fractal dimension

[Sam]

Hello

in getting the fractal dimension from a log log plot, and then best
fitting a line on the middle section, sure the parameters used to best
fit the line can give different fractal dimension. is there a mathematic
and not arithmetic method to avoid playing around with best-fit parameters.

for example, a usual log-log plot have flat extremes on both ends and a
slop between them, but what about the odd once, I have a 15 dimensions
point set which gave this log-log plot below, it is puzzling me on what
to fit the slope line on since most of the log-log points are either on
both sides of the flat extremes.

log(r), log(Nr)
0.30103, 1.23045
0.60206, 1.23045
0.90309, 1.23045
1.20412, 3.19145
1.50515, 3.19645
1.80618, 3.29951
2.10721, 3.427
2.40824, 3.43409
2.70927, 3.43409
3.0103 , 3.43409


thanks

[Roger Bagula]

Fitting a line to an s-shaped curve isn't a good idea.
y=1.14126466666666748`+0.947980620073102286` x
The result you have appears to be "multifractal":
that is it has different fractal characteristics at different scales
( actually it may be really fractal only in the transition scale region).
It appears like what we see in physics as a phase transition.
To do alteration of the data to get a better line
may be missing the point....

Post by Sam
Hello
in getting the fractal dimension from a log log plot, and then best
fitting a line on the middle section, sure the parameters used to best
fit the line can give different fractal dimension. is there a
mathematic and not arithmetic method to avoid playing around with
best-fit parameters.
for example, a usual log-log plot have flat extremes on both ends and
a slop between them, but what about the odd once, I have a 15
dimensions point set which gave this log-log plot below, it is
puzzling me on what to fit the slope line on since most of the log-log
points are either on both sides of the flat extremes.
log(r), log(Nr)
0.30103, 1.23045
0.60206, 1.23045
0.90309, 1.23045
1.20412, 3.19145
1.50515, 3.19645
1.80618, 3.29951
2.10721, 3.427
2.40824, 3.43409
2.70927, 3.43409
3.0103 , 3.43409
thanks