I am trying to recreate the following image in TikZ

Using some old code I was able to produce the following result

While I was able to produce the correct result, I feel that my solution was a bit strange as it required two passes. Any suggestions for alternative approaches, or improvements to the code are more than welcome.

documentclass[tikz]{standalone}



begin{document}



begin{tikzpicture}[x=1cm]

edefsize{4}

    foreach x in {0,...,size} foreach y in {0,...,size}

    {

        pgfmathparse{mod(x+y,size) ? "none" : "black"}

        edefcolour{pgfmathresult}

        path[draw=black, fill=colour] (x,y) rectangle ++ (1,1);



        pgfmathparse{x==y ? "black" : "none"}

        edefcolour{pgfmathresult}

        path[fill=colour] (x,y) rectangle ++ (1,1);

    }

    draw (0,0)--(0,size+1)--(size+1,size+1)--(size+1,0)--cycle;

end{tikzpicture}



end{document}

With tikz:

documentclass[tikz]{standalone}



begin{document}

    begin{tikzpicture}[

node distance = 0mm,

   box/.style = {draw, minimum size=10mm, fill=black,

                 outer sep=0pt},

                      ]

edefsize{4}

foreach y in {0,...,size}

foreach x in {0,...,size}

{ifnumx=y

node[box]   at (x,size-y) {};

node[box]   at (x,y) {};

 else

node[box,fill=none] at (x,y) {};

 fi

}

    end{tikzpicture}

end{document}

Note: Value of size had to be zero or any even natural number (0, 2, 4, ...)

addendum:

• default baseline of above image is as (current bounding box.south)˙ For series of those images for different value ofsize` is:

documentclass{article}

usepackage{tikz}

usepackage{tabularx}

newcolumntype{C}{>{centeringarraybackslash}X}



begin{document}

    begin{figure}

begin{tabularx}{linewidth}{>{hsize=0.5hsize}C C >{hsize=1.5hsize}C}

    begin{tikzpicture}[baseline=(current bounding box.south),

node distance = 0mm,

   box/.style = {draw, minimum size=10mm, fill=black,

                 outer sep=0pt},

                      ]

edefsize{0} % in this MWE the meaning of `size` is changed

foreach y in {0,...,size}

foreach x in {0,...,size}

{ifnumx=y

node[box]   at (x,size-y) {};

node[box]   at (x,y) {};

 else

node[box,fill=none] at (x,y) {};

 fi

}

    end{tikzpicture}

    caption{}

&

    begin{tikzpicture}[%baseline=(current bounding box.south),

node distance = 0mm,

   box/.style = {draw, minimum size=10mm, fill=black,

                 outer sep=0pt},

                      ]

edefsize{1}

foreach y in {0,...,2*size} % changed, now number of boxes is odd 

foreach x in {0,...,2*size} % changed,

{ifnumx=y

node[box]   at (x,size-y) {};

node[box]   at (x,y) {};

 else

node[box,fill=none] at (x,y) {};

 fi

}

    end{tikzpicture}

    caption{}

&

    begin{tikzpicture}[baseline=(current bounding box.south),

node distance = 0mm,

   box/.style = {draw, minimum size=10mm, fill=black,

                 outer sep=0pt},

                      ]

edefsize{2}

foreach y in {0,...,size}

foreach x in {0,...,size}

{ifnumx=y

node[box]   at (x,size-y) {};

node[box]   at (x,y) {};

 else

node[box,fill=none] at (x,y) {};

 fi

}

    end{tikzpicture}

    caption{}

end{tabularx}

    end{figure}

end{document}

A PSTricks solution only for fun purposes!

documentclass[border=1pt]{standalone}

usepackage{pstricks}

defobj#1{%

    pspicture[dimen=m](#1,#1)

        multips(0,0)(0,1){#1}{multips(0,0)(1,0){#1}{psframe(1,1)}}

        multips(0,0)(1,1){#1}{psframe*(1,1)}

        multips(0,#1)(1,-1){#1}{psframe*(1,-1)}

    endpspicture}



begin{document}

foreach i in {3,5,7}{obj{i}quad}

end{document}

Edit

I invented the algorithm (that has not been patented yet) as follows. No nested loop is needed.

documentclass[border=12pt]{standalone}

usepackage[nomessages]{fp}

usepackage{xintexpr}

usepackage{pstricks}

psset{unit=5mm}

defobj#1{%

    pspicture[dimen=m](#1,#1)

    FPevalN{#1*#1-1}

    foreach j in {0,...,N}

    {

        FPevaly{trunc(j/#1:0)}

        FPevalx{j-#1*y}

        xintifboolexpr{x=y||(x+y)=(#1-1)}

        {psframe[fillstyle=solid,fillcolor=black](x,y)(+x+1,y+1)}

        {psframe(x,y)(+x+1,y+1)}

    }

    endpspicture}

begin{document}

foreach i in {1,3,5,7,9}{obj{i}quad}

end{document}

Edit:
The following works for all values of size

documentclass[tikz]{standalone}



begin{document}



begin{tikzpicture}

edefsize{4}

    foreach x in {0,...,size} foreach y in {0,...,size} {

        pgfmathsetmacro{colour}{(x==y || x+y==size) ? "black" : "none"}

        draw[fill=colour] (x,y) rectangle ++ (1,1);

    }

end{tikzpicture}



end{document}

I do not see the reason for a double loop, nor complicated conditions.

documentclass[tikz,border=3.14mm]{standalone}

begin{document}

begin{tikzpicture}[xboard/.style={insert path={

(0,0) grid (#1,#1)

foreach X in {1,...,#1}

{(X-0.5,X-0.5) pic{bx} (X-0.5,#1-X+0.5) pic{bx}}}},

pics/bx/.style={code={fill (-0.5,-0.5) rectangle (0.5,0.5);}}]

draw[xboard=1] [xshift=2cm,xboard=3]

[xshift=4cm,xboard=5] [xshift=6cm,xboard=7];

end{tikzpicture}

end{document}