The obvious way to do this in Inkscape, using the Create Tiled Clones dialog, won't work as one cannot control the sizes and spacing properly. Instead, import into Inkscape the following simple PostScript program:

%!PS-Adobe-2.0
%% BoundingBox: 0 0 500 500
%% Copyright 2007 Tavmjong Bah
%% Squares...

/cell {

    /cell_y2 exch def
    /cell_x2 exch def
    /cell_y1 exch def
    /cell_x1 exch def

    newpath
    cell_x1 cell_y1 moveto
    cell_x1 cell_y2 lineto
    cell_x2 cell_y2 lineto
    cell_x2 cell_y1 lineto
    closepath
    gsave
    fill
    grestore
    0 setgray
    stroke

} def

% Move to center
250 250 translate

% Global constants
/divs    11 def
/boxsize 200 def

% x stuff
/xmul    0 def
/xdiv    divs def
/delxmul 1 xdiv 1 sub div def

xdiv 1 sub {

    /x1     1 xmul 2 exp sub boxsize mul def
    /xmul     xmul delxmul add def
    /x2     1 xmul 2 exp sub boxsize mul def
    /myblue 1 xmul 2 exp sub def
    
    % y stuff
    /ymul    0 def
    /ydiv    divs def
    /delymul 1 ydiv 1 sub div def
    ydiv 1 sub {

	/y1    1 ymul 2 exp sub boxsize mul def
	/ymul    ymul delymul add def
	/y2    1 ymul 2 exp sub boxsize mul def
        /myred 1 ymul 2 exp sub def

        myred myblue 0.5 setrgbcolor
	x1     y1     x2     y2     cell

	myred myblue 0.5 setrgbcolor
	x1 neg y1     x2 neg y2     cell
	
	myred myblue 0.5 setrgbcolor
	x1     y1 neg x2     y2 neg cell
	
	myred myblue 0.5 setrgbcolor
	x1 neg y1 neg x2 neg y2 neg cell
	
    } repeat
} repeat
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