Bill,
I will try to answer your questions
and give you my point of view.
As a friend said I have my own musical
language - in the beginning it was for
me alone but I detected that others
came to like it so it´s not all that
important if the term "Fractal Music"
is justified or not.
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"A geometrical structure that has a regular
or an uneven shape repeated over all scales
of measurement and that has a dimension
(frac′tal dimension), determined according
to definite rules, that is greater than the
spatial dimension of the structure."
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According to this definition the term
"Fractal Music" is impossible.
Shall we say we have "Fractal Music" if
fractal structures are used to generate
it to a high degree? 
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I am trying hard to understand. You use a fractal image as your underlying input structure, and sample points on it using another fractal image - the IFS fractal image - as it is generated one point at a time. Different IFS fractal images sample those points in different patterns, producing different sounds from the same underlying (fractal) image. I'm sure there is a lot more to what you are doing, but is that the gist of it? Would you agree that that still puts you on the "mapping" side of things as opposed to the "iterative" side?
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Agreed - if applicable I manipulate the IFS -
maybe turn it upside down or change parts.
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"What makes it Fractal Music is the IFS Fractal used for scanning."
I am a bit confused by your term "scanning". Is that another term for sampling? And, assuming that it is "fractal" what makes it "music"?
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It is and what makes it music is the cooperation
of the source and the scanning.
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" I use fractals because they quite often have a visible mathematical structure and order..."
Why is that important?
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See previous item - what is the difference
between noise and music? Music is also a mathematical language.
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" No photo or painting has that quality with one exception: Some abstract paintings look like fractals and some of my images look like paintings."
With all  due respect, that seems nonsensical to me. Your one exception immediately became several, and your premise is simply bizarre. On what basis can you make such an unequivocal statement?
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See the sample (by Paul Klee).  I´m talking about these grafical images only. It has an almost
mathematical structure, maybe I´ll try to convert it-;
https://www.dropbox.com/s/06ozfdfdh8rx3qp/index.jpg?dl=0
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BTW, what color depth are your input images?
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They are my Fractint originals converted to Bitmap with Irfan Viewer.
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"...uses the smallest possible parts of a note.."
The actual length depends on the speed of the music - possibly half a second, more or less
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A word about the procedure: The RGB values of a dot are converted to parameters of the music:
Pitch, Length, Duration and Articulation - differently for each voice (10 voices). So it´s nonsense
to say this source is not needed or can be disregarded. All other parameters are manually
defined. If you cannot hear the difference between Contemplation and Tranquillity listen
more closely - they are similar because the algorithm has not changed, only the note parameters.
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Up to now I have only one rhythm pattern. It is an extremely time absorbing procedure to create
and involves a lot of try and error. One of the main problems is to maintain the general structure
of the measures inspite of  infinite variations which NEVER repeat. I have reproduced a
grafical presentation  on my site.
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https://www.dropbox.com/sh/e5k0j4hkr87p9sl/AAA9P-fDVaTCp-ObT6O77jwAa?dl=0
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Any questions are welcome.
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Albrecht