Seventh Homework Set Answers
9. That the first generator is unifractal means
Log|dY
1
|/Log(dt
1
)
=
Log|dY
2
|/Log(dt
2
)
=
Log|dY
3
|/Log(dt
3
)
=
Log|dY
4
|/Log(dt
4
)
= H
Then
Log|dZ
i
|/Log(ds
i
)
=
Log|3 dY
i
|/Log(dt
i
)
= Log(3)/Log(dt
i
) + Log|dY
i
|/Log(dt
i
)
= Log(3)/Log(dt
i
) + H
So we see that in order for the second generator to be unifractal,
Log(3)/Log(dt
i
)
must have the same value for all i, that is, all t
i
are equal.
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Homework 7 Practice
.