breed [cells cell] breed [rules rule] breed [heads head] undirected-link-breed [borders border] directed-link-breed [arrows arrow] globals [ first-state second-state quint-input program-loaded? q-state rule-count rt-tape lt-tape blank-symbol corner the-head the-active-cell at-index input transition-rules rule-table-pressed? input-pressed? first-run? rules-list flat-rules data-list] cells-own [symbol] rules-own [current-state new-state current-symbol new-symbol new-location rule-counter] heads-own [current-state current-symbol] to startup setup end to setup ca set input [] set quint-input [] set q-state 15 let tape patches with [pycor = -4] let head-patch patches with [pycor = -5 and pxcor = 0] set blank-symbol "_" let initial-state blue output-print "Quintuple (x,y,x',y',d) Given a Current\nState and a Current Symbol (x,y)\nChange State and Symbol to (x', y')\nand move tape in direction (d)\n------------------------------" ask head-patch [ sprout-heads 1 [ set shape "triangle" set size 2 set current-state (word initial-state ) set color read-from-string current-state ] ] set the-head turtle 0 ask tape [ sprout-cells 1 [set shape "square" set color (gray - 2 - random 2) set symbol "_" set label symbol ]] ;create alan turing ask one-of tape with [pxcor = 4] [sprout-cells 1 [set size 1.2 set shape "person" set heading 0 fd 1 set color 135 set at-index 4]] set rt-tape [] set lt-tape [] set first-run? 1 end to set-tape-symbols [#input] let sorted-cells sort-on [pxcor] cells with [pycor = -4] let i 0 while [i < (length first #input - 1) ] [show item i first #input set i i + 1 ] ;[ ask item i sorted-cells [set symbol item i first #input set label item i first #input set color item i first #input ] set i i + 1 ] ;foreach sort-on [pxcor] cells [ ask ? [set symbol item i #input set label symbol set i i + 1]] end to make-rule-table [#rules ] set corner patch (min-pxcor + 2) (max-pycor - 1) let i 0 ;row counter let j 0 ;group counter let k 0 let m 0 ; for determining first-state and second state --ie the start and ending states foreach #rules [ let q first ? let col1 item 1 ? let col2 item 2 ? let col3 item 3 ? let spacer 1.5 ask corner [ sprout-rules 1 [ set rule-counter k set k k + 1 set heading 90 fd 10 * j ;move to correct group position if i mod 5 = 0 [ make-header ] set heading 180 fd (2 + (i mod 5) * spacer) set heading 90 set shape "circle" set size 1 set color read-from-string first q set label first q if m = 0 [set first-state read-from-string first q ] if m = 1 [set second-state read-from-string first q ] set m m + 1 ;column one hatch-rules 1 [ set rule-counter k set k k + 1 fd 2 set current-symbol "0" set new-symbol item 1 col1 set new-location item 2 col1 set current-state first q set new-state first col1 show word "new-state " new-state set color read-from-string new-state set label (word new-symbol "-" new-location) ] ;column two hatch-rules 1 [ set rule-counter k set k k + 1 fd 4 set current-symbol "1" set new-symbol item 1 col2 set new-location item 2 col2 set current-state first q set new-state first col2 set color read-from-string new-state set label (word new-symbol "-" new-location) ] ;column three hatch-rules 1 [ set rule-counter k set k k + 1 fd 6 set current-symbol "_" set new-symbol item 1 col3 set new-location item 2 col3 set current-state first q set new-state first col3 set color read-from-string new-state set label (word new-symbol "-" new-location) ] set shape "triangle" ] ] if i mod 5 = 4 [set j j + 1 ] ;make multiple tables for longer rule sets set i i + 1 ] initialize-head end to-report change [#show-tuple] ifelse [current-state] of the-head = (word 15) ;red [ report (sentence "_" "15" "X") ] [ let active-rule rules with [ current-state = [current-state] of the-head and current-symbol = [current-symbol] of the-head ] ask active-rule [ set size 1.5 if #show-tuple = "yes"[ output-print (word "( " current-state ", " current-symbol " ) -- > ( "new-state ", " new-symbol ", " new-location " )")] ] report (sentence [new-symbol] of active-rule [new-state] of active-rule [new-location] of active-rule) ] end to go read rite change-state-and-move if done? [stop] end to read set the-active-cell one-of turtles-on patch 0 -4 ask the-head [set current-symbol (word [label] of the-active-cell) set label current-symbol] end to rite ask the-active-cell [set label first change "no" set symbol (word first change "no")] ask the-head [set label "" ] ;but we leave current-symbol set so that change procedure works end to change-state-and-move let new-q item 1 change "yes" let dir last change "no" ask the-head [set current-state new-q set color read-from-string current-state] move-tape dir ask rules [set size 1] end to clear-check ask turtles with [shape = "check"][die] end to-report done? ifelse [color] of the-head = red [ ask patch 0 -1 [sprout 1 [set color green set shape "check" set size 4 set label "DONE"]] report true ] [report false] end to move-tape [#dir] if #dir = "X"[ stop ] ;exit move-tape procedure if #dir = "R" [ ;add the symbol about to go off the screen to the tape list set rt-tape fput (word one-of [symbol] of cells-on patch max-pxcor -4) rt-tape ; ask cells-on patch max-pxcor -4 [die] ask cells [set heading 90 fd 1 ] create-cells 1 [ setxy min-pxcor -4 set shape "square" ifelse length lt-tape > 0 [ set symbol last lt-tape set lt-tape but-last lt-tape set label symbol ifelse symbol = "1" or symbol = "0" [set color gray ] [set color (gray - 2 - random 2) ] ] [ set symbol blank-symbol set label symbol set color (gray - 2 - random 2) ] ] set at-index at-index + 1 ] if #dir = "L" [ set lt-tape lput (word one-of [symbol] of cells-on patch min-pxcor -4) lt-tape ask cells-on patch min-pxcor -4 [die] ask cells [set heading 270 fd 1 ] create-cells 1 [ setxy max-pxcor -4 set shape "square" ifelse length rt-tape > 0 [ set symbol first rt-tape set rt-tape but-first rt-tape set label symbol ifelse symbol = "1" or symbol = "0" [set color gray ] [set color (gray - 2 - random 2) ] ] [ set symbol blank-symbol set label symbol set color (gray - 2 - random 2) ] ] set at-index at-index - 1 ] update-head ;This just allows us to hide the little figure so that he does wrap and destroy the illusion of a moving tape. if at-index >= max-pxcor or at-index <= min-pxcor [ask cells with [pycor = -3] [ht] ] if at-index <= max-pxcor and at-index >= min-pxcor [ask cells with [pycor = -3] [st] ] end ;; extra stuff just to make things pretty to initialize-head ask heads [ let x first-state set color x set current-state (word x ) ] end to change-head ask heads [ let x [color] of one-of sort-on [who] rules set color x set current-state (word x ) ] end to load-input let sorted-cells sort-on [xcor] cells with [ ycor = -4 ] set data-list read-from-string input-symbols let i 0 foreach data-list [ ask item i sorted-cells [set label ? set symbol ? set color gray] set i i + 1 wait .22 ] repeat max-pxcor - 2 [ move-tape "R" wait .03 ] update-head end to update-head set the-active-cell one-of turtles-on patch 0 -4 ask the-head [let x (word [symbol] of the-active-cell) set label x set current-symbol x] end ;to read-program ; set the-active-cell one-of turtles-on patch 0 -4 ; let i 0 ; while [[size] of the-active-cell > .6 ] [ wait 1 ask rules with [ i = rule-counter] [st] move-tape "L" set the-active-cell one-of turtles-on patch 0 -4 set i i + 1 ] ; set program-loaded? 1 ;end to make-header ;borders hatch 1 [ set breed turtles set heading 90 fd .75 set heading 180 fd 1 ht hatch 1 [ set heading 90 fd 8 create-border-with myself] hatch 1 [ set heading 180 fd 8 create-border-with myself]] ;header hatch 1 [set shape "zero" set heading 90 fd 2 set color white ] hatch 1 [set shape "one" set heading 90 fd 4 set color white ] hatch 1 [set shape "underscore" set heading 90 fd 6 set color white ] end to-report make-row-groups [#list] let i 0 let grouped-list [] set #list but-first #list while [i < (length #list - 3)] [ set grouped-list lput (list item i #list item (i + 1) #list item (i + 2) #list item (i + 3) #list) grouped-list set i i + 4 ] report grouped-list end ;------------------------------------- to-report list-from-file [#filename] file-close-all file-open #filename let temp [] while [not file-at-end? ] [ set temp lput file-read-line temp ] let list-of-file-values [] foreach temp [ set list-of-file-values lput split ? "," list-of-file-values ] report list-of-file-values end ; split is a generic function to split strings remove quotes is added by the two read from string calls to-report split [ #string #sep ] ; #sep must be non-empty string let result [] ; return value let w length #sep loop ; exit when done [ let next-pos position #sep #string if not is-number? next-pos [ report reverse (fput #string result) ] set result fput (substring #string 0 next-pos) result set #string substring #string (next-pos + w) (length #string) ] end @#$#@#$#@ GRAPHICS-WINDOW 225 55 1272 375 30 8 17.0 1 12 1 1 1 0 1 1 1 -30 30 -8 8 0 0 1 ticks 30.0 BUTTON 15 385 160 440 Reset setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 1148 330 1253 363 Tape right >> move-tape \"R\" NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 244 327 356 360 << Tape left move-tape \"L\" NIL 1 T OBSERVER NIL NIL NIL NIL 1 TEXTBOX 20 10 365 51 Programmable Turing Machine 18 0.0 1 TEXTBOX 67 32 377 58 Load rules from a spreadsheet csv file. 12 0.0 1 BUTTON 675 335 815 368 Change State of Head change-head NIL 1 T OBSERVER NIL NIL NIL NIL 1 OUTPUT 230 440 865 580 12 BUTTON 10 105 130 138 Rule Table \nmake-rule-table make-row-groups list-from-file user-file\n\n;make-rule-table make-row-groups list-from-file \"test.csv\" NIL 1 T OBSERVER NIL NIL NIL NIL 1 INPUTBOX 10 230 205 290 input-symbols [ 1 1 1 \"_\" 0 1 1] 1 0 String BUTTON 12 190 132 223 Load Input load-input NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 15 340 78 373 NIL go NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 95 340 158 373 NIL go T 1 T OBSERVER NIL NIL NIL NIL 1 MONITOR 700 380 792 425 Current State [current-state] of the-head 17 1 11 BUTTON 795 385 865 418 reset head initialize-head\nclear-check NIL 1 T OBSERVER NIL NIL NIL NIL 1 TEXTBOX 15 70 185 101 1) Load CSV Rule Table 14 0.0 1 TEXTBOX 15 160 195 191 2) Load Input (1, 0, or \"_\") 14 0.0 1 TEXTBOX 15 310 165 328 3) Step through Rules 14 0.0 1 @#$#@#$#@ ## WHAT IS IT? In 1936 Alan Turing published a paper describing some fundamental limits to logic and mathematics. In order to build his argument, he needed to create a rigor and formal defintion of an algorithm, or as it is called now, computation. Computation is the stepwise process that we take when we solve math problems, build proofs and use deductive logic. ## HOW IT WORKS In order to explain his formalism, Turing described a hypothetical machine with an infinite tape, a head that reads and write to the tape, and a mechanism to move the tape right or left. The head can be in one of multiple states. At each step The state of the head AND the particular symbol under the head at that point in time define a particular transition rule that instructs the head to write a new (or the same) symbol, change (or remain in the same) state, and move the tape right or left. We can develop some notation for this situation: (q, sym) --> (q', sym', dir) that makes it quite clear that each logical step consists of five elements. A state potentially changing to at new state, a symbol on the tape potentially changing to a new symbol and the potential shift in environment (the tape). These simple steps are the essense of computation and, as we have seen in the decades since Turing, a great deal can be accomplished with these steps. In fact, all of conventional mathematics can be produced from the variation, combination and accumulation of these tiny pieces of logic. But, almost ironically, this was not Turing's objective. See below. ## HOW TO USE IT This Model imports a csv file from the same directory as the model. The imported file needs to be a CSV file with a header row and four columns (see/modify example.csv). It is crucial that the csv file have exactly one header row, 4 columns, and four rows for each state. The first row of each group of four is the number of the state (numbers ending in 0 will be black and not visible--use state numbers ending in 5, 6 or 7). Comments are recommended and should be placed in the fourth column. The second row in each group of 4 is represents the state when head is reading a 0, the thrid, when head is reading a 1, and the fourth, reading a blank or underscore. ## THE LARGER CONTEXT Turing paper was motivated by his interest in demonstrating the limits of what could be computed by the step-wise method of an algorithm. ## THINGS TO TRY Try to create a program that: -- turns 1's into 0's -- adds two binary numbers -- converts binary numbers to unary numbers -- add two unary numbers -- try creating a program in as few lines as possible, then again, in as many lines (with each step contributing miinutely to the solution) -- build an MP3 player (theoretically possible, but unlikely to play songs in real-time) ## NETLOGO FEATURES This model uses custom turtles for the table header, turles and links as arrows and labels. It also make extensive use of lists. There are no sophisticated programmming techniques employed. ## RELATED MODELS This model series includes four NetLogo models: -- Simple Turing Machine--this model An introduction to the basic parts/terminology of the Turing machine) -- Universal Turing Maching Illustration of a machine that accepts as input both program and data) --A Turing Machine that accepts input from a CSV file This is the model to use to develop programs that run on the Turing machine --The Halting Problem Turing's proof of the impossibility of proving that mathematically truths are reachable within a given system of logic. ## CREDITS AND REFERENCES @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 150 240 Polygon -7500403 true true 150 165 89 198 75 225 75 255 105 270 135 255 150 240 Polygon -7500403 true true 139 148 100 105 55 90 25 90 10 105 10 135 25 180 40 195 85 194 139 163 Polygon -7500403 true true 162 150 200 105 245 90 275 90 290 105 290 135 275 180 260 195 215 195 162 165 Polygon -16777216 true false 150 255 135 225 120 150 135 120 150 105 165 120 180 150 165 225 Circle -16777216 true false 135 90 30 Line -16777216 false 150 105 195 60 Line -16777216 false 150 105 105 60 car false 0 Polygon -7500403 true true 300 180 279 164 261 144 240 135 226 132 213 106 203 84 185 63 159 50 135 50 75 60 0 150 0 165 0 225 300 225 300 180 Circle -16777216 true false 180 180 90 Circle -16777216 true false 30 180 90 Polygon -16777216 true false 162 80 132 78 134 135 209 135 194 105 189 96 180 89 Circle -7500403 true true 47 195 58 Circle -7500403 true true 195 195 58 check false 0 Polygon -7500403 true true 55 138 22 155 53 196 72 232 91 288 111 272 136 258 147 220 167 174 208 113 280 24 257 7 192 78 151 138 106 213 87 182 circle false 0 Circle -7500403 true true 0 0 300 circle 2 false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 cow false 0 Polygon -7500403 true true 200 193 197 249 179 249 177 196 166 187 140 189 93 191 78 179 72 211 49 209 48 181 37 149 25 120 25 89 45 72 103 84 179 75 198 76 252 64 272 81 293 103 285 121 255 121 242 118 224 167 Polygon -7500403 true true 73 210 86 251 62 249 48 208 Polygon -7500403 true true 25 114 16 195 9 204 23 213 25 200 39 123 cylinder false 0 Circle -7500403 true true 0 0 300 dot false 0 Circle -7500403 true true 90 90 120 face happy false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 255 90 239 62 213 47 191 67 179 90 203 109 218 150 225 192 218 210 203 227 181 251 194 236 217 212 240 face neutral false 0 Circle -7500403 true true 8 7 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Rectangle -16777216 true false 60 195 240 225 face sad false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 168 90 184 62 210 47 232 67 244 90 220 109 205 150 198 192 205 210 220 227 242 251 229 236 206 212 183 fish false 0 Polygon -1 true false 44 131 21 87 15 86 0 120 15 150 0 180 13 214 20 212 45 166 Polygon -1 true false 135 195 119 235 95 218 76 210 46 204 60 165 Polygon -1 true false 75 45 83 77 71 103 86 114 166 78 135 60 Polygon -7500403 true true 30 136 151 77 226 81 280 119 292 146 292 160 287 170 270 195 195 210 151 212 30 166 Circle -16777216 true false 215 106 30 flag false 0 Rectangle -7500403 true true 60 15 75 300 Polygon -7500403 true true 90 150 270 90 90 30 Line -7500403 true 75 135 90 135 Line -7500403 true 75 45 90 45 flower false 0 Polygon -10899396 true false 135 120 165 165 180 210 180 240 150 300 165 300 195 240 195 195 165 135 Circle -7500403 true true 85 132 38 Circle -7500403 true true 130 147 38 Circle -7500403 true true 192 85 38 Circle -7500403 true true 85 40 38 Circle -7500403 true true 177 40 38 Circle -7500403 true true 177 132 38 Circle -7500403 true true 70 85 38 Circle -7500403 true true 130 25 38 Circle -7500403 true true 96 51 108 Circle -16777216 true false 113 68 74 Polygon -10899396 true false 189 233 219 188 249 173 279 188 234 218 Polygon -10899396 true false 180 255 150 210 105 210 75 240 135 240 hash false 0 Polygon -7500403 true true 135 45 165 45 120 270 90 270 Polygon -7500403 true true 195 45 225 45 180 270 150 270 Rectangle -7500403 true true 75 105 240 120 Rectangle -7500403 true true 75 180 225 195 house false 0 Rectangle -7500403 true true 45 120 255 285 Rectangle -16777216 true false 120 210 180 285 Polygon -7500403 true true 15 120 150 15 285 120 Line -16777216 false 30 120 270 120 leaf false 0 Polygon -7500403 true true 150 210 135 195 120 210 60 210 30 195 60 180 60 165 15 135 30 120 15 105 40 104 45 90 60 90 90 105 105 120 120 120 105 60 120 60 135 30 150 15 165 30 180 60 195 60 180 120 195 120 210 105 240 90 255 90 263 104 285 105 270 120 285 135 240 165 240 180 270 195 240 210 180 210 165 195 Polygon -7500403 true true 135 195 135 240 120 255 105 255 105 285 135 285 165 240 165 195 line true 0 Line -7500403 true 150 0 150 300 line half true 0 Line -7500403 true 150 0 150 150 one false 2 Rectangle -7500403 false false 135 45 150 270 Rectangle -955883 false true 135 45 150 270 Rectangle -7500403 false false 120 45 135 60 Rectangle -955883 false true 105 255 180 270 Line -7500403 false 135 60 150 60 Rectangle -955883 true true 135 45 150 270 Rectangle -955883 true true 120 45 150 60 Rectangle -955883 true true 105 255 180 270 Rectangle -955883 true true 120 60 135 75 Rectangle -955883 true true 105 60 120 75 Rectangle -955883 true true 90 240 195 270 Circle -16777216 true false 180 225 30 Circle -16777216 true false 75 225 30 Rectangle -955883 true true 120 45 105 60 Rectangle -955883 true true 105 45 120 75 Rectangle -955883 true true 90 45 105 75 Circle -16777216 true false 75 30 30 pentagon false 0 Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120 person false 0 Circle -7500403 true true 110 5 80 Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90 Rectangle -7500403 true true 127 79 172 94 Polygon -7500403 true true 195 90 240 150 225 180 165 105 Polygon -7500403 true true 105 90 60 150 75 180 135 105 plant false 0 Rectangle -7500403 true true 135 90 165 300 Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285 Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285 Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210 Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135 Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135 Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60 Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90 sheep false 0 Rectangle -7500403 true true 151 225 180 285 Rectangle -7500403 true true 47 225 75 285 Rectangle -7500403 true true 15 75 210 225 Circle -7500403 true true 135 75 150 Circle -16777216 true false 165 76 116 square false 0 Rectangle -7500403 true true 30 30 270 270 square 2 false 0 Rectangle -7500403 true true 30 30 270 270 Rectangle -16777216 true false 60 60 240 240 star false 0 Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108 target false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 Circle -7500403 true true 60 60 180 Circle -16777216 true false 90 90 120 Circle -7500403 true true 120 120 60 tree false 0 Circle -7500403 true true 118 3 94 Rectangle -6459832 true false 120 195 180 300 Circle -7500403 true true 65 21 108 Circle -7500403 true true 116 41 127 Circle -7500403 true true 45 90 120 Circle -7500403 true true 104 74 152 triangle false 0 Polygon -7500403 true true 150 30 15 255 285 255 triangle 2 false 0 Polygon -7500403 true true 150 30 15 255 285 255 Polygon -16777216 true false 151 99 225 223 75 224 truck false 0 Rectangle -7500403 true true 4 45 195 187 Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194 Rectangle -1 true false 195 60 195 105 Polygon -16777216 true false 238 112 252 141 219 141 218 112 Circle -16777216 true false 234 174 42 Rectangle -7500403 true true 181 185 214 194 Circle -16777216 true false 144 174 42 Circle -16777216 true false 24 174 42 Circle -7500403 false true 24 174 42 Circle -7500403 false true 144 174 42 Circle -7500403 false true 234 174 42 turtle true 0 Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210 Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105 Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105 Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87 Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210 Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99 two false 0 Circle -7500403 true true 75 15 150 Polygon -7500403 true true 90 60 150 30 150 45 105 75 90 60 150 30 Rectangle -7500403 true true 150 30 150 45 Polygon -7500403 true true 225 75 225 135 210 135 210 90 225 75 Polygon 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true true 0 225 300 270 wheel false 0 Circle -7500403 true true 3 3 294 Circle -16777216 true false 30 30 240 Line -7500403 true 150 285 150 15 Line -7500403 true 15 150 285 150 Circle -7500403 true true 120 120 60 Line -7500403 true 216 40 79 269 Line -7500403 true 40 84 269 221 Line -7500403 true 40 216 269 79 Line -7500403 true 84 40 221 269 x false 0 Polygon -7500403 true true 270 75 225 30 30 225 75 270 Polygon -7500403 true true 30 75 75 30 270 225 225 270 zero false 0 Circle -7500403 true true 16 16 268 Rectangle -16777216 true false 0 0 30 315 Rectangle -16777216 true false 270 0 330 300 Rectangle -16777216 true false 105 105 195 195 Circle -16777216 true false 89 44 122 Circle -16777216 true false 90 135 120 Rectangle -16777216 true false 90 120 210 195 @#$#@#$#@ NetLogo 5.0beta3 @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ default 0.0 -0.2 0 0.0 1.0 0.0 1 1.0 0.0 0.2 0 0.0 1.0 link direction true 0 Polygon -7500403 true true 150 0 105 75 195 75 150 0 arrow 0.0 -0.2 0 0.0 1.0 0.0 1 1.0 0.0 0.2 0 0.0 1.0 link direction true 0 Line -7500403 true 150 0 105 75 Line -7500403 true 150 0 195 75 Line -7500403 true 105 75 195 75 Polygon -7500403 true true 150 0 105 75 195 75 @#$#@#$#@ 1 @#$#@#$#@