacancy chains actually reached.
]

;; These variables belong to patches:
patches-own [elevation]  ;; the stratum of a patch, with 0 as the lowest stratum.


;; These variables belong to turtles:
turtles-own [cl]  ;; the length of a vacancy chain.







;; Repeats the sequence "setup-hierarchy" - "setup-vacancies" - "go" so many times as the parameter "times".
;; At the end, it prints on the Command Center the average number of chains for each chain length.

to iterate
  ;; The list is filled up with values. Counters are in order because this list may entail several instances of the same value.
  repeat times [
    setup-positions
    setup-vacancies
    go
    ;; The list of the cumulative number of chains of each length is initialized.
    set cum-num-chains-by-length-list []
    repeat max-chain-length
      [set cum-num-chains-by-length-list fput 0 cum-num-chains-by-length-list]
    ;; Introduces a counter.
    let i 0
    ;; Updates the list of the cumulative number of chains of each length.
    foreach cum-num-chains-by-length-list [
      set cum-num-chains-by-length-list replace-item i cum-num-chains-by-length-list (? + count turtles with [cl = i + 1])
      set i (i + 1)
    ]
  ]
  ;; The list is stripped of all last 0 values.
  set cum-num-chains-by-length-list reverse cum-num-chains-by-length-list
  let first-non-zero-value-found? false
  foreach cum-num-chains-by-length-list [
    ifelse (? = 0 and first-non-zero-value-found? = false)
      [set cum-num-chains-by-length-list remove ? cum-num-chains-by-length-list]
      [set first-non-zero-value-found? true]
  ]
  set cum-num-chains-by-length-list reverse cum-num-chains-by-length-list
  set max-chain-length-attained length cum-num-chains-by-length-list
  ;; Output is printed on the screen
  let i 0
  foreach cum-num-chains-by-length-list [
    set i (i + 1)
    type "Percent of chains of length "
    type i
    type ": "
    ifelse (sum cum-num-chains-by-length-list > 0)
      [print ? * 100 / sum cum-num-chains-by-length-list]
      [print 0]
  ]
  print ""
  let cum-num-chains-by-length-except-length-one-list remove-item 0 cum-num-chains-by-length-list
  type "Number of chains of length greater than 1: "
  print (sum cum-num-chains-by-length-except-length-one-list) / times
  type "Percent of chains of length greater than 1: "
  ifelse (sum cum-num-chains-by-length-list > 0)
    [print (sum cum-num-chains-by-length-except-length-one-list) * 100 / (sum cum-num-chains-by-length-list)]
    [print 0]
  print ""
  print ""
  print ""
end 

to setup-positions
  clear-all
  ;; Patches are assigned an "elevation" either according to a decreasing exponential or a uniform or an increasing exponential
  ;; distribution. Elevation takes integer values.
  ;; The elevation is reflected by a gray scale. Patches with highest elevation are white, patches with lowest elevation are black.
  ask turtles [die]
  ask patches [
    ;; Decreasing exponential distribution.
    if (strata-distribution = "hierarchical") [
      set elevation n-of-strata + 1
      while [elevation > n-of-strata]
        [set elevation round random-exponential ((1 + n-of-strata) / 4)]
    ]
    ;; The complement of a decreasing exponential distribution.
    if (strata-distribution = "inverse") [
      set elevation -1
      while [elevation < 0]
        [set elevation n-of-strata - round random-exponential ((1 + n-of-strata) / 4)]
    ]
    ;; Uniform distribution.
    if (strata-distribution = "linear")
      [set elevation random (1 + n-of-strata)]
    ;; Mixed: decreasing exponential for high strata, the complement of a poisson distribution for low strata.
    if (strata-distribution = "lean") [
      ifelse (random 2 = 0) [
        set elevation n-of-strata + 1
        while [elevation > n-of-strata]
          [set elevation round random-exponential (1 + n-of-strata) / 4]
      ][
        set elevation -1
        while [elevation < 0]
          [set elevation n-of-strata - round random-poisson (1 + n-of-strata) / 4]
      ]
    ]
    if (elevation <= n-of-strata)
      [set pcolor scale-color black elevation 0 n-of-strata]
  ]
  ;; Builds walls.
  if (n-walls > 0) [
    while [count patches with [pcolor = red] < n-walls] [
      ask patch (random-pxcor) (random-pycor) [
        set pcolor red
        set elevation n-of-strata + 1
      ]
    ]
    ask patches with [pcolor = red] [
      set wall-length (random max (list max-pxcor max-pycor) + 1)
      if (wall-length > 1) [
        set meter 1
        set direction random 360
        add-brick
      ]
    ]
  ]
  ;; Global variables keep track of the fact that positions have been made, whereas vacancies are still waiting.
  set positions-made? 1
  set vacancies-made? 0
end 
;; Bricks are added to walls. This procedure is called by "setup-positions".

to add-brick
  let next-brick patch-at-heading-and-distance direction 1
  let reach 1
  while [[pcolor] of next-brick = red and any? patches with [pcolor != red]] [
    set reach reach + 1
    if (random 10 <= 1)
      [set direction random 360]
    set next-brick patch-at-heading-and-distance direction reach
  ]
  ask next-brick [
    set pcolor red
    set elevation n-of-strata + 1
    set meter meter + 1
    if (meter < wall-length)
      [add-brick]
  ]
end 

to setup-vacancies
  ifelse (starting-stratum > n-of-strata) [
    print "The starting stratum cannot be greater than the number of strata."
  ][
    ifelse (positions-made? = 0) [
      print "Please press the Setup Positions button."
    ][       
      ;; Two nested WHILEs in order to scan the screen.
      ;; If a free patch of the required elevation is found, a new turtle is created and posed there.
      set x min-pxcor
      while [x <= max-pxcor] [
        set y min-pycor
        while [y <= max-pycor] [
          if ([elevation] of patch x y = starting-stratum) [
            set-default-shape turtles "vacancy"
            crt 1 [
              set color green
              set xcor x
              set ycor y
              set cl 0
            ]
          ]
          set y (y + 1)
        ]
        set x (x + 1)
      ]
      ;; A global variable keeps track of the fact that vacancies have been made available.
      set vacancies-made? 1
    ]
  ]
  reset-ticks
end 

to go
  ifelse (starting-stratum > n-of-strata) [
    print "The starting stratum cannot be greater than the number of strata."
  ][
    if (positions-made? = 0) [print "Please press the 'Setup Positions' button."]
    if (vacancies-made? = 0) [print "Please press the 'Setup Vacancies' button."]
    if (positions-made? = 1 and vacancies-made? = 1) [
      ask turtles [form-chains]
      ;; Vacancy chains cannot be formed again.
      set positions-made? 0
      set vacancies-made? 0
    ]
  ]
  tick
end 

to form-chains
  ;; This procedure calls itself recursively with decreasing values of elevation until two or more patches with equal elevation are found.
  ;; Elevation in neighboring patches. Angles are measured clockwise from pi/2.
  ;; Turtles are the heads of vacancy chains. Eventually, turtles move.
  ;; First, they look for a patch among the closest neighbors (4- or 8- or 24-neighborhood). In a second turn, they will look among the second-tier neighbors (24-neighborhood).
  ;; Each time the procedure "form-chains" is called, the chain lenght is increased by one unit.
  set cl (cl + 1)
  ;; If the 4-neighborhood has been chosen. 
  if (neighborhood = 4) [
    ;; Look north.
    ifelse (any? turtles-on patch-at 0 1 = false and ([elevation] of patch-at 0 1 = [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1)) [
      ask patch-here [set pcolor yellow]
      set ycor ycor + 1
      form-chains
    ][
      ;; Look east. 
      ifelse (any? turtles-on patch-at 1 0 = false and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 = [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1)) [
        ask patch-here [set pcolor yellow]
        set xcor xcor + 1
        form-chains
      ][
        ;; Look south.
        ifelse (any? turtles-on patch-at 0 -1 = false and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 = [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1)) [
          ask patch-here [set pcolor yellow]
          set ycor ycor - 1
          form-chains
        ][
          ;; Look west.   
          ifelse (any? turtles-on patch-at -1 0 = false and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 = [elevation] of patch-here - 1)) [
            ask patch-here [set pcolor yellow]
            set xcor xcor - 1
            form-chains
          ][
            if (verbose?) [
              type "Vacancy "
              type who
              type " produced a chain of length "
              print cl
            ]
          ]
        ]
      ]
    ]
  ]
  ;; If the 8-neighborhood has been chosen.
  if (neighborhood = 8) [
    ;; Look north.
    ifelse (any? turtles-on patch-at 0 1 = false and ([elevation] of patch-at 0 1 = [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1)) [
      ask patch-here [set pcolor yellow]
      set ycor ycor + 1
      form-chains
    ][
      ;; Look north-east.
      ifelse (any? turtles-on patch-at 1 1 = false and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 = [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1)) [
        ask patch-here [set pcolor yellow]
        setxy (xcor + 1) (ycor + 1)
        form-chains
      ][
        ;; Look east. 
        ifelse (any? turtles-on patch-at 1 0 = false and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 = [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1)) [
          ask patch-here [set pcolor yellow]
          set xcor xcor + 1
          form-chains
        ][
          ;; Look south-east.
          ifelse (any? turtles-on patch-at 1 -1 = false and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 = [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1)) [
            ask patch-here [set pcolor yellow]
            setxy (xcor + 1) (ycor - 1)
            form-chains
          ][
            ;; Look south.
            ifelse (any? turtles-on patch-at 0 -1 = false and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 = [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1)) [
              ask patch-here [set pcolor yellow]
              set ycor ycor - 1
              form-chains
            ][
              ;; Look south-west.
              ifelse (any? turtles-on patch-at -1 -1 = false and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 = [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1)) [
                ask patch-here [set pcolor yellow]
                setxy (xcor - 1) (ycor - 1)
                form-chains
              ][
                ;; Look west.   
                ifelse (any? turtles-on patch-at -1 0 = false and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 = [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1)) [
                  ask patch-here [set pcolor yellow]
                  set xcor xcor - 1
                  form-chains
                ][  
                  ;; Look north-west.
                  ifelse (any? turtles-on patch-at -1 1 = false and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 = [elevation] of patch-here - 1)) [
                    ask patch-here [set pcolor yellow]
                    setxy (xcor - 1) (ycor + 1)
                    form-chains
                  ][
                    if (verbose?) [
                      type "Vacancy "
                      type who
                      type " produced a chain of length "
                      print cl
                    ]
                  ]
                ]
              ]
            ]
          ]
        ]
      ]
    ]
  ]
  ;; If the 24-neighborhood has been chosen.
  if (neighborhood = 24) [
    ;; Look north.
    ;; North, first tier.
    set x-target xcor
    set y-target ycor + 1
    check-reachability
    ifelse (any? (turtles-on patch-at 0 1) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 = [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
      ask patch-here [set pcolor yellow]
      set xcor xcor + 1
      form-chains
    ][
      ;; North, second tier.
      set x-target xcor
      set y-target ycor + 2
      check-reachability
      ifelse (any? (turtles-on patch-at 0 2) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 = [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
        ask patch-here [set pcolor yellow]
        set xcor xcor + 2
        form-chains
      ][
        ;; Look north-northeast (only the second tier).
        set x-target xcor + 1
        set y-target ycor + 2
        check-reachability
        ifelse (any? (turtles-on patch-at 1 2) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 = [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
          ask patch-here [set pcolor yellow]
          setxy (xcor + 1) (ycor + 2)
          form-chains
        ][
          ;; Look north-east.
          ;; North-East, first tier.
          set x-target xcor + 1
          set y-target ycor + 1
          check-reachability
          ifelse (any? (turtles-on patch-at 1 1) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 = [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
            ask patch-here [set pcolor yellow]
            setxy (xcor + 1) (ycor + 1)
            form-chains
          ][
            ;; North-East, second tier.
            set x-target xcor + 2
            set y-target ycor + 2
            check-reachability
            ifelse (any? (turtles-on patch-at 2 2) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 = [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
              ask patch-here [set pcolor yellow]
              setxy (xcor + 2) (ycor + 2)
              form-chains
            ][
              ;; Look east-northeast (only the second tier).
              set x-target xcor + 2
              set y-target ycor + 1
              check-reachability
              ifelse (any? (turtles-on patch-at 2 1) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 = [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                ask patch-here [set pcolor yellow]
                setxy (xcor + 2) (ycor + 1)
                form-chains
              ][
                ;; Look east.
                ;; East, first tier.
                set x-target xcor + 1
                set y-target ycor
                check-reachability
                ifelse (any? (turtles-on patch-at 1 0) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 = [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                  ask patch-here [set pcolor yellow]
                  set xcor xcor + 1
                  form-chains
                ][
                  ;; East, second tier.
                  set x-target xcor + 2
                  set y-target ycor
                  check-reachability
                  ifelse (any? (turtles-on patch-at 2 0) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 = [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                    ask patch-here [set pcolor yellow]
                    set xcor xcor + 2
                    form-chains
                  ][
                    ;; Look east-southeast (only the second tier).
                    set x-target xcor + 2
                    set y-target ycor - 1
                    check-reachability
                    ifelse (any? (turtles-on patch-at 2 -1) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 = [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                      ask patch-here [set pcolor yellow]
                      setxy (xcor + 2) (ycor - 1)
                      form-chains
                    ][
                      ;; Look southeast.
                      ;; South-East, first tier.
                      set x-target xcor + 1
                      set y-target ycor - 1
                      check-reachability
                      ifelse (any? (turtles-on patch-at 1 -1) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 = [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                        ask patch-here [set pcolor yellow]
                        setxy (xcor + 1) (ycor - 1)
                        form-chains
                      ][
                        ;; South-East, second tier.
                        set x-target xcor + 2
                        set y-target ycor - 2
                        check-reachability
                        ifelse (any? (turtles-on patch-at 2 -2) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 = [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                          ask patch-here [set pcolor yellow]
                          setxy (xcor + 2) (ycor - 2)
                          form-chains
                        ][
                          ;; Look south-southeast (only the second tier).
                          set x-target xcor + 1
                          set y-target ycor - 2
                          check-reachability
                          ifelse (any? (turtles-on patch-at 1 -2) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 = [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                            ask patch-here [set pcolor yellow]
                            setxy (xcor + 1) (ycor - 2)
                            form-chains
                          ][
                            ;; Look south.
                            ;; South, first tier.
                            set x-target xcor
                            set y-target ycor - 1
                            check-reachability
                            ifelse (any? (turtles-on patch-at 0 -1) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 = [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                              ask patch-here [set pcolor yellow]
                              set ycor ycor - 1
                              form-chains
                            ][
                              ;; South, second tier.
                              set x-target xcor
                              set y-target ycor - 2
                              check-reachability
                              ifelse (any? (turtles-on patch-at 0 -2) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 = [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                                ask patch-here [set pcolor yellow]
                                set ycor ycor - 2
                                form-chains
                              ][
                                ;; Look south-southwest (only the second tier).
                                set x-target xcor - 1
                                set y-target ycor - 2
                                check-reachability
                                ifelse (any? (turtles-on patch-at -1 -2) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 = [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                                  ask patch-here [set pcolor yellow]
                                  setxy (xcor - 1) (ycor - 2)
                                  form-chains
                                ][
                                  ;; Look south-west.
                                  ;; South-West, first tier.
                                  set x-target xcor - 1
                                  set y-target ycor - 1
                                  check-reachability
                                  ifelse (any? (turtles-on patch-at -1 -1) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 = [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                                    ask patch-here [set pcolor yellow]
                                    setxy (xcor - 1) (ycor - 1)
                                    form-chains
                                  ][
                                    ;; South-West, second tier.
                                    set x-target xcor - 2
                                    set y-target ycor - 2
                                    check-reachability
                                    ifelse (any? (turtles-on patch-at -2 -2) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 = [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                                      ask patch-here [set pcolor yellow]
                                      setxy (xcor - 2) (ycor - 2)
                                      form-chains
                                    ][
                                      ;; Look west-southwest (only the second tier).
                                      set x-target xcor - 2
                                      set y-target ycor - 1
                                      check-reachability
                                      ifelse (any? (turtles-on patch-at -2 -1) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 = [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                                        ask patch-here [set pcolor yellow]
                                        setxy (xcor - 2) (ycor - 1)
                                        form-chains
                                      ][
                                        ;; Look west.
                                        ;; West, first tier.
                                        set x-target xcor - 1
                                        set y-target ycor
                                        check-reachability
                                        ifelse (any? (turtles-on patch-at -1 0) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 = [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                                          ask patch-here [set pcolor yellow]
                                          set xcor xcor - 1
                                          form-chains
                                        ][
                                          ;; West, second tier.
                                          set x-target xcor - 2
                                          set y-target ycor
                                          check-reachability
                                          ifelse (any? (turtles-on patch-at -2 0) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 = [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                                            ask patch-here [set pcolor yellow]
                                            set xcor xcor - 2
                                            form-chains
                                          ][
                                            ;; Look west-northwest (only the second tier).
                                            set x-target xcor - 2
                                            set y-target ycor + 1
                                            check-reachability
                                            ifelse (any? (turtles-on patch-at -2 1) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 = [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                                              ask patch-here [set pcolor yellow]
                                              setxy (xcor - 2) (ycor + 1)
                                              form-chains
                                            ][
                                              ;; Look northwest.
                                              ;; North-West, first tier.
                                              set x-target xcor - 1
                                              set y-target ycor + 1
                                              check-reachability
                                              ifelse (any? (turtles-on patch-at -1 1) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 = [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                                                ask patch-here [set pcolor yellow]
                                                setxy (xcor - 1) (ycor + 1)
                                                form-chains
                                              ][
                                                ;; North-West, second tier.
                                                set x-target xcor - 2
                                                set y-target ycor + 2
                                                check-reachability
                                                ifelse (any? (turtles-on patch-at -2 2) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 = [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 != [elevation] of patch-here - 1)) [
                                                  ask patch-here [set pcolor yellow]
                                                  setxy (xcor - 2) (ycor + 2)
                                                  form-chains
                                                ][
                                                  ;; Look north-northwest (only the second tier).
                                                  set x-target xcor - 1
                                                  set y-target ycor + 2
                                                  check-reachability
                                                  ifelse (any? (turtles-on patch-at -1 2) with [color = green] = false and reachable? and ([elevation] of patch-at 0 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at 2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at 0 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 -1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 0 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 1 != [elevation] of patch-here - 1) and ([elevation] of patch-at -2 2 != [elevation] of patch-here - 1) and ([elevation] of patch-at -1 2 = [elevation] of patch-here - 1)) [
                                                    ask patch-here [set pcolor yellow]
                                                    setxy (xcor - 1) (ycor + 2)
                                                    form-chains
                                                  ][
                                                    if (verbose?) [
                                                      type "Vacancy "
                                                      type who
                                                      type " produced a chain of length "
                                                      print cl
                                                    ]
                                                  ]
                                                ]
                                              ]
                                            ]
                                          ]
                                        ]
                                      ]
                                    ]
                                  ]
                                ]
                              ]
                            ]
                          ]
                        ]
                      ]
                    ]
                  ]
                ]
              ]
            ]
          ]
        ]
      ]
    ]
  ]
  ;; Although the turtles at the head of vacancy chains are green, showing a green patch looks nicer.
  ask patch-here
    [set pcolor green]
end 
;; This procedure checks that a position in the 24-neighborhood is not forbidden by a wall.

to check-reachability
  set reachable? false
  foreach sort neighbors [
    if ([pcolor] of ? != red and any? turtles-on ? = false) [
      hatch 1 [
        setxy [pxcor] of ? [pycor] of ?
        set color blue
        set hidden? true
        repeat 20 [
          set heading random 360
          if ([pcolor] of patch-ahead 1 != red and member? (patch-ahead 1) ([patches in-radius 3] of myself)) [
            setxy ([pxcor] of patch-ahead 1) ([pycor] of patch-ahead 1)
            if (xcor = x-target and ycor = y-target) [
              set reachable? true
              stop
            ]
          ]
        ]
        die
      ]
    ]
  ]
end