| 3(e) |
 |
 |
| The empty length 2 addresses are 22, 23, 24, 31, 32, and 33. Thus the forbidden
transitions are 2 → 2, 3 → 2, 4 → 2,
3 → 1, 2 → 3, and
3 → 3. These are the missing arrows in the diagram. |
| This fractal has two romes, address 1 and address 4. Moreover, there is a path from the rome (1) to
the non-rome (2), and a path from the rome (4) to the non-rome (3), so this fractal can be generated by an
IFS without memory. Because there is no loop through only non-romes, this IFS can be generated without
memory, using finitely many transformations |
| r |
s |
θ |
φ |
e |
f |
| 0.5 |
0.5 |
0 |
0 |
0.0 |
0.0 |
| 0.5 |
0.5 |
0 |
0 |
0.5 |
0.5 |
| 0.25 |
0.25 |
0 |
0 |
0.5 |
0.0 |
| 0.25 |
0.25 |
0 |
0 |
0.25 |
0.75 |
|