newtonfractal9.m

%newton fractal
%Note: this script takes about 7 seconds to complete the fractal
%equation (z+0.5-0.866i)*(z+0.5+0.866i)*((z-1)^(0.4+0.9i))
%
x = linspace(-1.5,1.5,700);
y = linspace(-1.5,1.5,700);
c = zeros(length(y),length(x));



  len_x = length(x);
  len_y = length(y);

for n=1:len_x
    c(n,:) = y(n)+i*x(:);
end

h_msg   = msgbox(' Please Wait ',' ');
zvalues = zeros(len_x,len_y);
    z   = 0+i*0; 
  rough = 0; 
 rough1 = 0; 
 rough2 = 0;  
     m  =  1;
     n  =  len_x*len_y;
   const=0.7+0.9*i;
tic
for m=1:n
     
    k = 0;
    z = c(m);
    rough1 = 0.06;
    rough  = 0;
     while ((k<=30)&&(abs(rough1)> 0.03))
         rough2=  const/(z-1)+1/(z+0.5 - 0.866i)+1/(z+0.5 + 0.866i);   
              z = z - 1/rough2;
         rough1 = z - rough;
         rough  = z;
             k  = k+1;
     end
   zvalues(m) = k;

end
toc
close(h_msg);
%you can also try any one of these colormaps
%cmap = flipud(colormap(hsv));  
%cmap = flipud(colormap(copper));  
%cmap = flipud(colormap(hot));  
%cmap = flipud(colormap(gray));  
%cmap = flipud(colormap(jet));  
%cmap = flipud(colormap(summer)); 
%cmap = flipud(colormap(winter));  
%cmap = flipud(colormap(spring));  
%cmap = flipud(colormap(bone));    
%cmap = colormap(hsv);  
%cmap = colormap(copper);  
%cmap = colormap(hot);  
%cmap = colormap(gray);  
%cmap = colormap(jet);  
%cmap = colormap(summer); 
%cmap = colormap(winter);  
%cmap = colormap(spring);  
%cmap = colormap(bone);    
cmap=flipud(colormap(hot));
colormap(cmap);
image(x,y,zvalues)
axis tight square

%remove comments '%' from 70-75 to save the image
%clear x y c
%zval8 = uint8(zvalues);
%clear zvalues
%rgb   = ind2rgb8( zval8 , cmap );
%imwrite(rgb ,'newton9.png','png') ;