假设一个6*6的平面,这个平面的行和列可以自由的变换。
已知一个4点的结构数列顺序为
9 | 1 | 10 | 6 | 16 | 14 | 5 | 15 | 8 | 12 | 11 | 13 | 7 | 2 | 4 | 3 |
让这个数列按照4-5-4的方式演化
得到顺序为
1 | 9 | 1 | 10 | 6 | 16 | 14 | 5 | 15 | 8 | 12 | 11 | 13 | 7 | 2 | 4 | 3 |
2 | 16 | 6 | 9 | 10 | 15 | 5 | 1 | 14 | 8 | 11 | 12 | 4 | 13 | 2 | 7 | 3 |
3 | 16 | 6 | 10 | 15 | 9 | 5 | 11 | 14 | 8 | 4 | 1 | 2 | 12 | 3 | 13 | 7 |
4 | 16 | 6 | 10 | 15 | 9 | 11 | 5 | 4 | 14 | 8 | 2 | 3 | 1 | 12 | 7 | 13 |
5 | 16 | 6 | 10 | 15 | 9 | 11 | 4 | 5 | 14 | 8 | 3 | 2 | 1 | 12 | 7 | 13 |
6 | 16 | 6 | 10 | 15 | 11 | 9 | 4 | 14 | 5 | 3 | 8 | 2 | 12 | 1 | 7 | 13 |
7 | 16 | 6 | 10 | 15 | 11 | 4 | 9 | 14 | 5 | 3 | 2 | 8 | 12 | 1 | 7 | 13 |
8 | 16 | 6 | 10 | 15 | 4 | 11 | 9 | 14 | 5 | 3 | 2 | 12 | 8 | 1 | 7 | 13 |
9 | 16 | 10 | 6 | 15 | 4 | 11 | 14 | 9 | 5 | 3 | 2 | 12 | 1 | 8 | 7 | 13 |
10 | 16 | 10 | 6 | 15 | 4 | 11 | 14 | 9 | 3 | 5 | 12 | 2 | 1 | 8 | 7 | 13 |
11 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 5 | 2 | 1 | 8 | 7 | 13 |
12 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
13 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
14 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
15 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
16 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
这个数列需要11次迭代才能收敛
标定值为
2 | 7 | 7.571 | 7.588 | 7.846 | 8.833 | 15.85 | 16.71 | 17.14 | 18.17 | 18.45 | 22.67 | 22.73 | 23 | 24.25 | 25.06 | 25.27 |
3 | 2.857 | 5.429 | 7.154 | 7.833 | 10.18 | 14.23 | 16.45 | 17.29 | 17.83 | 19.18 | 21.29 | 24.25 | 24.33 | 25 | 25.3 | 27.47 |
4 | 2.714 | 5.143 | 6.154 | 6.667 | 11.94 | 13.64 | 14.77 | 16.55 | 16.71 | 18.83 | 23.08 | 24 | 25.14 | 25.67 | 28.35 | 29 |
5 | 2.286 | 5 | 5.692 | 7 | 12.59 | 12.64 | 15.27 | 16.15 | 17.43 | 20.67 | 22.18 | 22.5 | 26 | 26 | 28.59 | 30.1 |
6 | 2.286 | 5 | 5.462 | 6.833 | 12.73 | 13 | 13.73 | 16.71 | 17 | 21 | 22.67 | 23 | 25.67 | 25.71 | 28.41 | 30.3 |
7 | 2.143 | 5.143 | 5.538 | 6.833 | 12 | 13.27 | 13.53 | 15.71 | 17.85 | 20.36 | 22.75 | 24.17 | 24.33 | 25.86 | 28.88 | 30.1 |
8 | 2 | 5.286 | 5.462 | 7.167 | 11.73 | 12 | 14.71 | 15.14 | 18.69 | 19.91 | 21.83 | 23.67 | 25.67 | 25.86 | 29 | 30.8 |
9 | 1.857 | 5.462 | 5.571 | 7.333 | 10.82 | 12.55 | 14.57 | 14.65 | 19.54 | 20 | 21.5 | 22.67 | 26.14 | 26.83 | 28.88 | 30.7 |
10 | 1.714 | 5.308 | 6.429 | 7.167 | 10.09 | 13.09 | 13.29 | 15.35 | 19.09 | 20.15 | 20.33 | 21.5 | 24.71 | 28 | 29.29 | 30.9 |
11 | 1.714 | 5.308 | 6.429 | 7.5 | 9.727 | 13 | 13.09 | 16 | 17.45 | 19.67 | 20.62 | 22.08 | 23.43 | 27.83 | 29.35 | 31.1 |
12 | 1.714 | 5.308 | 6.429 | 7.167 | 9.727 | 12.14 | 14.27 | 15.59 | 17.55 | 18.33 | 21.42 | 21.62 | 23.86 | 28.67 | 29.41 | 31 |
13 | 1.714 | 5.308 | 7 | 7 | 9.364 | 11.71 | 14.55 | 15.53 | 17.82 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
14 | 1.714 | 5.308 | 7 | 7 | 9.364 | 11.71 | 14.55 | 15.53 | 17.82 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
15 | 1.714 | 5.308 | 7 | 7 | 9.364 | 11.71 | 14.55 | 15.53 | 17.82 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
16 | 1.714 | 5.308 | 7 | 7 | 9.364 | 11.71 | 14.55 | 15.53 | 17.82 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
特别值得注意的是,第5行的结构1和12的标定值是相同的,都是26.所以如果按照标定值排序1,12和12,1都是合理的,相同的13行的6,15的标定值也相同。
所以这个数列的演化过程中有两个分枝,首先计算第5行的分枝,调换12,1
1 | 16 | 6 | 10 | 15 | 9 | 11 | 4 | 5 | 14 | 8 | 3 | 2 | 12 | 1 | 7 | 13 |
2 | 16 | 6 | 10 | 15 | 11 | 9 | 4 | 14 | 5 | 3 | 2 | 8 | 12 | 1 | 7 | 13 |
3 | 16 | 6 | 10 | 15 | 11 | 4 | 9 | 14 | 5 | 3 | 2 | 12 | 8 | 1 | 7 | 13 |
4 | 16 | 6 | 10 | 15 | 4 | 11 | 9 | 14 | 5 | 3 | 2 | 12 | 1 | 8 | 7 | 13 |
5 | 16 | 10 | 6 | 15 | 4 | 11 | 14 | 9 | 3 | 5 | 12 | 2 | 1 | 8 | 7 | 13 |
6 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 5 | 2 | 1 | 8 | 7 | 13 |
7 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
8 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
9 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
10 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
11 | 16 | 10 | 6 | 15 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
2 | 2.286 | 5 | 5.462 | 6.833 | 12.82 | 13.12 | 13.55 | 16.29 | 17.08 | 21.09 | 22.75 | 22.83 | 25.33 | 26.29 | 28.53 | 30.3 |
3 | 2.143 | 5.286 | 5.462 | 6.667 | 11.82 | 13.36 | 13.47 | 15.57 | 18.77 | 20.73 | 21.67 | 24 | 25.83 | 26.43 | 28.82 | 30.3 |
4 | 2 | 5.429 | 5.462 | 7.167 | 11.55 | 12 | 14.65 | 14.86 | 19.08 | 20.18 | 21.5 | 23 | 26.14 | 26.83 | 28.88 | 30.7 |
5 | 1.857 | 5.462 | 5.571 | 7.333 | 10.82 | 12.73 | 14.43 | 14.82 | 19.27 | 19.85 | 21.33 | 21.42 | 24.86 | 28.5 | 29.12 | 30.8 |
6 | 1.714 | 5.308 | 6.429 | 7.5 | 9.727 | 13 | 13.09 | 16 | 17.45 | 19.67 | 20.62 | 22.08 | 23.43 | 27.83 | 29.35 | 31.1 |
7 | 1.714 | 5.308 | 6.429 | 7.167 | 9.727 | 12.14 | 14.27 | 15.59 | 17.55 | 18.33 | 21.42 | 21.62 | 23.86 | 28.67 | 29.41 | 31 |
8 | 1.714 | 5.308 | 7 | 7 | 9.364 | 11.71 | 14.55 | 15.53 | 17.82 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
9 | 1.714 | 5.308 | 7 | 7 | 9.364 | 11.71 | 14.55 | 15.53 | 17.82 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
10 | 1.714 | 5.308 | 7 | 7 | 9.364 | 11.71 | 14.55 | 15.53 | 17.82 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
11 | 1.714 | 5.308 | 7 | 7 | 9.364 | 11.71 | 14.55 | 15.53 | 17.82 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
分枝5的第8行再次分枝,调换6,15
1 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
2 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
3 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
4 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
2 | 1.571 | 5.077 | 6.333 | 8.429 | 9.273 | 11.71 | 14.64 | 15.29 | 18 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
3 | 1.571 | 5.077 | 6.333 | 8.429 | 9.273 | 11.71 | 14.64 | 15.29 | 18 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
4 | 1.571 | 5.077 | 6.333 | 8.429 | 9.273 | 11.71 | 14.64 | 15.29 | 18 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
分枝5-8-2再次分枝,调换3,12
1 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 12 | 3 | 2 | 5 | 1 | 8 | 7 | 13 |
2 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 12 | 3 | 2 | 1 | 5 | 8 | 7 | 13 |
3 | 16 | 10 | 15 | 4 | 6 | 14 | 11 | 9 | 12 | 3 | 2 | 1 | 5 | 8 | 7 | 13 |
4 | 16 | 10 | 15 | 4 | 6 | 14 | 11 | 9 | 12 | 3 | 2 | 1 | 5 | 8 | 7 | 13 |
5 | 16 | 10 | 15 | 4 | 6 | 14 | 11 | 9 | 12 | 3 | 2 | 1 | 5 | 8 | 7 | 13 |
2 | 1.571 | 5 | 6.333 | 8.857 | 9.182 | 11.57 | 14.36 | 15.12 | 18 | 19.36 | 20.08 | 23.43 | 23.46 | 29.17 | 29.29 | 31.1 |
3 | 1.571 | 5 | 6.333 | 9 | 9.143 | 11.57 | 14.73 | 15.12 | 17.33 | 18.91 | 19.83 | 22.86 | 24.62 | 29.17 | 29.18 | 31.1 |
4 | 1.571 | 4.846 | 6.167 | 8.818 | 11 | 11.14 | 14 | 15 | 17.33 | 19.27 | 19.83 | 22.71 | 24.92 | 29.17 | 29.18 | 30.9 |
5 | 1.571 | 4.846 | 6.167 | 8.818 | 11 | 11.14 | 14 | 15 | 17.33 | 19.27 | 19.83 | 22.71 | 24.92 | 29.17 | 29.18 | 30.9 |
这个分枝最终稳定.
计算原始的13分枝,把6,15调换顺序
1 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
2 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
3 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
4 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 3 | 12 | 2 | 5 | 1 | 8 | 7 | 13 |
2 | 1.571 | 5.077 | 6.333 | 8.429 | 9.273 | 11.71 | 14.64 | 15.29 | 18 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
3 | 1.571 | 5.077 | 6.333 | 8.429 | 9.273 | 11.71 | 14.64 | 15.29 | 18 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
4 | 1.571 | 5.077 | 6.333 | 8.429 | 9.273 | 11.71 | 14.64 | 15.29 | 18 | 18 | 20.5 | 23.38 | 23.43 | 29.17 | 29.29 | 31.1 |
有新的分枝第二行3,12
把3,12调换顺序
1 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 12 | 3 | 2 | 5 | 1 | 8 | 7 | 13 |
2 | 16 | 10 | 15 | 6 | 4 | 14 | 11 | 9 | 12 | 3 | 2 | 1 | 5 | 8 | 7 | 13 |
3 | 16 | 10 | 15 | 4 | 6 | 14 | 11 | 9 | 12 | 3 | 2 | 1 | 5 | 8 | 7 | 13 |
4 | 16 | 10 | 15 | 4 | 6 | 14 | 11 | 9 | 12 | 3 | 2 | 1 | 5 | 8 | 7 | 13 |
5 | 16 | 10 | 15 | 4 | 6 | 14 | 11 | 9 | 12 | 3 | 2 | 1 | 5 | 8 | 7 | 13 |
2 | 1.571 | 5 | 6.333 | 8.857 | 9.182 | 11.57 | 14.36 | 15.12 | 18 | 19.36 | 20.08 | 23.43 | 23.46 | 29.17 | 29.29 | 31.1 |
3 | 1.571 | 5 | 6.333 | 9 | 9.143 | 11.57 | 14.73 | 15.12 | 17.33 | 18.91 | 19.83 | 22.86 | 24.62 | 29.17 | 29.18 | 31.1 |
4 | 1.571 | 4.846 | 6.167 | 8.818 | 11 | 11.14 | 14 | 15 | 17.33 | 19.27 | 19.83 | 22.71 | 24.92 | 29.17 | 29.18 | 30.9 |
5 | 1.571 | 4.846 | 6.167 | 8.818 | 11 | 11.14 | 14 | 15 | 17.33 | 19.27 | 19.83 | 22.71 | 24.92 | 29.17 | 29.18 | 30.9 |
13-2分枝最终稳定。
所以原始数列在5,13行分两枝,第二代8行,2行各分1枝,第三代2行分1枝。
1 | 12 | 1 | 12 | 1 | 12 | ||
12 | 1 | → | 6 | 15 | 6 | 15 | |
15 | 6 | → | 3 | 12 | |||
12 | 3 | ||||||
5行 | 8行 | 2行 | |||||
6 | 15 | 6 | 15 | ||||
15 | 6 | → | 3 | 12 | |||
12 | 3 | ||||||
13行 | 2行 | ||||||
第一代 | 第二代 | 第三代 |