breeds [magnets bob] magnets-own [x-from-bob y-from-bob] turtles-own [mass xvelocity yvelocity accx accy newx newy radius init-radius] globals [time pull oldZoom clock] to setup ;Creates the number of magnets indicated by the slider "NumMagnets" and randomly positions ;them within the distance boundaries indicated by two sliders, "MagMaxRadius" and "MagMinRadius". ;It also sets up a "swinging" bob by calling setup-bob described below. ca cc set Zoom 1 set oldZoom 1 set-pull ;These sliders specify the minimum and maximum distance from center for magnet placement, as a percent of the total screen width. ;Setting them equal results in all magnets equidistant from the center. If the minimum is set larger than the maximum, the minimum is ;automatically set equal to the maximum. if MagMinRadius > MagMaxRadius [set MagMinRadius MagMaxRadius] ask patch-at 0 0 [ sprout NumMagnets [ set breed magnets set shape "circle" set color green set init-radius random-int-or-float screen-edge-x * (MagMaxRadius - MagMinRadius) / 100 + MagMinRadius * screen-edge-x / 100 ] ] ;This translates a radius into corresponding coordinates randomly positioned on the screen. Using these coordinates ;rather than screen coordinates permits easy scaling during runs. ;init-radius is treated as hypotenuse of right triangle and newx and newy are the two other sides. ask magnets [ ifelse random-int-or-float 2 = 0 ;;newx can be positive or negative and up to length of radius [set newx random-int-or-float init-radius] [set newx 0 - random-int-or-float init-radius] ifelse random-int-or-float 2 = 0 [set newy sqrt (init-radius ^ 2 - newx ^ 2)] ;;newy can be positive or negative [set newy 0 - sqrt (init-radius ^ 2 - newx ^ 2)] ] ask magnets [ set label who + 1 set label-color green ] ask patch-at 0 0 [ set pcolor red ] ask turtles [ ;;if magnet or bob would be off-screen, hide it - otherwise show according to current scaling ifelse abs (newx / Zoom) > screen-edge-x or abs (newy / Zoom) > screen-edge-x [set hidden? true] [set hidden? false setxy newx / Zoom newy / Zoom] ] setup-bob end to toggle-labels ;turns labels for magnets on or off when button is pushed ask magnets [ ifelse label = no-label [set label who + 1 set label-color green] [set label no-label] ] end to setup-bob ;Positions a bob on the screen using same type scheme as for positioning magnets, so a minimum and maximum radius can be specified with sliders ClearTrace if bobMinRadius > bobMaxRadius [set bobMinRadius bobMaxRadius] if any bob = true [ask bob [die]] ;;kill any existing bob(s) before creating a new one ask patch-at 0 0 [ sprout 1 [ set color yellow set breed bob set init-radius random-int-or-float screen-edge-x * (bobMaxRadius - bobMinRadius) / 100 + bobMinRadius * screen-edge-x / 100 ] ] ask bob [ ifelse random-int-or-float 2 = 0 [set newx random-int-or-float (init-radius)] [set newx 0 - random-int-or-float (init-radius)] ifelse random-int-or-float 2 = 0 [set newy sqrt (init-radius ^ 2 - newx ^ 2)] [set newy 0 - sqrt (init-radius ^ 2 - newx ^ 2)] ] ask bob [ set shape "circle" if distancexy 0 0 > 0 [ set heading towardsxy-nowrap 0 0 ] ] init-bob end to init-bob ;Sets the initial accelerations and velocities in x and y directions for the bob. ;A button "Reset Beginning" can be used at any time to call this routine, which resets the bob ;to initial conditions at its current position ClearTrace set-pull ;initial acceleration in x and y directions is based on simple harmonic motion where velocity = sqrt(k/m(acceleration ^2 - x^2)) where ;x is distance from center, in this case at time = 0, and the constant "gravity" set via slider, is substituted for k/m. ask bob [ set xvelocity 0 set yvelocity 0 set accx 0 - gravity * newx set accy 0 - gravity * newy ] ;the magnets own the values of distance of themselves from the bob ask magnets [ set x-from-bob newx-of one-of bob - newx set y-from-bob newy-of one-of bob - newy ] ;;the bob asks each magnet to add its contribution to acceleration using formula, ;;acceleration in x direction = -(x distance from bob) * (magnet strength)/ (radius from bob) ^ 3 ask bob [ ask magnets [ set radius sqrt ((x-from-bob)^ 2 + (y-from-bob)^ 2) set accx-of myself accx-of myself - (pull * x-from-bob / radius ^ 3) set accy-of myself accy-of myself - (pull * y-from-bob / radius ^ 3) ] ] ;initially add to velocity the acceleration resulting from first time interval, but applied over half the time to give average acceleration ask bob [ set xvelocity xvelocity + accx * time / 2 set yvelocity yvelocity + accy * time / 2 ] ask turtles [ ifelse abs (newx / Zoom) > screen-edge-x or abs (newy / Zoom) > screen-edge-x [set hidden? true] [set hidden? false setxy newx / Zoom newy / Zoom] ] end to go swing end to swing ;using the same formulas described above this routine updates acceleration and velocity of bob based on new position ;the variable settings for magnet strength, gravity, and speed can be changed during a run ;pressing the "Setup bob" button will kill the curent bob, erase any trace, and start a new one running ;pressing the "Reset Beginning" button will use the current bob and start it running from its current position as though it were just placed there set-pull if Trace = true and fade-rate != 0 and clock = 500 [ ;;run fade routine only every 500 steps to avoid slowing run speed too much set clock 0 ask patches with [shade-of? pcolor yellow = true][ fade] ] ask bob [ if Trace = true [stamp yellow] set newx newx + xvelocity * time set newy newy + yvelocity * time ] ;the Zoom slider can be used to view the bob if its coordinates are off-screen, but traces are not scaled ask bob [ ifelse abs (newx / Zoom) > screen-edge-x or abs (newy / Zoom) > screen-edge-x [set hidden? true] [set hidden? false setxy newx / Zoom newy / Zoom] ] if Zoom != oldZoom ;;if Zoom slider has not been reset, do not redraw magnets. Redrawing them each time greatly reduces run speed. [set oldZoom Zoom ask magnets [ ifelse abs (newx / Zoom) > screen-edge-x or abs (newy / Zoom) > screen-edge-x [set hidden? true] [set hidden? false setxy newx / Zoom newy / Zoom] ] ] ask magnets [ set x-from-bob newx-of one-of bob - newx set y-from-bob newy-of one-of bob - newy ] ask bob [ set accx 0 - gravity * newx set accy 0 - gravity * newy ask magnets [ set radius sqrt ((x-from-bob)^ 2 + (y-from-bob)^ 2) ;in the formula below, the value 5 is added to the radius cubed to simulate an actual volume for the magnets and keep the "distance" between bob ;and magnet from being so near zero that huge accelerations result set accx-of myself accx-of myself - (pull * x-from-bob /(5 + radius ^ 3)) set accy-of myself accy-of myself - (pull * y-from-bob /(5 + radius ^ 3)) ] ] ask bob [ set xvelocity (xvelocity + accx * time) set yvelocity (yvelocity + accy * time) ] set clock clock + 1 end to ClearTrace ask patches with [shade-of? pcolor yellow = true][ set pcolor black ] ask patch-at 0 0 [ set pcolor red ] end to fade ;; Patch Procedure locals [new-color] set new-color pcolor - fade-rate * 5 / 100 ;; if the new-color is no longer the same shade then it's faded to black. ifelse (shade-of? pcolor new-color) [ set pcolor new-color ] [ set pcolor black ] end to set-pull ;all magnets have the same "pull" indicated by the slider "Magstrength" set pull MagStrength * 1000 set time speed / 1500 ;;The higher the speed the longer the time intervals and greater distances between computations end ;;resulting in less accuracy. @#$#@#$#@ GRAPHICS-WINDOW 413 10 1026 644 100 100 3.0 1 10 1 1 1 CC-WINDOW 7 566 408 688 Command Center BUTTON 19 42 145 75 Setup Setup NIL 1 T OBSERVER T BUTTON 268 42 349 75 Go Go T 1 T OBSERVER NIL SLIDER 261 356 364 389 Zoom Zoom 1 10 1 1 1 NIL BUTTON 23 371 119 404 Setup bob Setup-bob NIL 1 T OBSERVER T BUTTON 269 92 374 125 Reset Beginning Init-bob NIL 1 T OBSERVER T SLIDER 23 152 143 185 NumMagnets NumMagnets 0 10 6 1 1 NIL SLIDER 19 318 140 351 MagStrength MagStrength 0 100 30 5 1 NIL SLIDER 21 525 142 558 gravity gravity 0 10 4 1 1 NIL SWITCH 268 258 371 291 Trace Trace 0 1 -1000 BUTTON 268 165 373 198 Clear Trace ClearTrace NIL 1 T OBSERVER T BUTTON 21 93 139 126 Labels On/Off toggle-labels NIL 1 T OBSERVER T SLIDER 261 305 371 338 Speed Speed 1 10 5 1 1 NIL SLIDER 23 198 141 231 MagMaxRadius MagMaxRadius 0 100 50 1 1 NIL SLIDER 20 243 141 276 MagMinRadius MagMinRadius 0 100 30 1 1 NIL SLIDER 20 422 144 455 bobMaxRadius bobMaxRadius 0 100 20 1 1 NIL SLIDER 18 469 145 502 bobMinRadius bobMinRadius 0 100 15 1 1 NIL SLIDER 267 214 373 247 fade-rate fade-rate 0 50 10 1 1 NIL @#$#@#$#@ This model mimics the behavior of a magnet suspended over other magnets fixed on a surface such that the suspended magnet is attracted by the fixed ones, but cannot contact them. The resulting motion of the suspended magnet is random. In this model the suspended magnet, called the bob, is a turtle which slides among the fixed magnets, but is not "allowed" to collide with them. The bob can act like a pendulum with simple harmonic motion by setting the force attracting the bob to the center to a non-zero value. Unlike a pendulum the bob does not separate vertically from the fixed magnets as it "swings" away from its equilibrium point. The number of fixed magnets can be varied from 0 to 10. The magnetic force between each fixed magnet and the bob can be varied, but is the same for all fixed magnets. How to Play Before pressing the Setup button: Select the number of fixed magnets using the slider "NumMagnets". Select the minimum and maximum distance from the center to locate the fixed magnets using the sliders "MagMaxRadius" and "MagMinRadius". If the maximum is set to less than the minimum, it defaults to the minimum and all magnets will be placed at that same distance. Otherwise they are randomly placed within the range specified. Select the magnetic strenth to apply using slider "MagStrength". If it is set to zero, only the "gravity" force on the bob will attract it and the bob will simply move back and forth. Select the minimum and maximum distance from the center to locate the bob using the sliders "bobMaxRadius" and "bobMinRadius". If the maximum is set to less than the minimum, it defaults to the minimum and the bob will be placed at that same distance. Otherwise it is randomly placed within the range specified. Select the force on the bob using the slider "gravity". If it is set to zero, only the fixed magnets will attract the bob. Note: Speed settings actually change the size of time intervals between computation of position of the bob. The further the bob travels between these updates, the less accurate the updates are. Stronger magnet strength and bob gravity causes higher acceleration and velocity, which, like increasing speed, results in larger position changes between computations. This means that if you use higher magnet strength and/or bob gravity, you may need to use slower speed settings to keep accuracy of trajectory calculations acceptable. After pressing the Setup button and before pressing the Go button: If you don't like the positioning of the magnets and bob, press Setup again. At any time: If you like the positioning of the fixed magnets but not that of the bob, press the "Setup bob" button. This will reposition the bob but not the fixed magnets. If the model is running, this will clear any existing trace and the model will continue running as though it were just started with the bob at its new location. Press the "Labels On/Off" button to toggle the display of the fixed magnet labels, which is simply their number ID. Set the "Trace On/Off" switch as desired. Set the "fade-rate" slider to vary the speed with which the trace fades out. Fading is not executed for each point plotted, but only every 500 points. This greatly speeds up the model. Change the execution speed using the "Speed" slider. Because this actually changes the size of the time steps between computation of new positions, if the speed is changed during a run, the bob path may not be exactly the same as it would have been without a speed change. Use the "Zoom" slider to zoom in or out on the screen. The bob and magnet coordinates are maintained separately and then mapped onto the screen. The bob can "swing" off screen and then come back into view again. Because an existing trace cannot be zoomed, it is cleared whenever the Zoom setting is changed. Press "Clear Trace" button to clear an existing trace without affecting anything else. If the model is running the bob will continue its motion, leaving a new trace from that point, if the "Trace On/Off" switch is "On". If you would like to have the bob, at its current position, whether the model is running or not, behave as though the model were just started running, press the "Reset Beginning" button. Except that the bob is started from its current location and not randomly repositioned, this button acts like the "Reset bob" button. You can change the magnet strength. You can change the bob's gravity. Have fun, but don't get hypnotized! @#$#@#$#@ default true 0 Polygon -7566196 true true 150 5 40 250 150 205 260 250 ant true 0 Polygon -7566196 true true 136 61 129 46 144 30 119 45 124 60 114 82 97 37 132 10 93 36 111 84 127 105 172 105 189 84 208 35 171 11 202 35 204 37 186 82 177 60 180 44 159 32 170 44 165 60 Polygon -7566196 true true 150 95 135 103 139 117 125 149 137 180 135 196 150 204 166 195 161 180 174 150 158 116 164 102 Polygon -7566196 true true 149 186 128 197 114 232 134 270 149 282 166 270 185 232 171 195 149 186 149 186 Polygon -7566196 true true 225 66 230 107 159 122 161 127 234 111 236 106 Polygon -7566196 true true 78 58 99 116 139 123 137 128 95 119 Polygon -7566196 true true 48 103 90 147 129 147 130 151 86 151 Polygon -7566196 true true 65 224 92 171 134 160 135 164 95 175 Polygon -7566196 true true 235 222 210 170 163 162 161 166 208 174 Polygon -7566196 true true 249 107 211 147 168 147 168 150 213 150 arrow true 0 Polygon -7566196 true true 150 0 0 150 105 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-1 false 163 241 171 249 Line -1 false 171 249 190 254 Line -1 false 192 253 203 248 Line -1 false 205 249 218 235 Line -1 false 218 235 200 144 bird1 false 0 Polygon -7566196 true true 2 6 2 39 270 298 297 298 299 271 187 160 279 75 276 22 100 67 31 0 bird2 false 0 Polygon -7566196 true true 2 4 33 4 298 270 298 298 272 298 155 184 117 289 61 295 61 105 0 43 boat1 false 0 Polygon -1 true false 63 162 90 207 223 207 290 162 Rectangle -6524078 true false 150 32 157 162 Polygon -16776961 true false 150 34 131 49 145 47 147 48 149 49 Polygon -7566196 true true 158 33 230 157 182 150 169 151 157 156 Polygon -7566196 true true 149 55 88 143 103 139 111 136 117 139 126 145 130 147 139 147 146 146 149 55 boat2 false 0 Polygon -1 true false 63 162 90 207 223 207 290 162 Rectangle -6524078 true false 150 32 157 162 Polygon -16776961 true false 150 34 131 49 145 47 147 48 149 49 Polygon -7566196 true true 157 54 175 79 174 96 185 102 178 112 194 124 196 131 190 139 192 146 211 151 216 154 157 154 Polygon -7566196 true true 150 74 146 91 139 99 143 114 141 123 137 126 131 129 132 139 142 136 126 142 119 147 148 147 boat3 false 0 Polygon -1 true false 63 162 90 207 223 207 290 162 Rectangle -6524078 true false 150 32 157 162 Polygon -16776961 true false 150 34 131 49 145 47 147 48 149 49 Polygon -7566196 true true 158 37 172 45 188 59 202 79 217 109 220 130 218 147 204 156 158 156 161 142 170 123 170 102 169 88 165 62 Polygon -7566196 true true 149 66 142 78 139 96 141 111 146 139 148 147 110 147 113 131 118 106 126 71 box true 0 Polygon -7566196 true true 45 255 255 255 255 45 45 45 butterfly1 true 0 Polygon -16777216 true false 151 76 138 91 138 284 150 296 162 286 162 91 Polygon -7566196 true true 164 106 184 79 205 61 236 48 259 53 279 86 287 119 289 158 278 177 256 182 164 181 Polygon -7566196 true true 136 110 119 82 110 71 85 61 59 48 36 56 17 88 6 115 2 147 15 178 134 178 Polygon -7566196 true true 46 181 28 227 50 255 77 273 112 283 135 274 135 180 Polygon -7566196 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231 119 215 143 213 160 208 173 189 187 169 190 154 190 126 180 106 171 72 171 73 126 122 126 144 123 159 123 Polygon -6524078 true true 201 99 214 69 215 99 Polygon -6524078 true true 207 98 223 71 220 101 Polygon -6524078 true true 184 172 189 234 203 238 203 246 187 247 180 239 171 180 Polygon -6524078 true true 197 174 204 220 218 224 219 234 201 232 195 225 179 179 Polygon -6524078 true true 78 167 95 187 95 208 79 220 92 234 98 235 100 249 81 246 76 241 61 212 65 195 52 170 45 150 44 128 55 121 69 121 81 135 Polygon -6524078 true true 48 143 58 141 Polygon -6524078 true true 46 136 68 137 Polygon -6524078 true true 45 129 35 142 37 159 53 192 47 210 62 238 80 237 Line -16777216 false 74 237 59 213 Line -16777216 false 59 213 59 212 Line -16777216 false 58 211 67 192 Polygon -6524078 true true 38 138 66 149 Polygon -6524078 true true 46 128 33 120 21 118 11 123 3 138 5 160 13 178 9 192 0 199 20 196 25 179 24 161 25 148 45 140 Polygon -6524078 true true 67 122 96 126 63 144 @#$#@#$#@ NetLogo 2.0beta4 @#$#@#$#@ @#$#@#$#@ @#$#@#$#@