% global unstable manifold of the origin in the Lorenz system
    
s = 10; rh = 28; b = 8/3;                       % Lorenz system
dim = 3;
v = @(x) [s*(x(:,2)-x(:,1)) ...
          rh*x(:,1)-x(:,2)-x(:,1).*x(:,3) ...
          x(:,1).*x(:,2)-b*x(:,3)];
h = 0.01; n = 10; f = @(x) rk4(v,x,h,n);        % flow map
n = 20; X1 = linspace(-1,1,n)'; E = ones(size(X1));    
X = [ X1 -E -E; X1 -E E; X1 E -E; X1 E E; ...
      -E X1 -E; -E X1 E; E X1 -E; E X1 E; ...
      -E -E X1; -E E X1; E -E X1; E E X1];      % sample points 
c = [0 0 0]; r = [25 25 25]; 
tree = Tree(c,r);                               % the box collection

%% continuation algorithm
newBox = 1; todo = 2;

x = [0 0 0];      % equilibrium  
depth = 21; 
tree.insert(x'*ones(1,size(X,1))+1E-6*X', depth);

while  % ...
  % TODO
    
    
  fprintf('%d boxes\n', n1);
  clf; boxplot3(tree,'alpha',0.9); axis tight;
  light('position',[-1,2,2]); view(20,30); drawnow;
end


%% cleanup
delete(tree);