Untitled

RelTol=1.e-06; AbsTol=1.e-09;
% Write Newton's method using every grid point as the initial condition
% Perform enough iterations that every initial condition converges to a root 
% Save the x-values of the converged roots in the matrix X
% To pass the assessment, every pixel in the figure must be correctly colored

%!!!!!!!!! Set initial value y=3*sqrt(2) for all values (x,z) on the grid !!!!!!!!!!
% It's ok to change the for loop of j and i
for j = 1:nz
    for i = 1:nx
        % setting the x y z value
        x = X(j, i);
        y = 3*sqrt(2);
        z = Z(j, i);
        error=Inf;
        while error > max(RelTol*max(abs([x,y,z])),AbsTol)
        J=  [-sigma sigma 0 ; r-z -1 -x; y x -beta]; % DEFINE THE JACOBIAN MATRIX
        rhs = -[sigma*(y-x); r*x-y-x*z; x*y-beta*z]; % DEFINE THE RIGHT-HAND SIDE
        delta_xyz=J\rhs;
        x = x + delta_xyz(1);
        y = y + delta_xyz(2);
        z = z + delta_xyz(3);
        error = max(abs(delta_xyz));
        end
    X(j, i) = x;
    Z(j, i) = z;
    end
end