;;Implemented in NetLogo by: Desi Suyamto, Bogor, Indonesia, April 2010 ;;Dedicated for my beloved rubicists: Aryo Adhi Condro and Panji Adhi Nuso globals [ cublets-xy cublets'-xy number-of-rotations ] turtles-own [ moved? ] to mark ask turtles [ set label "" ] ask turtles with[xcor = 4 and ycor = 1] [ set label "BOTTOM" ] ask turtles with[xcor = 4 and ycor = 4] [ set label "FRONT" ] ask turtles with[xcor = 4 and ycor = 7] [ set label "TOP" ] ask turtles with[xcor = 4 and ycor = 10] [ set label "BACK" ] ask turtles with[xcor = 1 and ycor = 4] [ set label "LEFT" ] ask turtles with[xcor = 7 and ycor = 4] [ set label "RIGHT" ] ask turtles [ set label-color ifelse-value (color = white or color = yellow) [ blue - 2 ] [ white ] ] end to scramble setup let scrambling-style [["left" "right" "front" "back" "up" "down"] ["equator" "slice" "middle"] ["x" "y" "z"]] let data[] repeat scrambling-number [ let s one-of scrambling-style if position s scrambling-style = 0 [ let c one-of s let clock-wise? (random-float 1 < .5) rotate-edges c clock-wise? ] if position s scrambling-style = 1 [ let c one-of s let clock-wise? (random-float 1 < .5) rotate-centers c clock-wise? ] if position s scrambling-style = 2 [ let c one-of s let clock-wise? (random-float 1 < .5) rotate-axes c clock-wise? ] ] set number-of-rotations 0 end to setup ca arrange-cublets mark end to arrange-cublets ask patches [ if pxcor >= 3 and pxcor <= 5 and pycor >= 0 and pycor <= 2 [ sprout 1 [ set heading 0 set shape "square" set color blue ] ] if pxcor >= 3 and pxcor <= 5 and pycor >= 3 and pycor <= 5 [ sprout 1 [ set heading 0 set shape "square" set color white ] ] if pxcor >= 3 and pxcor <= 5 and pycor >= 6 and pycor <= 8 [ sprout 1 [ set heading 0 set shape "square" set color green ] ] if pxcor >= 3 and pxcor <= 5 and pycor >= 9 and pycor <= 11 [ sprout 1 [ set heading 0 set shape "square" set color yellow ] ] if pxcor >= 0 and pxcor <= 2 and pycor >= 3 and pycor <= 5 [ sprout 1 [ set heading 0 set shape "square" set color red ] ] if pxcor >= 6 and pxcor <= 8 and pycor >= 3 and pycor <= 5 [ sprout 1 [ set heading 0 set shape "square" set color orange ] ] ] end to rotate-edges[edges clock-wise?] ask turtles [ set moved? false ] if edges = "front" [ set cublets-xy [[3 5] [4 5] [5 5] [5 4] [5 3] [4 3] [3 3] [3 4] [3 6] [4 6] [5 6] [6 5] [6 4] [6 3] [5 2] [4 2] [3 2] [2 3] [2 4] [2 5]] ] if edges = "left" [ set cublets-xy [[0 5] [1 5] [2 5] [2 4] [2 3] [1 3] [0 3] [0 4] [3 8] [3 7] [3 6] [3 5] [3 4] [3 3] [3 2] [3 1] [3 0] [3 11] [3 10] [3 9]] ] if edges = "right" [ set cublets-xy [[6 5] [7 5] [8 5] [8 4] [8 3] [7 3] [6 3] [6 4] [5 6] [5 7] [5 8] [5 9] [5 10] [5 11] [5 0] [5 1] [5 2] [5 3] [5 4] [5 5]] ] if edges = "back" [ set cublets-xy [[5 9] [4 9] [3 9] [3 10] [3 11] [4 11] [5 11] [5 10] [5 8] [4 8] [3 8] [0 5] [0 4] [0 3] [3 0] [4 0] [5 0] [8 3] [8 4] [8 5]] ] if edges = "up" [ set cublets-xy [[3 8] [4 8] [5 8] [5 7] [5 6] [4 6] [3 6] [3 7] [3 9] [4 9] [5 9] [8 5] [7 5] [6 5] [5 5] [4 5] [3 5] [2 5] [1 5] [0 5]] ] if edges = "down" [ set cublets-xy [[3 2] [4 2] [5 2] [5 1] [5 0] [4 0] [3 0] [3 1] [3 3] [4 3] [5 3] [6 3] [7 3] [8 3] [5 11] [4 11] [3 11] [0 3] [1 3] [2 3]] ] set cublets'-xy sentence sublist cublets-xy 2 8 sentence sublist cublets-xy 0 2 sentence sublist cublets-xy 11 20 sublist cublets-xy 8 11 ifelse clock-wise? [ set cublets'-xy cublets'-xy ] [ set cublets'-xy sentence sublist cublets'-xy 4 8 sentence sublist cublets'-xy 0 4 sentence sublist cublets'-xy 14 20 sublist cublets'-xy 8 14 ] move-cublets cublets-xy cublets'-xy ask turtles [ set moved? false ] mark set number-of-rotations number-of-rotations + 1 end to rotate-centers[centers clock-wise?] ask turtles [ set moved? false ] if centers = "equator" [ set cublets-xy [[3 4] [4 4] [5 4] [6 4] [7 4] [8 4] [5 10] [4 10] [3 10] [0 4] [1 4] [2 4]] ] if centers = "slice" [ set cublets-xy [[3 7] [4 7] [5 7] [7 5] [7 4] [7 3] [5 1] [4 1] [3 1] [1 3] [1 4] [1 5]] ] if centers = "middle" [ set cublets-xy [[4 5] [4 4] [4 3] [4 2] [4 1] [4 0] [4 11] [4 10] [4 9] [4 8] [4 7] [4 6]] ] ifelse clock-wise? [ set cublets'-xy sentence sublist cublets-xy 9 12 sublist cublets-xy 0 9 ] [ set cublets'-xy sentence sublist cublets-xy 3 12 sublist cublets-xy 0 3 ] move-cublets cublets-xy cublets'-xy ask turtles [ set moved? false ] mark set number-of-rotations number-of-rotations + 1 end to rotate-axes[axes clock-wise?] if axes = "x" [ set cublets-xy [[6 5] [7 5] [8 5] [8 4] [8 3] [7 3] [6 3] [6 4] [2 5] [1 5] [0 5] [0 4] [0 3] [1 3] [2 3] [2 4]] ifelse clock-wise? [ ask turtles with[xcor > 2 and xcor < 6] [ set heading 0 fd 3 ] set cublets'-xy sentence sublist cublets-xy 2 8 sentence sublist cublets-xy 0 2 sentence sublist cublets-xy 10 16 sublist cublets-xy 8 10 ] [ ask turtles with[xcor > 2 and xcor < 6] [ set heading 180 fd 3 ] set cublets'-xy sentence sublist cublets-xy 6 8 sentence sublist cublets-xy 0 6 sentence sublist cublets-xy 14 16 sublist cublets-xy 8 14 ] ] if axes = "y" [ set cublets-xy [ [5 11] [4 11] [3 11] [3 10] [3 9] [4 9] [5 9] [5 10] [3 5] [4 5] [5 5] [5 4] [5 3] [4 3] [3 3] [3 4] [0 3] [1 3] [2 3] [0 4] [1 4] [2 4] [0 5] [1 5] [2 5] [3 8] [3 7] [3 6] [4 8] [4 7] [4 6] [5 8] [5 7] [5 6] [8 5] [7 5] [6 5] [8 4] [7 4] [6 4] [8 3] [7 3] [6 3] [5 0] [5 1] [5 2] [4 0] [4 1] [4 2] [3 0] [3 1] [3 2] ] ifelse clock-wise? [ set cublets'-xy sentence sublist cublets-xy 2 8 sentence sublist cublets-xy 0 2 sentence sublist cublets-xy 10 16 sentence sublist cublets-xy 8 10 sentence sublist cublets-xy 25 34 sentence sublist cublets-xy 34 43 sentence sublist cublets-xy 43 52 sublist cublets-xy 16 25 ] [ set cublets'-xy sentence sublist cublets-xy 6 8 sentence sublist cublets-xy 0 6 sentence sublist cublets-xy 14 16 sentence sublist cublets-xy 8 14 sentence sublist cublets-xy 43 52 sentence sublist cublets-xy 16 25 sentence sublist cublets-xy 25 34 sublist cublets-xy 34 43 ] ] if axes = "z" [ set cublets-xy [ [5 2] [4 2] [3 2] [3 1] [3 0] [4 0] [5 0] [5 1] [3 8] [4 8] [5 8] [5 7] [5 6] [4 6] [3 6] [3 7] [2 3] [2 4] [2 5] [1 3] [1 4] [1 5] [0 3] [0 4] [0 5] [3 11] [3 10] [3 9] [4 11] [4 10] [4 9] [5 11] [5 10] [5 9] [8 3] [8 4] [8 5] [7 3] [7 4] [7 5] [6 3] [6 4] [6 5] [5 3] [5 4] [5 5] [4 3] [4 4] [4 5] [3 3] [3 4] [3 5] ] ifelse clock-wise? [ set cublets'-xy sentence sublist cublets-xy 2 8 sentence sublist cublets-xy 0 2 sentence sublist cublets-xy 10 16 sentence sublist cublets-xy 8 10 sentence sublist cublets-xy 25 34 sentence sublist cublets-xy 34 43 sentence sublist cublets-xy 43 52 sublist cublets-xy 16 25 ] [ set cublets'-xy sentence sublist cublets-xy 6 8 sentence sublist cublets-xy 0 6 sentence sublist cublets-xy 14 16 sentence sublist cublets-xy 8 14 sentence sublist cublets-xy 43 52 sentence sublist cublets-xy 16 25 sentence sublist cublets-xy 25 34 sublist cublets-xy 34 43 ] ] ask turtles [ set moved? false ] move-cublets cublets-xy cublets'-xy ask turtles [ set moved? false ] mark set number-of-rotations number-of-rotations + 1 end to move-cublets[elements-xy elements'-xy] foreach elements-xy [ let xy ? let x item 0 xy let y item 1 xy let xy' item (position xy elements-xy) elements'-xy let x' item 0 xy' let y' item 1 xy' ask turtles-on patch x y [ if (not moved?) [ move-to patch x' y' set moved? true ] ] ] end @#$#@#$#@ GRAPHICS-WINDOW 242 19 612 530 -1 -1 40.0 1 11 1 1 1 0 1 1 1 0 8 0 11 0 0 1 ticks BUTTON 13 17 93 50 NIL scramble NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 643 20 706 53 F rotate-edges \"front\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 817 20 880 53 F' rotate-edges \"front\" false NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 644 62 707 95 L rotate-edges \"left\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 817 62 880 95 L' rotate-edges \"left\" false NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 718 61 781 94 R rotate-edges \"right\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 889 62 952 95 R' rotate-edges \"right\" false NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 718 18 781 51 B rotate-edges \"back\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 888 20 951 53 B' rotate-edges \"back\" false NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 644 104 707 137 U rotate-edges \"up\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 817 104 880 137 U' rotate-edges \"up\" false NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 716 104 779 137 D rotate-edges \"down\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 890 104 953 137 D' rotate-edges \"down\" false NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 680 173 743 206 E rotate-centers \"equator\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 854 170 917 203 E' rotate-centers \"equator\" false NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 680 217 743 250 S rotate-centers \"slice\" false NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 854 214 917 247 S' rotate-centers \"slice\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 680 261 743 294 M rotate-centers \"middle\" false NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 854 258 917 291 M' rotate-centers \"middle\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 681 335 744 368 X rotate-axes \"x\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 856 333 919 366 X' rotate-axes \"x\" false NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 683 423 746 456 Z rotate-axes \"z\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 857 424 920 457 Z' rotate-axes \"z\" false NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 682 378 745 411 Y rotate-axes \"y\" true NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 857 378 920 411 Y' rotate-axes \"y\" false NIL 1 T OBSERVER NIL NIL NIL NIL SLIDER 10 71 210 104 scrambling-number scrambling-number 1 50 50 1 1 rotations HORIZONTAL MONITOR 12 120 101 165 fixing-number number-of-rotations 0 1 11 @#$#@#$#@ WHAT IS IT? ----------- The idea comes when my sons are addicted to rubic cubes puzzle. Using standard algorithm available in the internet, they can fix the scrambled 3x3x6 rubic cublets for about 1-2 minutes in average. Although it is still far away from the world record, but they already make me as the real loser at home! Then, I am interested not only at the speed of fixing a scrambled rubic, but also at what I term as 'problem solving efficiency'. Thus, I challenge my sons. I scrambled the cubes for given number of rotations and ask them to fix in a very slow motion, so I could count the total number of rotations they make for fixing the cube. When I scrambled the cube for less than 4 rotations, my sons can still fix it in the same number of rotations. Certainly they sometimes can fix in a number of rotations that is less than the scrambling number of rotations, when I did pair of rotations which cancelled the scrambling (e.g. I turned the front side of the cube in a clock-wise direction and then turn the same part in a counter-clock-wise direction). But, when I did more than 4 scrambling rotations, their fixing number of rotations are always more than my scrambling number of rotations. *** What I can learn from this simple game (from my sons precisely!) is that when equilibrium of a system is perturbed, human efficiency to fix the system would likely never approach 100%. Here, efficiency is measured as the cost of fixing the problem, relative to the cost of perturbation that causes the problem. And of course, when the system is very complex, composed by number of elements, where interdependency of some elements is relatively high, then problem-solving efficiency is just like a dream. Perhaps, this is the reason of Ulrich Beck in hypothesing his thesis about 'risk society'. I am sure that this idea can be explored further with regards to some issues. For example, one of the efforts in mitigating global warming (i.e. REDD: Reducing Emissions from Deforestation and Degradation) put efficiency as one of the assessment indicators for the approach. *** However, this NetLogo version of rubic is still a toy. The different form the real rubic is that here, you can notice the number of scrambling rotations and the number of fixing rotations. I use standard notations on the type of rubic rotations, adopted world wide. So, have fun with it and hope you find yourself as the most efficient problem solver :) HOW TO USE IT ------------- This game is running under NetLogo 4.1. [1] To scramble the cublets, just press "scramble" button. Slider "scrambling-number" defines how many rotations is made to scramble the rubic. [2] To fix the scrambled rubic, press the buttons provided in the right side. As I mentionded, standard notations on the type of rubic rotations, adopted world wide: For rotating cublets at the edges: L: rotating the left part of the cube in clock-wise direction R: rotating the right part of the cube in clock-wise direction F: rotating the front part of the cube in clock-wise direction B: rotating the back part of the cube in clock-wise direction U: rotating the top part of the cube in clock-wise direction D: rotating the bottom part of the cube in clock-wise direction For rotating cublets at the centers: M: rotating the center part of the cube toward x axis in clock-wise direction S: rotating the center part of the cube toward y axis in clock-wise direction E: rotating the center part of the cube toward z axis in clock-wise direction For rotating the whole rubic cube (only to change the viewing perspective): X: rotating the whole cube toward x axis in clock-wise direction Y: rotating the whole cube toward y axis in clock-wise direction Z: rotating the whole cube toward z axis in clock-wise direction The accented notes (L', R', etc.) are for the similar rotation, but in counter-clock-wise direction. So, when you press L' after pressing L, cublets are moved back to the previous positions before pressing L. While playing, you can notice how many rotation that you have made for fixing the scrambled rubic cubes! CREDITS AND REFERENCES ---------------------- Many thanks to Uri Wilensky and NetLogo team! God bless you! @#$#@#$#@ 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 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