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Consider the following function that draws an animated plot of cicloid. 

 function animate1()
    clear, clc

    R = 1; 
    na = -pi/2; 
    t = 0:0.05:6;
    v = 4; 

    for i = 1:length(t)
        x0 = v*t(i); 
        y0 = R;
        na = -v*t(i)/R; 
        fi = linspace(na,na+2*pi,100); 
        x = x0 + R*cos(fi); 
        y = y0 + R*sin(fi);

        xc(i) = x0 + R*cos(na);
        yc(i) = y0 + R*sin(na);

        plot(x,y,'b',... 
            xc(i),yc(i),'*m',... 
            xc,yc,'r') 
        axis([-1 25 0 1.5])
        axis equal
        pause(0.01)
    end

Is it possible to modify the code in such a way that it output animated plot e.g. to a gif?

Thank you in advance! 

Yes, imwrite does support animated GIFs. Like for AVI videos, you grab frames via getframe sequentially. Then pass them to imwrite though for GIFs you have to convert them from RGB to a 256 colormap before. Like this: 

for i = 1:nFrames

    % draw stuff

    frame = getframe(gcf);
    img =  frame2im(frame);
    [img,cmap] = rgb2ind(img,256);
    if i == 1
        imwrite(img,cmap,'animation.gif','gif','LoopCount',Inf,'DelayTime',1);
    else
        imwrite(img,cmap,'animation.gif','gif','WriteMode','append','DelayTime',1);
    end
end 

Have a look at openExample('matlab/WriteAnimatedGIFExample') and at doc imwrite for more information.