lyapunovfractal2.m

%lyapunov fractal
%for further reference visit these links
%http://en.wikipedia.org/wiki/Lyapunov_fractal
%http://pagesperso-orange.fr/charles.vassallo/en/lyap_art/lyapdoc.html
%this script takes about 7 seconds to generate the fractal
seq_list  = {'[1 1 0 1 0]'  ;'[1 1 1 0 0 0]';...
             '[1 0 1 0 0 1]';};

[s,v]     = listdlg('PromptString','Select sequence:',...
                'SelectionMode','single',...
                'ListString',seq_list);

if v==1                
seq=str2num(seq_list{s});

hell = [];
N    = 150;
for rough=1:90            
    hell=[hell seq];          %repeat the sequence
end
    seq = hell(1:N);    clear hell
seq_len = length(seq);
lambda  = 0;
   a    = linspace(3,4,500);  %image plane
   b    = linspace(3,4,500);  %image plane
   a0   = 0;
   b0   = 0;
   r    = 0;
   x    = 0;
sum_log = 0;
  rough = 0;
 rough1 = 0;
   lena = length(a);
   lenb = length(b);
   zval = zeros(lena,lenb);
      c = zeros(lena,lenb);
for n=1:lena
    c(n,:) = b(n)+i*a(:);
end

total  =lena*lenb;
prod_deriv = 0;
tic
h_msg = msgbox(' Please Wait ',' ');
for m=1:total
            x=0.5;
            b0=imag(c(m));
            a0=real(c(m));
            for rough=1:seq_len
                if seq(rough)==1
                  r=a0;
                else
                  r=b0;
                end
                 x=1*r*x*(1-x);
            end
       sum_log=0;
       prod_deriv = 1;    
       rough=1;
       while ((rough<=N)&&(prod_deriv<200))
               if seq(rough)==1
                  r=a0;
               else
                  r=b0;
               end
              x = r*x*(1-x);
              prod_deriv =prod_deriv*r*(1-2*x); 
              sum_log=sum_log+log(0.00001+abs(prod_deriv));
              rough=rough+1;
       end
      lambda = sum_log / N;
      zval(m)=10+abs(lambda);
end
toc
close(h_msg);
cmap=fliplr(colormap(hot));
%cmap=colormap(hot);
%cmap=colormap(copper);
colormap(cmap);
h=imagesc(b,a,zval);

%remove these comments to save the figure as an image
%zval2=get(h,'cdata');
%rgb=ind2rgb8(zval2,colormap);
%imwrite(rgb,'lyapunov.png','png');
end