;;; ISING MODEL WITH THE BA NETWORK ;;; modified it so it matches description of potts, changed spins to opinions to match what was in the patch version turtles-own [ opinion ] globals [ sum-of-opinions moving-turtle moving-turtles ] ;;;;;;;;;;;;;;;;;;;;; ;; SETUP PROCEDURE ;; ;;;;;;;;;;;;;;;;;;;;; to setup ;; (for this model to work with NetLogo's new plotting features, ;; __clear-all-and-reset-ticks should be replaced with clear-all at ;; the beginning of your setup procedure and reset-ticks at the end ;; of the procedure.) clear-all set-default-shape turtles "circle" set moving-turtle nobody set moving-turtles turtle-set nobody ;; depending on which type of network the user chooses ;; we can create different types of networks if network-type = "Preferential Attachment" [ create-initial-nodes repeat N - m0 [ make-node-with preferential-group ] ask turtles [recolor-potts ]] if network-type = "Fully Connected" [ make-node N ask turtles [ create-links-with other turtles set size 3 ] layout-circle turtles 0.9 * max-pxcor ask turtles[recolor-potts]] if network-type = "Random Network" [ make-node N ask turtles [ repeat m [ create-link-with one-of other turtles set size 3 ] ] layout-circle turtles 0.9 * max-pxcor ask turtles [recolor-potts ]] set sum-of-opinions sum [opinion] of turtles setup-plot plotxy 0 magnetization plot-degree reset-ticks end ;; Creating a Preferential Attachment Network ;; ;; create m0 initial nodes so that every node is connected to to create-initial-nodes repeat m0 [ make-node-with one-of other turtles ]; with [not link-neighbor? self] ] ;;do we need this part? end ;; Idea: first create a function that takes two turtles as inputs and when executed, links the two ;; Next, repeat N times the following: create new node, link to m separate lottery winners to make-node [arg] crt arg ask turtles [set opinion random number-states] ;; [ ifelse random-float 2 < initial-magnetization + 1 ;; [ set spin 1 ] ;; [ set spin -1 ] ;; recolor ] end to recolor-potts set color blue + 2 * opinion end ;; used for creating a new node. ;; if TARGET is a single agent, link with that agent ;; if TARGET is a set of agents, link with all agents. to make-node-with [target] make-node 1 ask max-one-of turtles [who] ;; the last turtle added [ if target != nobody [ if is-agent? target [ create-link-with target [ set color gray ] move-to target ] if is-agentset? target [ create-links-with target[ set color gray ] move-to one-of target ] ;; position the new node near its partner fd 20 ] ] end to-report preferential-group ;; connect the turtle to m number of partners ;; start by creating one target let targets (turtle-set find-partner) repeat (m - 1) [ let next-node find-partner ;; add a target that is not already a target while [member? next-node targets] [set next-node find-partner ] set targets (turtle-set targets next-node) ] report targets end ;; This code is borrowed from Lottery Example (in the Code Examples ;; section of the Models Library). ;; The idea behind the code is a bit tricky to understand. ;; Basically we take the sum of the degrees (number of connections) ;; of the turtles, and that's how many "tickets" we have in our lottery. ;; Then we pick a random "ticket" (a random number). Then we step ;; through the turtles to figure out which node holds the winning ticket. to-report find-partner let total random-float sum [count link-neighbors] of turtles let partner nobody ask turtles [ let nc count link-neighbors ;; if there's no winner yet... if partner = nobody [ ifelse nc > total [ set partner self ] [ set total total - nc ] ] ] report partner end ;; This is the coloring procedure for an individual turtle ;;to recolor ;; ifelse spin = 1 ;; [ set color blue + 2 ] ;; [ set color blue - 2 ] ;;end ;;;;;;;;;;;;;; ;;; Layout ;;; ;;;;;;;;;;;;;; ;; resize-nodes, change back and forth from size based on degree to a size of 1 to resize-nodes ifelse all? turtles [size <= 1] [ ;; a node is a circle with diameter determined by ;; the SIZE variable; using SQRT makes the circle's ;; area proportional to its degree ask turtles [ set size sqrt count link-neighbors ] ] [ ask turtles [ set size 1 ] ] end to layout ;; the number 3 here is arbitrary; more repetitions slows down the ;; model, but too few gives poor layouts repeat 3 [ ;; the more turtles we have to fit into the same amount of space, ;; the smaller the inputs to layout-spring we'll need to use let factor sqrt count turtles ;; numbers here are arbitrarily chosen for pleasing appearance ifelse manual-layout? [ layout-spring turtles links spring-constant spring-length repulsion-constant ] [ layout-spring turtles links (1 / (factor)) (7 / factor) (7 / factor) ] display ;; for smooth animation ] ;; don't bump the edges of the world let x-offset max [xcor] of turtles + min [xcor] of turtles let y-offset max [ycor] of turtles + min [ycor] of turtles ;; big jumps look funny, so only adjust a little each time set x-offset limit-magnitude x-offset 0.1 set y-offset limit-magnitude y-offset 0.1 ask turtles [ setxy (xcor - x-offset / 2) (ycor - y-offset / 2) ] end to-report limit-magnitude [number limit] if number > limit [ report limit ] if number < (- limit) [ report (- limit) ] report number end ;;;;;;;;;;;;;; ;;;; GO ;;;; ;;;;;;;;;;;;;; to go ask one-of turtles [ update-metropolis ] tick if ticks mod plotting-interval = 0 [ set-current-plot "Magnetization" plotxy ticks magnetization ] plot-degree end to update-metropolis ;; turtle procedure, this is for potts ;; Consider a number-states state Potts model ;; consider a spin Si ;; choose a random spin out of the (number-states)-1 states, call it Sj ;; ediff is # neighboring spins that are Si - # neighboring spins that are Sj ;; if ediff <= 0, change Si to Sj ;; if ediff = n, change with prob exp(-n/T) let Sj random number-states while [Sj = opinion] [ set Sj random number-states ] let di count link-neighbors with [opinion = [opinion] of myself] let dj count link-neighbors with [opinion = Sj] let Ediff (di - dj) let rf random-float 1.0 if (Ediff <= 0) or (temperature > 0 and (rf < exp ((- Ediff) / temperature))) [ set opinion Sj set sum-of-opinions sum [opinion] of turtles recolor-potts] end ;;;;;;;;;;;;;;;;;;;;;;;;; ;;; PLOTTING PROCEDURE ;; ;;;;;;;;;;;;;;;;;;;;;;;;; to-report magnetization report (sum-of-opinions / (count turtles)) end to setup-plot set-current-plot "Magnetization" ;; draw a horizontal line to show the x axis set-current-plot-pen "axis" auto-plot-off plotxy 0 0 plotxy 1000000000000000 0 auto-plot-on set-current-plot-pen "average opinion" let max-degree max [count link-neighbors] of turtles set-current-plot "Degree Distribution" plot-pen-reset set-plot-x-range 1 (max-degree + 1) histogram [count link-neighbors] of turtles end to plot-degree let max-degree max [count link-neighbors] of turtles set-current-plot "Degree Distribution" plot-pen-reset set-plot-x-range 1 (max-degree + 1) histogram [count link-neighbors] of turtles end ;;;;;;;;;;;;;;;;;;;;;;;;;; ;; ADJUSTING PROCEDURES ;; ;;;;;;;;;;;;;;;;;;;;;;;;;; ;; The user has the option of changing the nodes ;; in order to make it easier to visualize, or test stuff. to move-node if style = "click and drag" [ if mouse-inside? [ do-highlight if mouse-down? [while [mouse-down?] [move display] ] ] ] if style = "radial layout" [ if mouse-inside? [ do-highlight if mouse-down? [ if moving-turtle != nobody [ layout-radial turtles links moving-turtle display] ]] ] if style = "circle" [ if mouse-inside? [ do-highlight if mouse-down? [ if moving-turtle != nobody [ layout-circle turtles 0.9 * max-pxcor] ]] ] if mouse-inside? != true [ reset-perspective ask turtles [recolor-potts] ask links [set color gray] ] display end to do-highlight ;; getting the node closest to the mouse let min-d min [distancexy mouse-xcor mouse-ycor] of turtles let node one-of turtles with [count link-neighbors > 0 and distancexy mouse-xcor mouse-ycor = min-d] if node != moving-turtle [ ask links [set color gray] ask turtles [recolor-potts] ] set moving-turtle node if node != nobody [ ;; highlight the chosen node ask node [ set color pink - 1 watch-me ] let neighbor-nodes [ link-neighbors ] of node set moving-turtles neighbor-nodes let direct-links [ my-links ] of node ;; highlight neighbors ask neighbor-nodes [ set color orange + 2 ;; highlight edges connecting the chosen node to its neighbors ask my-links [ ifelse (end1 = node or end2 = node) [ set color blue - 1 ] [ if (member? end1 neighbor-nodes and member? end2 neighbor-nodes) [ set color yellow ] ] ] ] ] end to move let factor sqrt count turtles if moving-turtle != nobody [ let number count moving-turtles if move-type = "agent and neighbors" [ set moving-turtles [link-neighbors] of moving-turtle ask moving-turtle [setxy mouse-xcor mouse-ycor] ; ask moving-turtles [set heading towards moving-turtle - 180] ; ask (turtle-set moving-turtle moving-turtles) [setxy mouse-xcor mouse-ycor] layout-spring moving-turtles [my-links] of moving-turtle (1 / (factor)) (70 / (factor)) (70 / (factor)) ] if move-type = "agent" [ ask moving-turtle [setxy mouse-xcor mouse-ycor ] ] if move-type = "agent and subordinates" [ set moving-turtles ([link-neighbors] of moving-turtle) with [count link-neighbors < [count link-neighbors] of moving-turtle] ask moving-turtle [setxy mouse-xcor mouse-ycor] ; ask moving-turtles [set heading towards moving-turtle - 180] ; ask (turtle-set moving-turtle moving-turtles) [setxy mouse-xcor mouse-ycor] layout-spring moving-turtles [my-links] of moving-turtle (1 / (factor)) (70 / (factor)) (70 / (factor)) ] ] end @#$#@#$#@ GRAPHICS-WINDOW 265 15 758 529 80 80 3.0 1 10 1 1 1 0 0 0 1 -80 80 -80 80 0 0 1 ticks 30.0 SLIDER 30 385 202 418 N N 0 1000 357 1 1 NIL HORIZONTAL SLIDER 30 420 202 453 m0 m0 2 10 2 1 1 NIL HORIZONTAL BUTTON 25 40 87 73 Setup setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 95 235 162 268 Layout layout T 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 865 225 1037 258 plotting-interval plotting-interval 1 1000 217 1 1 NIL HORIZONTAL SLIDER 25 130 197 163 temperature temperature 0 10 0.25 0.01 1 NIL HORIZONTAL PLOT 765 15 1035 215 Magnetization time NIL 0.0 20.0 0.0 1.0 true false "" "" PENS "average opinion" 1.0 0 -13345367 true "" "" "axis" 1.0 0 -16777216 true "" "" BUTTON 25 235 88 268 Go go T 1 T OBSERVER NIL NIL NIL NIL 1 MONITOR 765 225 855 270 NIL magnetization 3 1 11 SLIDER 30 455 202 488 m m 1 10 1 1 1 NIL HORIZONTAL SLIDER 30 545 202 578 spring-length spring-length 0 100 57.3 0.1 1 NIL HORIZONTAL SLIDER 30 580 202 613 repulsion-constant repulsion-constant 0 10 0.7 0.01 1 NIL HORIZONTAL SLIDER 30 615 202 648 spring-constant spring-constant 0 10 0.38 0.01 1 NIL HORIZONTAL SWITCH 30 510 150 543 manual-layout? manual-layout? 1 1 -1000 CHOOSER 25 80 206 125 network-type network-type "Preferential Attachment" "Fully Connected" "Random Network" 0 PLOT 1040 15 1325 215 Degree Distribution degree # of nodes 1.0 10.0 0.0 10.0 true false "" "" PENS "default" 1.0 1 -16777216 true "" "" BUTTON 765 370 859 403 NIL move-node T 1 T OBSERVER NIL NIL NIL NIL 1 CHOOSER 765 420 940 465 style style "click and drag" "radial layout" "circle" 1 CHOOSER 945 420 1122 465 move-type move-type "agent" "agent and neighbors" "agent and subordinates" 0 BUTTON 25 275 100 308 Resize resize-nodes NIL 1 T OBSERVER NIL NIL NIL NIL 1 MONITOR 945 360 1022 405 #neighbors [count link-neighbors ] of moving-turtle 17 1 11 BUTTON 860 370 923 403 calib set sum-of-opinions sum [opinion] of turtles NIL 1 T OBSERVER NIL NIL NIL NIL 1 MONITOR 1025 360 1112 405 moving-turtle [who] of moving-turtle 17 1 11 SLIDER 30 350 202 383 number-states number-states 2 10 4 1 1 NIL HORIZONTAL TEXTBOX 25 25 175 43 Setup 12 0.0 1 TEXTBOX 25 220 175 238 Running the model 12 0.0 1 TEXTBOX 30 335 180 353 Variables 12 0.0 1 TEXTBOX 30 495 180 513 Layout options 12 0.0 1 TEXTBOX 765 355 915 373 Moving nodes 12 0.0 1 @#$#@#$#@ ## WHAT IS IT? This model studies how social decision, known as magnetization, changes over time. Social decision is modeled as the average opinion of all agents. The number of potential opinions varies, and it is measured by the number-states variable. Agents adjust their opinion over time based on their current opinion, the opinions of their related agents, and the global ease of opinion change. As agent opinion changes, so does social decision. ## HOW IT WORKS Over time, agents interact with their neighbors. As they interact, their opinions change. They change based on the number of their neighbors who have the same opinion as the agent compared to the number of neighbors who have a certain different opinion. If there are more linked agents with the specific different opinion than agents who have the same opinion as the agent, then the agent will switch to the new opinion. The different opinion is selected at random from the set of opinions that the linked agents possess. Furthermore, there is a random component that allows the agent to change their opinion even if it has more neighbors that match its opinion than neighbors with the new opinion. This is where the temperature variable, measuring global ease of opinion change, comes into play. As the simulation runs and agents change their opinion, the user can track the magnetization over time. ## HOW TO USE IT There are three different options in the setup of the simulation: Preferential Attachment, Fully Connected, and Random Network. -Preferential Attachment: Arranges N agents into preferential groups determined by the m0 and m variables. -Fully Connected: Arranges N agents into a circle and connects each agent with every other agent. -Random Network: Arranges N agents into a circle. Then each agent creates links with m random other agents. Though each agent may only select m targets, it is possible for one agent to be the target of more than m other agents. After selecting the setup procedure, the agents will appear on the screen. Agents are colored different shades of blue to represent different opinions. To get a better look at the colors of the agents, press the resize button to increase their size. Press it again to change the agent size back to normal. When using the Preferential Attachment setup, the Layout button may be pushed to give a better view of the structure. Press the Layout button again to stop the movement. By selecting On from the manual-layout? switcher, you can use the spring-length, repulsion-constant, and spring-constant sliders to adjust the layout options. You may now start the simulation by pressing the Go button. Agent's will adjust their opinion and change their color. In addition, the change in magnetization will be tracked on the plot on the right side of the interface. Adjusting the plotting-interval slider will change the update frequency of the plot. When you have finished, press the Go button again to stop the simulation. The magnetization will be recorded in the monitor box labeled magnetization. This is the average opinion of all the agents, and it represents the social decision of the agents. If you wish to move the agents around, press the move-nodes button. This will allow you to move the various agents. There are three options under the style chooser. These will allow you to adjust the layout of the agents. Furthermore, the move-type chooser will allow you to adjust which agents move, if it is just the agent you select, or if additional agents will move as well. The agent being moved and the number of other agents being moved with it are tracked by the two corresponding monitor boxes. ## THINGS TO NOTICE Notice how magnetization changes over time, and how this differs how models of the three setup types. Adjust the sliders under the Variables header to see how they affect the various setups, and therefore the magnetization. ## THINGS TO TRY Adjust the temperature variable to alter the likelihood of opinion changing, which in turn will affect the magnetization and social decision of the simulation. ## EXTENDING THE MODEL Given that it is still possible for an agent to change its opinion despite complete magnetization given a high enough temperature variable, it may be interesting to see what happens when one adjusts the procedure that determines if an agent changes its opinion due to change. This function depends on the temperature, the difference in opinion among the agent's neighbors, and a random draw. By changing this function, one may change the outcome of the magnetization in this simulation. The function is found in the GO section of the code. Furthermore, one could try to incorporate a variable measuring initial magnetization. Currently, the model randomly assigns initial opinions uniformly. By adjusting the initial distribution of opinions, one may be able to model more interesting and realistic situations. ## RELATED MODELS Axelrod Confident Voter Heterogeneous Voter Social Consensus Ising Turnout @#$#@#$#@ 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 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 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-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 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 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