Calculate the Fractal Dimension D. It has a relation with Detrended Fluctuation Analysis of 3-D.
Purpose: Calculating the fractal dimension D
Step1: Get the length of the curve,L(m,k) m: initial time k: interval time L(m,k)=sum(i=1,[(N-m)/k],|X(m+i*k)-X(m+(i-1)*k)|/k)
Step2: Get the average of L(m,k)& its Standard_dev
ave_Lmk=sum(m=1,k,L(m,k))/k
std_dev_Lmk=sqrt(k*L(m,k)**2-sum(L(m,k))**2))/(k*(k-1))
References:
! 1.Higuchi,T.,1988.Approach to an irregular time
! series on the basis of fractal theory.
! Physica D 31.277-283
! 2.Burlaga,L.F., Klein,L.W.,1986.Fractal structure of
! the interplanetary magnetic field. J.Geophys.Res.91,374-350
! 3.Gotoh,K.,Hayakawa,M.,Smirnova,N.A.,etal.2004. Fractal
! analysis of seimogenic ULF emissions. Physis and Chemistry of
! the Earth.29,419-424
! Record of revisions:
! Date Programmer Description of change
! ==== ========== =====================
! 2012/1/5 Q.Wang Original code
! 2012/1/8 Q.Wang Revised
! 2012/1/9 Q.Wang Revised
! 01/14/12 Q.Wang Revised
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