2

I wish to shade multiples regions (labelled A) that are formed by two quarter circles, making a sort of matrix.

\documentclass[10pt]{standalone}
\usepackage{pgf,tikz}
\pagestyle{empty}
\begin{document}
\begin{tikzpicture}
\draw (8.,12.) -- (4.,12.) -- (4.,8.) -- (8.,8.) -- cycle;
\draw (8.,12.) -- (8.,8.) -- (12.,8.) -- (12.,12.) -- cycle;
\draw (12.,12.) -- (12.,8.) -- (16.,8.) -- (16.,12.) -- cycle;
\draw (16.,12.) -- (16.,8.) -- (20.,8.) -- (20.,12.) -- cycle;
\draw (8.,8.) -- (4.,8.) -- (4.,4.) -- (8.,4.) -- cycle;
\draw (12.,8.) -- (8.,8.) -- (8.,4.) -- (12.,4.) -- cycle;
\draw (16.,8.) -- (12.,8.) -- (12.,4.) -- (16.,4.) -- cycle;
\draw (20.,8.) -- (16.,8.) -- (16.,4.) -- (20.,4.) -- cycle;

\draw [shift={(4.,12.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=-1.5707963267948966:0.,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(8.,8.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=1.5707963267948966:3.141592653589793,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(8.,8.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=0.:1.5707963267948966,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(12.,12.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=3.141592653589793:4.71238898038469,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(4.,4.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=0.:1.5707963267948966,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(8.,8.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=3.141592653589793:4.71238898038469,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(12.,4.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=1.5707963267948966:3.141592653589793,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(8.,8.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=-1.5707963267948966:0.,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(12.,12.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=-1.5707963267948966:0.,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(16.,8.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=1.5707963267948966:3.141592653589793,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(20.,12.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=3.141592653589793:4.71238898038469,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(16.,8.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=0.:1.5707963267948966,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(20.,4.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=1.5707963267948966:3.141592653589793,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(16.,8.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=-1.5707963267948966:0.,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(12.,4.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=0.:1.5707963267948966,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;
\draw [shift={(16.,8.)},color=black,fill=white,fill opacity=0.1]  (0,0) --  plot[domain=3.141592653589793:4.71238898038469,variable=\t]({1.*4.*cos(\t r)+0.*4.*sin(\t r)},{0.*4.*cos(\t r)+1.*4.*sin(\t r)}) -- cycle ;

\node at (6, 10) {$A$};
\node at (10, 10) {$A$};
\node at (14, 10) {$A$};
\node at (18, 10) {$A$};


\node at (6, 6) {$A$};
\node at (10, 6) {$A$};
\node at (14, 6) {$A$};
\node at (18, 6) {$A$};

\end{tikzpicture}
\end{document}

enter image description here

3

Like this:

enter image description here

\documentclass[ border=3mm,
                tikz,
                12pt]{standalone}

\begin{document}
    \begin{tikzpicture}
\draw[fill=blue!20] ( 0,0) circle (4);
\draw[fill=white]   (-4,0) arc ( 90:  0:4)
                           arc (180: 90:4)
                           arc (270:180:4)
                           arc (  0:-90:4);
\foreach \i in {45,135,225,315}{\node at (\i:3) {$A$};}
\draw[dashed] (-4,0) -- (4,0)   (0,-4) -- (0,4);
    \end{tikzpicture}
\end{document}

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