File:COMM Effects section Example.jpg
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Applet of commutator used in this image.
The image above gives a visual indication of which pieces of a cube are affected by the different sequences of a commutator. In the example commutator chosen, the sequence A is F and the sequence B is U, giving the simple commutator [F, U]. Referring to the image, the sequence A changes the pieces at a set of locations we will call J. The sequence B changes the pieces at a set of locations we will call K. We will call the intersection of J and K, N.
There is a set of locations that we will be calling NA'. This name is appropriate because the pieces can be identified by applying the inverse of A to the locations N. Referring to the lowest right hand cube, these particular locations are identified using two shades of grey. Pieces that are lighter grey are pieces that will be brought into the intersection region N, pieces that are darker grey are pieces that are already within the intersection region and will remain in the region. Such pieces will however be moved within the region, as in this case, or will be twisted in place.
All of the above which has been stated regarding the NA' region is also true for NB' region.
The only pieces that are affected by any commutator are the ones located in the union of N, NA' and NB'. In other words, pieces that are affected by a commutator are those who are at the intersection of both moves, or are brought into the intersection by A or B. Other pieces, even if they are temporarily mixed up after the sequences A and B are executed, will be put back into their original locations with sequences A' and B'.
This restoration of all the pieces that are not in the union of N, NA' and NB' is the reason the commutator is such a powerful tool.
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This JPG image was created for the speedsolving.com wiki page Commutators (www.speedsolving.com/wiki/index.php/Commutator) . It is an example that helps understand the terms J, K, N, NA’,NB’ used to describe how the commutator works.
It is PNG version of a SVG image. (Presently (2013 04 10) the Wiki does not support SVG images) It was created using the free opensource program Inkscape. If there is an error or something needs to be changed contact Dave3457.
Colors used White: 5% Grey F2F2F2 (242,242,242) Red: BB0000 (187,0,0) L=94 Blue: 000077 (0, 0, 119) L=60 Green: 005500 (0,85,0) L=43 Orange: DD6000 (255,68,0) L=128 Yellow: FFCC00 (255,204,0) L=128 (same) Light grey: 808080 (128,128,128) L=128 Dark grey: 404040 (64,64,64) L=64
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current | 14:15, 9 April 2013 | 2,500 × 1,575 (896 KB) | Dave3457 (talk | contribs) | ||
21:37, 8 April 2013 | 1,500 × 2,470 (869 KB) | Dave3457 (talk | contribs) | This JPG image was created for the speedsolving.com wiki page Commutators (www.speedsolving.com/wiki/index.php/Commutator) . It is an example that helps understand the terms J, K, N, NA’,NB’ used to describe how the commutator works. It is PNG ve... |
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