some confuse problems in the results of fractal and multifract dimension calculation

[Jason Z]

Hi,

 In my  fractal dimension study process,  I found that when use the box
counting method for fractal dimension analysis, between the mono fractal
and multifractal dimension,  the graph pattern of analysis result generated
by the ImageJ  is the same.
For example, from the theory and the official website, The graphical
spectrum D(Q) makes against Q decreasing is a marvellous feature of
multifractal analysis.But the same result also appeared in the in
monofractal dimension analysis.

And also from the website it said in the graph of D(Q) vs Q, non- and
mono-fractals tend to have flatter D(Q) spectra than multifractals. But
after I analysis the this two kinds of image, the graph all is tend to
decreasing (e.g. custom fat vs Henon multifractal map). There is not too
much difference  between the mono-fractals and multifractl dimension.

Look forward your explain to help me understanding this problem.

Thanks,

Yang

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[Gabriel Landini]

On Saturday 22 Jun 2013 12:11:18 Jason Z <[hidden email]> wrote:
>  In my  fractal dimension study process,  I found that when use the box
> counting method for fractal dimension analysis, between the mono fractal
> and multifractal dimension,  the graph pattern of analysis result generated
> by the ImageJ  is the same.

ImageJ does not compute the multifractal spectrum. You are probably using a
user written plugin. (I think Fraclac does this).

> For example, from the theory and the official website, The graphical
> spectrum D(Q) makes against Q decreasing is a marvellous feature of
> multifractal analysis.But the same result also appeared in the in
> monofractal dimension analysis.

It could be many things, eg the data is not monofractal, or the analysis is
not being done correctly or your images are too small or have very small
resolution or you are using the wrong range of box sizes.

Do all the plots for estimating the various D(q) look straight? Are the slopes
fitting the plot well? What are their R^2?

> And also from the website it said in the graph of D(Q) vs Q, non- and
> mono-fractals tend to have flatter D(Q) spectra than multifractals. But
> after I analysis the this two kinds of image, the graph all is tend to
> decreasing (e.g. custom fat vs Henon multifractal map). There is not too
> much difference  between the mono-fractals and multifractl dimension.

You have to be careful about the kind of image being analysed and the range of
boxes used. Unless images are quite large to enable collecting lots of data,
you might be getting a wrong D(q). Doing this blindly and accepting a D(q)
value without making sure that the slope is a realistic representation of the
plot is a recipe for disaster.

Something you might want to try is to use various ranges of boxes and see how
stable your results are.
Since all of this is "estimation" depending on the slope of regression fit you
might get different values and not those you expect from the theory.

Cheers
Gabriel

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