%script file to make a movie zooming in to a plot of a
%newton iteration function

%parameters for the function C(z)=z^3+a*z+b
a=1.5;
b=0;
p=[1 0 a b];
%numerical values for the roots
rts=roots(p);
%input zoom parameters
center=1+0*i;
lbo=-2;
ubo=2;
rate=.3
maxzoom=10;
gridsize=200;
%loop through window sizes, plotting at each stop
for g=1:maxzoom
lb=center+(lbo*rate^g);
ub=center+(ubo*rate^g);
increment=(ub-lb)/gridsize;
[X,Y]=meshgrid([lb:increment:ub]);
[m,n]=size(X);
maxiters=30;
T=64*ones(m,n);
for j=1:m
    fprintf ('on iterate %d\n',j);
    for k=1:n
        z=X(j,k)+i*Y(j,k);
        for t=1:maxiters
            y=z-(z^3+a*z+b)/(3*z^2+a);
            z=y;
            if abs(z-rts(1))<.001
                T(j,k)=1+t*(20/maxiters);
                break;
            end
            if abs(z-rts(2))<.001
                T(j,k)=26+t*(15/maxiters);
                break;
            end
            if abs(z-rts(3))<.001
                T(j,k)=45+t*(24/maxiters);
                break;
            end
        end
    end
end
image(T)
pause(0.1);
%get the image as a movie frame
M(:,g)=getframe;
end
movie(M,3);