 |
| From the graph we see no state is a rome, and so |
| A1 = T1(A2) ∪
T1(A3) ∪ T1(A4),
not a scaled copy of A |
| A2 = T2(A2) ∪
T2(A3) ∪ T2(A4),
not a scaled copy of A |
| A3 = T3(A1) ∪
T3(A2) ∪ T3(A4),
not a scaled copy of A |
| A4 = T4(A1) ∪
T4(A2) ∪ T4(A4),
not a scaled copy of A |
|
| That is, none of the 4 address length 1 regions is a scaled copy of the whole shape. |
| It follows that none of the 12 address length 2 regions - A12, A13,
A14, A22, A23, A24, A31,
A32, A34, A41, A42, and A44 - is a
scaled copy of A because, for example, A24 = T2(A4), not
a copy of A scaled by 1/4 because A4 is not a copy of A scaled by 1/2. |
| Continuing this way, we see for all n, none of the address length n regions is a
scaled copy of the whole shape. |