Second Homework Set Answers

3(d)

The empty length 2 addresses are 22, 24, 33, and 34. Thus the forbidden transitions are 2 → 2, 4 → 2, 3 → 3, and 4 → 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 a rome (1) to each of the non-romes, so this fractal can be generated by an IFS without memory. Because there is a loop 2 → 3 → 2 through only non-romes, infinitely many transformations are required to generate this fractal without memory.

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3(d)
The empty length 2 addresses are 22, 24, 33, and 34. Thus the forbidden transitions are 2 → 2, 4 → 2, 3 → 3, and 4 → 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 a rome (1) to each of the non-romes, so this fractal can be generated by an IFS without memory. Because there is a loop 2 → 3 → 2 through only non-romes, infinitely many transformations are required to generate this fractal without memory.