 |
| From the graph we see there are edges from each vertex to vertex 1,
and from each vertex to vertex 2. Consequently, 1 and 2 are the full states.
Notice A1 = T1(A) and
A2 = T2(A) are copies of A scaled by
1/2. |
| The only edges leading into vertex 4 come from vertex 2 and from vertex 4.
So the parts of the attractor in the upper right square are
A42 =
T4(A2) (A scaled by 1/4),
A442 =
T4(A42) (A scaled by 1/8),
A4442 =
T4(A442) (A scaled by 1/16),
..., and so on, for an infinite cascade of smaller and smaller copies of A. |
| The only edges leading into vertex 3 come from vertex 2 and from vertex 4.
So the only parts of the attractor in the upper left square are
A32 =
T3(A2) (A scaled by 1/4),
A342 =
T3(A42) (A scaled by 1/8),
A3442 =
T3(A442) (A scaled by 1/16),
..., and so on, for an infinite cascade of smaller and smaller copies of A. |
| Unlike the previous example, here we have arbitrarily long paths
through non-romes. These are responsible for the infinite cascades of smaller
and smaller copies of A. |
| 2 → 3 → rome |
| 2 → 4 → 3 → rome |
| 2 → 4 → 4 → 3 → rome |
| 2 → 4 → 4 → 4 → 3 → rome |
| 2 → 4 → 4 → 4 → 4 → 3 → rome |
| ..., and |
| 2 → 4 → rome |
| 2 → 4 → 4 → rome |
| 2 → 4 → 4 → 4 → full |
| 2 → 4 → 4 → 4 → 4 → rome |
| 2 → 4 → 4 → 4 → 4 → 4 → rome |
| ... |
|