Higuchi1988

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

bridgeW/Higuchi1988

Higuchi1988