| Suppose we start by generating the line between 1∞
and 2∞ by allowing the transitions 1 → 1,
1 → 2, 2 → 1,and 2 → 2. |
| |
|
| Allowing also 1 → 3 and 2 → 3 makes a copy of the
line between 1∞
and 2∞ along the base of the address 3 square. |
| |
| Because all transitions 3 → i are forbidden, this line (of
length 1/2) does not generate any additional lines. |
|
| Allowing also 1 → 4 and 2 → 4 makes a copy of the
line between 1∞
and 2∞ along the base of the address 4 square. |
| |
|
| Exercise 1 How many pairs of horizontal and vertical lines can be generated in
this way? Try it first before consulting the
answers. |
| Exercise 2 Can you generate the middle line without generating a line on the
side of the square? Try it first before consulting the
answer. |
