Second Homework Set Answers

3(c)

The empty length 2 addresses are 14, 24, and 34. Thus the forbidden transitions are 4 → 1, 4 → 2, and 4 → 3. These are the missing arrows in the diagram.

This fractal has one rome, address 4. However, there is no path from the rome (4) to any of the non-romes, so this shape cannot be generated by an IFS without memory.

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3(c)
The empty length 2 addresses are 14, 24, and 34. Thus the forbidden transitions are 4 → 1, 4 → 2, and 4 → 3. These are the missing arrows in the diagram.
This fractal has one rome, address 4. However, there is no path from the rome (4) to any of the non-romes, so this shape cannot be generated by an IFS without memory.