I need help animating the evolution of a polar plot and saving it as a gif.

I'm trying to animate a polar plot for a student. The plot is r=theta^2 on the interval [-2pi,2pi]. This what I have so far, and all I'm getting are empty graphs. Also, how can I fix the polar grid so that it's limits are constant?

clc

theta=linspace(-2*pi,2*pi,201);
rho=theta.^2;

figure;
grid on

filename='polarplot1.gif';

for i=1:length(theta)
    polarplot(theta(i),rho(i),'-');
    drawnow;

    [imind,cm] = rgb2ind(im,256);
    if i == 1
          imwrite(imind,cm,filename,'gif', 'Loopcount',inf);
    else
          imwrite(imind,cm,filename,'gif','WriteMode','append');
    end
    
    pause(0.025)
end

Answer 1

[DGM]

A few things:

You're only plotting one point at a time, so if you use a linestyle but no marker style, there's nothing to plot. Set a marker style if you want to plot a single point.

You need to capture the figure somehow. Nothing in your code appears to do that.

You'll probably want to set the GIF frame delay.

theta=linspace(-2*pi,2*pi,201);
rho=theta.^2;

delay = 0.1; % set the frame delay
figure;
grid on

filename='polarplot1.gif';
for i=1:length(theta)
    polarplot(theta(i),rho(i),'o'); % use a marker style
    
    drawnow;
    im = frame2im(getframe(gcf)); % capture the frame
    
    [imind,cm] = rgb2ind(im,256);
    if i == 1
        imwrite(imind,cm,filename,'gif','delaytime',delay,'Loopcount',inf);
    else
        imwrite(imind,cm,filename,'gif','delaytime',delay,'WriteMode','append');
    end
    
    %pause(0.025)
end

You also might want to set the axes limits to some fixed value so that it's not constantly changing.