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Rubicism2

by Desi Suyamto (Submitted: 04/03/2010)

[screen shot]

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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!

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