## Monday, June 25, 2007

### Matlab: Mandelbrot set

Recently I read article on Free Software Magazine titled Generating cool fractals. I was very pleased to find source code for generation of Mandelbrot set.
`function mandelFrac% MATLAB and Octave code to generate%a Mandelbrot fractal% Number of points in side of image and% number of iterations in the Mandelbrot% fractal calculationnpts=1000;niter=51;% Generating z = 0 (real and% imaginary part)zRe=zeros(npts,npts);zIm=zeros(npts,npts);% Generating the constant k (real and% imaginary part)kRe=repmat(linspace(-1.5,0.5,npts),npts,1);kIm=repmat(linspace(-1,1,npts)',1,npts);% Iteratingfor j=1:niter% Calculating q = z*z + k in complex space% q is a temporary variable to store the resultqRe=zRe.*zRe-zIm.*zIm+kRe;qIm=2.*zRe.*zIm+kIm;% Assigning the q values to z constraining between% -5 and 5 to avoid numerical divergenceszRe=qRe;qgtfive= find(qRe > 5.);zRe(qgtfive)=5.;qltmfive=find(qRe<-5.);zRe(qltmfive)=-5.;zIm=qIm;hgtfive=find(qIm>5.);zIm(hgtfive)=5.;hltmfive=find(qIm<-5.);zIm(hltmfive)=-5.;end% Lines below this one are commented out when making% the benchmark.% Generating plot% Generating the image to plotima=log( sqrt(zRe.*zRe+zIm.*zIm) + 1);% Plotting the imageimagesc(ima);`