function [N,dim]=boxdim(num)
%Computes the box dimension of the Henon Attractor
%Use a grid with 2^num times 2^num points
xmin=-2.0;
xmax=2.0;
step=2^num;
epsilon = (xmax-xmin)/step
Boxes=zeros(step+1);
x=1.77;
y=0.0;
% first get rid of some transients
for t=1:100,
	[x,y]=henon(x,y);
end
%now iterate and increment boxes array each time we land in one
tmax = max(100000,10*step*step);  %choose # of iterates
for t=1:tmax,
    i=ceil((x-xmin)/epsilon);  %which box are we in
	j=ceil((y-xmin)/epsilon);
    Boxes(i,j) = Boxes(i,j)+1;
    [x,y] =henon(x,y);
end
%contourf(Boxes)
bmax = max(max(Boxes));
image(256*Boxes/bmax)  % plot the matrix as an image & scale to colormap
colorbar
colormap(hot)
%
%Count the number of boxes filled
N=0;
for i=1:step,
	   for j=1:step,
	      if Boxes(i,j) > 0
			  N=N+1;
		  end
	  end
  end
  dim=-log(N)/log(epsilon);