In many ways, the Mandelbrot Set is similar to the Julia Sets we just discussed.

Code

function MandelbrotSet(r,w,makeVideo)
% Draws a Mandelbrot Set with iterations r and resolution w. Set makeVideo
% to 1 if you want to record a video.
    
    if makeVideo==1
         writerObj = VideoWriter('mandelbrotSet4.avi'); % Name it.
         writerObj.FrameRate = 2;
         writerObj.Quality=100;
         open(writerObj)    
    end
    % Create the real and imaginary parts of each number in a temporary
    % variable
    temp=zeros(w,w,2);
    for i=1:w
        temp(i,:,1)=linspace(-2,1,w);
        temp(:,i,2)=linspace(-1.25,1.25,w);
    end
    
    % Set the initial values based on their real and imaginary components
    values=zeros(w,w,2);
    for i=1:w
        for j=1:w
            values(i,j,1)=temp(i,j,1)+1i*temp(i,j,2);
        end
    end
    
    % Initialize the output
    output=zeros(w,w);
    
    % Create the figure
    figure('Position',[100,100,1400,800],'Color',[0 0 0]);

    % For each iteration, cycle through data and perform the desired
    % computatation
    for i=1:r 
        for m=1:w
            for k=1:w
                values(m,k,2)=(values(m,k,2))^2+values(m,k,1);
                
                % Essentially, set output(m,k) equal to the current
                % iteration if the series diverges
                if abs(values(m,k,2))>10 && output(m,k)==0
                    output(m,k)=i;
                end
            end
        end
        
        % Plot the data
        clims=[0,r];
        imagesc(output(:,:),clims);
        colormap('hot');
        axis off
        if makeVideo==1
            frame = getframe(1);
            writeVideo(writerObj, frame)  
        end
        pause(.001)
    end
    
  if makeVideo==1
      for i=1:10
         frame = getframe(1);
         writeVideo(writerObj, frame)
      end
      close(writerObj)
  end
end