Is this a fractal ... ?

From: James J Albert (jimal1971_at_yahoo.co.uk)
Date: 10/17/04 

Date: 17 Oct 2004 07:28:04 -0700

Hi folks,

I am going to describe a certain procedure
for manipulating a signal and would like
to hear what you all think:

Consider a signal (say potential or any
quantity against time or distance). It is
2x wide (+/- x around origin).

Now I take a portion 2d wide were d < x, and
I magnify it so it is 2x wide.

I repeat this process for various smaller and
smaller values of d. Then I superimpose all
the magnified signals (which are all 2x wide)
on each other, and on the original and add
up the total new signal.

Then I do box-counting on the result and ... lo
and behold! A fractal dimension! (But one that
varies across the signal.) Now the original signal
I started with did NOT have a fractal dimension.

Is this really a technique for creating a fractal?
In other words ... would it work with any random
signal, or does it mean that the original signal
has some special (fractal?) quality?

Or is there something faulty in the technique
that gives rise to a "false" fractal of some sorts?

Any illumination on this point much appreciated!
(And please give any references you may have.)

Thanks a lot in advance!

PS. One second mini-question: is it true that
in nature any naturally occuring fractal means
there must be chaos to generate it?

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