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% Spinning Fibonacci spiral
n = 500;
R = linspace(0,1,n);
T = 4/(1+sqrt(5))*pi*(1:n);
X = R.*cos(T);
Y = R.*sin(T);
newplot
tf = hgtransform;
scatter(tf,X,Y,R*30+10,R,'filled')
daspect([1 1 1])
axis off
speed = 0;
angle = 0;
for i = [1 2 3 4 3 2]
    speed = T(i); % Align with next point in spiral
    for k=1:150
        angle = angle+speed;
        tf.Matrix = makehgtform('zrotate',-angle);
        pause(1/120)
    end
end

Note: For older versions of MATLAB, adjust the scatter function to: scatter(X,Y,R*30+10,R,'filled','Parent',tf)