turtles-own [ ;; Axelrod Culture Dissemination model culture ;; vector of length 5, containing values 1~10 similarity ;; an integer between 0 and 4 ] ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;; AGENT INITIALIZATION ;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to initialize-axelrod ask turtles [ set similarity 0 set culture n-values 5 [(random 9) + 1] ] ask turtles [ set-similarity do-coloring ] end to set-similarity set similarity 0 foreach (sort link-neighbors) [set similarity similarity + (similarity-between ? self)] end to do-coloring set color 109.9 - (2 * similarity) end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;; UPDATE RULES ;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to go ifelse simultaneous? [ask turtles [ let neighbor one-of link-neighbors if random-float 1 < (similarity-between neighbor self) [interact-with neighbor] set-similarity do-coloring]] [ask one-of turtles [ let neighbor one-of link-neighbors if random-float 1 < (similarity-between neighbor self) [interact-with neighbor] set-similarity do-coloring]] tick end to-report similarity-between [turtle1 turtle2] let culture1 [culture] of turtle1 let culture2 [culture] of turtle2 let same 0 ;; if the two lists contain the same traits, increase similarity ( foreach culture1 culture2 [ if ?1 = ?2 [set same same + 1] ] ) report (same / 5) ;; since 5 traits end to-report different-features [turtle1 turtle2] let culture1 [culture] of turtle1 let culture2 [culture] of turtle2 let values (list) foreach n-values 5 [?] [ if (item ? culture1 != item ? culture2) [ set values lput ? values ] ] report values end ;; select at random a feature on which the active site and its neighbor ;; differ (if there is one) and changing the active site's trait on this feature ;; to the neighbor's trait on this feature to interact-with [neighbor] ;; patch procedure if similarity-between self neighbor != 1 [ let index one-of (different-features self neighbor) let new-feature item index [culture] of neighbor set culture replace-item index culture new-feature ] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;; COLORING RULES ;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to recolor let different-cultures remove-duplicates [culture] of turtles foreach different-cultures [ ask turtles with [culture = ?] [set color 1 + position ? different-cultures] ] display end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;; NETWORK STRUCTURES ;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to setup-patch-lattice end to setup-lattice [len dim] ;; called Lattice __clear-all-and-reset-ticks crt len ^ dim initialize-axelrod ask turtles [ let id [who] of self let coordinates [] let temp 0 let target (turtle-set) foreach n-values dim [? + 1] [ set coordinates lput (id mod len ^ ? / len ^ (? - 1)) coordinates set id id - (id mod len ^ ?) ] ;; we want to add one to each coordinate, then create links with those coordinates foreach n-values dim [?] [ let temp-coordinates replace-item ? coordinates (item ? coordinates + 1) ;; add 1 to one of the coordinates if item ? temp-coordinates >= len [ set temp-coordinates replace-item ? temp-coordinates 0 ] foreach n-values dim [?] [ set temp temp + item ? temp-coordinates * len ^ ? ;; retrieve the turtle number from coordinates ] set target (turtle-set target turtle temp) set temp 0 ] create-links-with target ] end to setup-fully-connected ;; called Mean Field __clear-all-and-reset-ticks crt N initialize-axelrod ask turtles [create-links-with other turtles] end to setup-random ;; called Random __clear-all-and-reset-ticks crt N initialize-axelrod ask turtles [create-link-with one-of other turtles] end to setup-small-world ;; called Small World __clear-all-and-reset-ticks crt N initialize-axelrod ask turtles [ set shape "circle" ] layout-circle (sort turtles) max-pxcor - 1 let c 0 while [c < count turtles] [ ask turtle c [create-link-with turtle ((c + 1) mod count turtles)] set c c + 1 ] end to setup-preferential ;; called Scale Free __clear-all-and-reset-ticks create-initial-nodes repeat N - m0 [make-node-with preferential-group] initialize-axelrod end 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 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 to-report limit-magnitude [number limit] if number > limit [ report limit ] if number < (- limit) [ report (- limit) ] report number end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;; LAYOUT ;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 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 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 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 @#$#@#$#@ GRAPHICS-WINDOW 210 10 798 619 20 20 14.1 1 10 1 1 1 0 0 0 1 -20 20 -20 20 0 0 1 ticks 30.0 BUTTON 10 35 117 68 Lattice setup-lattice cube-length dimension NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 10 395 182 428 dimension dimension 0 10 3 1 1 NIL HORIZONTAL SLIDER 10 430 182 463 cube-length cube-length 0 50 7 1 1 NIL HORIZONTAL SLIDER 10 465 182 498 N N 0 1000 96 1 1 NIL HORIZONTAL BUTTON 10 75 97 108 Mean Field setup-fully-connected NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 100 75 200 108 Random setup-random NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 75 180 142 213 Layout layout T 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 10 180 73 213 Go go T 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 10 285 82 318 Recolor recolor NIL 1 T OBSERVER NIL NIL NIL NIL 1 PLOT 805 15 1070 225 Distinct cultures NIL NIL 0.0 10.0 0.0 10.0 true false "" "" PENS "default" 1.0 0 -16777216 true "" "plot length remove-duplicates [culture] of turtles" BUTTON 10 110 97 143 Scale Free setup-preferential NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 10 500 182 533 m0 m0 0 5 3 1 1 NIL HORIZONTAL SLIDER 10 535 182 568 m m 0 5 2 1 1 NIL HORIZONTAL BUTTON 85 285 187 318 Resize resize-nodes NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 10 320 122 353 radial-central layout-radial turtles links max-one-of turtles [count link-neighbors] NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 100 110 200 143 Small World setup-small-world NIL 1 T OBSERVER NIL NIL NIL NIL 1 SWITCH 10 220 142 253 simultaneous? simultaneous? 1 1 -1000 TEXTBOX 10 165 160 183 Running the model 12 0.0 1 TEXTBOX 10 20 160 38 Setup 12 0.0 1 TEXTBOX 10 270 185 296 Additional visualization options 12 0.0 1 TEXTBOX 10 380 160 398 Variables 12 0.0 1 MONITOR 805 230 905 275 Distinct cultures length remove-duplicates [culture] of turtles 17 1 11 @#$#@#$#@ ## WHAT IS IT? This model simulates how people become similar through interaction. The idea is based on Robert Axelrod’s _Dissemination of Culture_ (1997). In his paper, Axelrod notes that one universal feature of culture is that it is "something people learn from each other" and makes two assumptions: 1) People are more likely to interact with similar people, and 2) people become more similar after interactions. He goes on to cite three principles upon which his study is based on: 1) Agent-based modeling, 2) no central authority, and 3) adaptive (as opposed to rational) agents. ## HOW IT WORKS In this model, each agent has two properties: culture and similarity. Culture represents the distinctive characteristics of an agent, and similarity represents how similar its culture is to its linked neighbors. Culture is randomly assigned to each agent in the simulation, and similarity is determined by the amount of overlap in cultures between an agent and its neighbors. Users do not know the assigned cultures, but they can see how similar an agent is to its neighbors. In each tick, an agent potentially interacts with one of its linked neighbors. Interaction depends on the similarity between two agents; the more similar an agent is to its neighbor, the more likely they are to interact. If an agent does interact with its neighbor, then its own culture is modified to become more similar to its neighbor. If agents do not interact, then culture is unaffected. ## HOW TO USE IT To start, select one of five setup versions. These versions differ in how the agents are connected to one another. The options are Lattice, Mean Field, Random, Scale Free, and Small World. -Lattice: Creates cube-length^dimension agents and arranges and links them to represent a lattice. -Mean Field: Creates N agents and connects every agent to every other agent. -Random: Creates N agents. Each agent then randomly selects one other agent and makes a link with that agent. Though each agent may only select one target, it is possible for one agent to be the target of many other agents. -Scale Free: Arranges N agents into preferential groups determined by the m0 and m variables. -Small World: Creates N agents and arranges them in a circle. Each agent is linked with its adjacent agents. When using the Lattice, Random, or Scale Free setup, the Layout button may be pushed to assist in visualization. Push Layout again to stop the agent rearrangement. The radial-central button may also be useful for visualization purposes. Once the model is setup and you are ready to run the simulation, press the Go button. The simulation may be run simultaneously, on each tick every agent interacts with a neighbor, or not, on each tick one agent is randomly selected to interact with a neighbor. As the simulation runs, agents will change color from gray to various shades of blue. The darker the shade of blue, the more similar an agent is to its linked neighbors. The number of distinct cultures is tracked during this simulation. Press the Go button again to stop the simulation. Press the Recolor button to examine the distribution of culture. Each color represents a distinct culture. The resize button can help better see the color of the agents if they are too small. ## THINGS TO NOTICE Notice the change in shades of blue as the simulation goes on; concurrently, notice how the number of distinct cultures changes. When pressing the Recolor button, notice the relation between same culture/color and linked agents. ## THINGS TO TRY Adjust the five sliders under the variable section to play with larger or smaller network sizes. Adjusting the m and m0 sliders will also change the composition of the preferential groups used in the Scale Free setup. ## EXTENDING THE MODEL Whether or not an agent interacts with its randomly selected neighbor depends on their level of similarity. The more similar two agents are, the more likely they are to interact, and thus adjust the interactor's culture. By changing the interaction rule, one may examine how culture changes when agents are more or less likely to interact with those they are dissimilar too. This may be examined by adjusting the go function under the UPDATE RULES section of the code. Additional setup procedures may also be coded and tested under this Axelrod model. Under the current modeling choice, only the interactor changes its culture, the interactee is not affected by interaction. One potential extension is to have only the interactee change its culture, or to have both agents adjust their culture after interaction. It may be interesting to test how the simulation runs if there are agents who never adjust their culture mixed in with those who do. It may also be interesting to model situations where two agents have asymmetric likelihoods of culture-changing interactions between themselves, e.g. for fixed similarity, agent A is more likely to adjust its culture after interacting with agent B than agent B is after interacting with agent A. ## RELATED MODELS Confident Voter Heterogeneous Voter Social Consensus Ising Potts Turnout ## CREDITS AND REFERENCES Axelrod, Robert. 1997. 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