|---|---|---|---|---|
| a | | | b | |
| | | | | |
| 2 | 1 | | 1 | |
| 1 | | | 2 | 1 |
随机用结构a或者b填充平面，让两个结构只能以2-1-2的方式连接，让平面的高度是100，宽度分别是4，6，8，10，12，14，16，18,比较密度变化。
其中一组100*4的数据为
|----|---|---|---|---|---|---|----|---|----|---|---|-----|---|---|---|---|---|---|----|---|----|---|
| 1 | | 2 | 1 | 2 | 1 | | 1 | | 0 | | | 51 | | 2 | 1 | 2 | 1 | | 50 | | 49 | |
| 2 | | 1 | | 1 | | | | | | | | 52 | | 1 | | 1 | | | | | | |
| 3 | | 2 | 1 | 2 | 1 | | 2 | | 3 | | | 53 | | 2 | 1 | 2 | 1 | | 52 | | 51 | |
| 4 | | 1 | | 1 | | | | | | | | 54 | | 1 | | 1 | | | | | | |
| 5 | | 2 | 1 | 2 | 1 | | 6 | | 4 | | | 55 | | 2 | 1 | 2 | 1 | | 53 | | 57 | |
| 6 | | 1 | | 1 | | | | | | | | 56 | | 1 | | 1 | | | | | | |
| 7 | | 2 | 1 | 2 | 1 | | 7 | | 5 | | | 57 | | 2 | 1 | 2 | 1 | | 54 | | 61 | |
| 8 | | 1 | | 1 | | | | | | | | 58 | | 1 | | 1 | | | | | | |
| 9 | | 2 | 1 | 2 | 1 | | 11 | | 8 | | | 59 | | 2 | 1 | 2 | 1 | | 55 | | 56 | |
| 10 | | 1 | | 1 | | | | | | | | 60 | | 1 | | 1 | | | | | | |
| 11 | | 2 | 1 | 2 | 1 | | 10 | | 9 | | | 61 | | 2 | 1 | 2 | 1 | | 65 | | 58 | |
| 12 | | 1 | | 1 | | | | | | | | 62 | | 1 | | 1 | | | | | | |
| 13 | | 2 | 1 | 2 | 1 | | 12 | | 13 | | | 63 | | 2 | 1 | 2 | 1 | | 60 | | 59 | |
| 14 | | 1 | | 1 | | | | | | | | 64 | | 1 | | 1 | | | | | | |
| 15 | | 2 | 1 | 2 | 1 | | 14 | | 15 | | | 65 | | 2 | 1 | 2 | 1 | | 62 | | 67 | |
| 16 | | 1 | | 1 | | | | | | | | 66 | | 1 | | 1 | | | | | | |
| 17 | | 2 | 1 | 2 | 1 | | 17 | | 16 | | | 67 | | 2 | 1 | 2 | 1 | | 63 | | 64 | |
| 18 | | 1 | | 1 | | | | | | | | 68 | | 1 | | 1 | | | | | | |
| 19 | | 2 | 1 | 2 | 1 | | 18 | | 30 | | | 69 | | 2 | 1 | 2 | 1 | | 68 | | 66 | |
| 20 | | 1 | | 1 | | | | | | | | 70 | | 1 | | 1 | | | | | | |
| 21 | | 2 | 1 | 2 | 1 | | 19 | | 20 | | | 71 | | 2 | 1 | 2 | 1 | | 69 | | 70 | |
| 22 | | 1 | | 1 | | | | | | | | 72 | | 1 | | 1 | | | | | | |
| 23 | | 2 | 1 | 2 | 1 | | 21 | | 22 | | | 73 | | 2 | 1 | 2 | 1 | | 71 | | 73 | |
| 24 | | 1 | | 1 | | | | | | | | 74 | | 1 | | 1 | | | | | | |
| 25 | | 2 | 1 | 2 | 1 | | 23 | | 24 | | | 75 | | 2 | 1 | 2 | 1 | | 72 | | 74 | |
| 26 | | 1 | | 1 | | | | | | | | 76 | | 1 | | 1 | | | | | | |
| 27 | | 2 | 1 | 2 | 1 | | 25 | | 26 | | | 77 | | 2 | 1 | | | | 75 | | | |
| 28 | | 1 | | 1 | | | | | | | | 78 | | 1 | | 1 | | | | | 78 | |
| 29 | | 2 | 1 | 2 | 1 | | 27 | | 29 | | | 79 | | 2 | 1 | 2 | 1 | | 76 | | | |
| 30 | | 1 | | 1 | | | | | | | | 80 | | 1 | | 1 | | | | | 79 | |
| 31 | | 2 | 1 | 2 | 1 | | 28 | | 31 | | | 81 | | 2 | 1 | 2 | 1 | | 77 | | | |
| 32 | | 1 | | 1 | | | | | | | | 82 | | 1 | | | | | | | | |
| 33 | | | | 2 | 1 | | | | 32 | | | 83 | | 2 | 1 | 2 | 1 | | 80 | | 81 | |
| 34 | | 1 | | 1 | | | 34 | | | | | 84 | | 1 | | 1 | | | | | | |
| 35 | | 2 | 1 | 2 | 1 | | | | 33 | | | 85 | | 2 | 1 | 2 | 1 | | 85 | | 82 | |
| 36 | | 1 | | 1 | | | 38 | | | | | 86 | | 1 | | 1 | | | | | | |
| 37 | | 2 | 1 | 2 | 1 | | | | 35 | | | 87 | | 2 | 1 | 2 | 1 | | 84 | | 83 | |
| 38 | | | | 1 | | | | | | | | 88 | | 1 | | 1 | | | | | | |
| 39 | | 2 | 1 | 2 | 1 | | 39 | | 36 | | | 89 | | 2 | 1 | 2 | 1 | | 86 | | 87 | |
| 40 | | 1 | | 1 | | | | | | | | 90 | | 1 | | 1 | | | | | | |
| 41 | | 2 | 1 | 2 | 1 | | 41 | | 37 | | | 91 | | 2 | 1 | 2 | 1 | | 88 | | 89 | |
| 42 | | 1 | | 1 | | | | | | | | 92 | | 1 | | 1 | | | | | | |
| 43 | | 2 | 1 | 2 | 1 | | 42 | | 40 | | | 93 | | 2 | 1 | 2 | 1 | | 90 | | 91 | |
| 44 | | 1 | | 1 | | | | | | | | 94 | | 1 | | 1 | | | | | | |
| 45 | | 2 | 1 | 2 | 1 | | 45 | | 43 | | | 95 | | 2 | 1 | 2 | 1 | | 92 | | 93 | |
| 46 | | 1 | | 1 | | | | | | | | 96 | | 1 | | 1 | | | | | | |
| 47 | | 2 | 1 | 2 | 1 | | 46 | | 44 | | | 97 | | 2 | 1 | 2 | 1 | | 94 | | 95 | |
| 48 | | 1 | | 1 | | | | | | | | 98 | | 1 | | 1 | | | | | | |
| 49 | | 2 | 1 | 2 | 1 | | 47 | | 48 | | | 99 | | 2 | 1 | 2 | 1 | | 96 | | 97 | |
| 50 | | 1 | | 1 | | | | | | | | 100 | | 1 | | 1 | | | | | | |
这个结构有4个b，94个a，空余2个，密度是0.98
共测5组得到平均值为
|-----|---------|
| | 100*4 |
| 数量 | 95 |
| b | 20.2 |
| a | 74.8 |
| | |
| 密度 | 0.95 |
| b/a | 0.27005 |
其余所有数据为
|-----|---------|---------|---------|---------|---------|---------|---------|---------|
| | 100*4 | 100*6 | 100*8 | 100*10 | 100*12 | 100*14 | 100*16 | 100*18 |
| 数量 | 95 | 140 | 185 | 230.6 | 275.2 | 321.6 | 363.6 | 411.4 |
| b | 20.2 | 40 | 63.6 | 67.6 | 92.4 | 95.4 | 121.6 | 140.6 |
| a | 74.8 | 100 | 121.4 | 163 | 182.8 | 226.2 | 242 | 270.8 |
| | | | | | | | | |
| 密度 | 0.95 | 0.93333 | 0.925 | 0.9224 | 0.91733 | 0.91886 | 0.909 | 0.91422 |
| b/a | 0.27005 | 0.4 | 0.52389 | 0.41472 | 0.50547 | 0.42175 | 0.50248 | 0.5192 |
随着n变大平均密度是变小的，
已经得到这种随机结构密度的算法
其中m是与结构平均密度相同的最小平面的高，2n是宽
代入2n=4，ρ=0.95
解得m=13.33，这里取整让m=12
将m=12，n=2，3，4，....代入得到
|----|---------|---------|---------|
| n | | ρ计算 | ρ实测 |
| 2 | 0.05556 | 0.94444 | 0.95 |
| 3 | 0.07143 | 0.92857 | 0.93333 |
| 4 | 0.07778 | 0.92222 | 0.925 |
| 5 | 0.08065 | 0.91935 | 0.9224 |
| 6 | 0.08201 | 0.91799 | 0.91733 |
| 7 | 0.08268 | 0.91732 | 0.91886 |
| 8 | 0.08301 | 0.91699 | 0.909 |
| 9 | 0.08317 | 0.91683 | 0.91422 |
| 10 | 0.08325 | 0.91675 | |
| 11 | 0.08329 | 0.91671 | |
| 12 | 0.08331 | 0.91669 | |
计算密度和实测密度接近。
计算当n无穷大的极限，得到当高度为100时，结构的极限平均密度是1-1/12=0.9167
对比上次计算当平面的高为20时，m=8，所以平面高度变大，m也会变大，极限密度也会随之变大。