% routine to create a Newton's method plot
% this will  be a row oriented approach

n  = 81;   % an odd number prevents a zero
n = input('enter resolution ->');
dx = 3/n;
nits = 10;
tol = 0.25;
report = 25; % frequency of reporting


% roots of x^3-1=0
w1 = 1;
w2 = exp(2*pi*i/3);
w3 = w2*w2;

range = [-1.5:dx:1.5];
mm = zeros(length(range));


for r = 1:(n+1)
	m = range(r) +  i*range;
	% do the whole line with real = r nits times
	for k=1:nits
		m = m - (m.^3-1)./(3*m.^2);
	end;
	% record the results in mmr (mm row)
	mmr = (abs(m-w1)<tol)+2*(abs(m-w2)<tol)+3*(abs(m-w3)<tol);
	% find the errors
	errs = find(mmr==0);
	for j=errs    % for every sick entry we do...
		x = m(j);
		while (1)
			numer = x*x*x-1;
			if (abs(numer) < tol), break; end;
			x = x - numer/(3*x*x);
		end; %of while
		mmr(j)=(abs(x-w1)<tol)+2*(abs(x-w2)<tol)+3*(abs(x-w3)<tol);
	end; % end the for j=errs
	% copy the finished line into mm
	mm(:,r)=mmr';
	if(rem(r,report)==0), 
		disp(['Finished line #',int2str(r)]); 
	end;
end;


image(mm);
axis('image');
axis('off');

% uncomment just one of the following lines
colormap(gray(3));	% for grayscale monitors
%colormap(eye(3));	% for color monitors