dim_fract.m

calculates the fractal dimension of a set in the 2D plane using the box counting method.

function  Dim_Fract(a,b)

%   initialisation des variables
T_x=a;
T_y=b;
x=a;
y=b;
Kmax=100;
Lm_T=0;
%****************************************************
N=length(y);
for k=1:Kmax
    L(k)=(N-1)/k*sum(sqrt((y(1:end-k)-y(1+k:end)).^2+(x(1:end-k)-x(1+k:end)).^2));
end

%****************************************************
for i=1:Kmax
   if(L(:,i)~=0 )
    x2(:,i)=log(i);
    y2(:,i)=log(L(:,i));
   end 
end   
l=length(x2)
p2=polyfit(x2(1:30),y2(1:30),1);
BestFit2=polyval(p2,x2);
D_T=1-p2(:,1);
for i=1:l
Lm_T=Lm_T+L(:,i);
end
Lm_T=Lm_T/l;
save Lm_T Lm_T;
save DF_T D_T;
plot(x2,y2,'b.','LineWidth',1)
hold on
plot(x2(1:l), BestFit2(1:l),'r-','Linewidth',2)
xlabel('Jauge, log N', 'FontSize',10)
ylabel('Longueur mesur閑, log N(s)' , 'FontSize',10)
title(['Longueur Moyenne= ',num2str(Lm_T,'%10.4f'),' Dimension fractale= ',num2str(D_T,'%10.4f')]);
h = legend('sujet normal',-1);
set(h,'Interpreter','none');
hold off
saveas(gcf,'Courbe_T.fig');