I used Paul Bourke FDC box
dimension calculator on the scatter diagram.
I got a dimension of:
1.10369
RSquared -> 0.994111
which means it is a pretty good line.
Since the Sunspot data as I posted is very near
Cantor dimension at Log[2]/Log[3],
Actually my two estimates ( correlation and modified Zipf frequency
counting) are
s1 = 0.6376053551998503
s2 = 0.3781094484568289
s1+s2=1.01571
which is a 0.1 lower than this slope.
So it appear that some other fractal process is involved.
Mathematica:
(* box dimension data from Paul Bourke's FDC*)
fdc = {1, 0, 2998, 8.0057,
2, -0.693147 , 1277 , 7.15227,
4, -1.38629, 668, 6.50429,
14, -2.63906 , 209, 5.34233,
24, -3.17805 , 118 , 4.77068,
36, -3.58352, 74 , 4.30407,
49, -3.89182 , 47, 3.85015,
61, -4.11087, 35, 3.55535,
73, -4.29046 , 23 , 3.13549,
85, -4.44265 , 23 , 3.13549,
98, -4.58497 , 19 , 2.94444,
196, -5.27811, 8 , 2.07944
}
d = Table[{fdc[[n]], fdc[[n + 2]]}, {n, 2, Length[fdc], 4}]
g = ListPlot[d]
f[x_] = Fit[d, {1, x}, x]
8.067269801326825`\[InvisibleSpace]+ 1.1036948478623085` x
g1 = Plot[f[x], {x, 0, -7}]
Show[{g, g1}]
<< Statistics`LinearRegression`
Regress[d, {1, x}, x]
s1 = 0.6376053551998503
s2 = 0.3781094484568289
s1 + s2
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