| We have seen that forbidding * → i → j
in 2-step memory produces the same picture as forbidding i → j in
1-step memory. |
| Suppose instead we forbid i → j → *. Then |
| i → j → 1 forbids i → j in square 1, |
| i → j → 2 forbids i → j in square 2, |
| i → j → 3 forbids i → j in square 3, and |
| i → j → 4 forbids i → j in square 4. |
|
| That is, we get four copies of the gap caused by forbidding i → j. |
| From the software
representation we see this is achieved by copying the 1-step memory table forbidding i → j
into each face of the representation. |
| For example, consider this 1-step memory picture, paired with this
2-step memory picture. |
|
| Here are two exercises, based on these 1-step memory pictures. |
|
| (a) How is the 1-step memory table copied into the
2-step memory table to produce the 1-step memory picture? |
| (b) How is the 1-step memory table copied into the
2-step memory table to produce four copies of the 1-step memory picture? |
| (c) In addition to those copying methods shown in (a) and (b), there is another simple way to copy
the 1-step memory table into the 2-step memory table. For exercise 1, explain how the resulting
picture is related to the 1-step memory picture? |
| Click each table for the solution. |
| 3. Take some interesting 1-step pictures and find the corresponding
2-step memory tables to produce four copies of the 1-step picture.
Test your ideas with the software. |
