%script file to make a movie of newton iteration function plots
%varying with a parameter

%create real and imaginary value arrays
[X,Y]=meshgrid([-2:0.01:2]);
[m,n]=size(X);
maxiters=30;
%parameters for the function C(z)=z^3+a*z+b
a=0;
%vary real part of b
br=-1:0.1:1;
for q=1:length(br)
b=br(q)+0*i;
%numerical values for the roots(must be calculated each time)
p=[1 0 a b];
rts=roots(p);
r1=rts(1);
r2=rts(2);
r3=rts(3);
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-r1)<.001
                T(j,k)=1+t*(20/maxiters);
                break;
            end
            if abs(z-r2)<.001
                T(j,k)=30+t*(20/maxiters);
                break;
            end
            if abs(z-r3)<.001
                T(j,k)=45+t*(20/maxiters);
                break;
            end
        end
    end
end
image(T);
%save picture as movie frame
M(:,q)=getframe;
end
movie(M,3);