\begin{tikzpicture}[scale=5]
  % Define grid parameters
  \def\gridsize{5}
  \def\cellsize{0.2}
  
 
  \def\circleradius{0.04}
  
  \fill[myred,opacity=0.3] (0.03,0.15) circle (\circleradius);
  \fill (0.03,0.15) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.27,0.08) circle (\circleradius);
  \fill (0.27,0.08) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.48,0.17) circle (\circleradius);
  \fill (0.48,0.17) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.63,0.12) circle (\circleradius);
  \fill (0.63,0.12) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.85,0.06) circle (\circleradius);
  \fill (0.85,0.06) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.15,0.38) circle (\circleradius);
  \fill (0.15,0.38) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.22,0.25) circle (\circleradius);
  \fill (0.22,0.25) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.46,0.32) circle (\circleradius);
  \fill (0.46,0.32) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.68,0.37) circle (\circleradius);
  \fill (0.68,0.37) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.83,0.28) circle (\circleradius);
  \fill (0.83,0.28) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.08,0.55) circle (\circleradius);
  \fill (0.08,0.55) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.35,0.48) circle (\circleradius);
  \fill (0.35,0.48) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.42,0.58) circle (\circleradius);
  \fill (0.42,0.58) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.75,0.52) circle (\circleradius);
  \fill (0.75,0.52) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.88,0.47) circle (\circleradius);
  \fill (0.88,0.47) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.12,0.73) circle (\circleradius);
  \fill (0.12,0.73) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.28,0.68) circle (\circleradius);
  \fill (0.28,0.68) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.45,0.78) circle (\circleradius);
  \fill (0.45,0.78) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.62,0.72) circle (\circleradius);
  \fill (0.62,0.72) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.87,0.75) circle (\circleradius);
  \fill (0.87,0.75) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.07,0.92) circle (\circleradius);
  \fill (0.07,0.92) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.33,0.88) circle (\circleradius);
  \fill (0.33,0.88) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.41,0.95) circle (\circleradius);
  \fill (0.41,0.95) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.78,0.89) circle (\circleradius);
  \fill (0.78,0.89) circle (0.01);
  
  \fill[myred,opacity=0.3] (0.82,0.93) circle (\circleradius);
  \fill (0.82,0.93) circle (0.01);
  \draw[thick] (0,0) rectangle (1,1);
  
  \foreach \i in {1,2,3,4} {
    \draw[mygray] (\i*\cellsize,0) -- (\i*\cellsize,1);
    \draw[mygray] (0,\i*\cellsize) -- (1,\i*\cellsize);
  }
  
  \draw[<->] (1.1,0) -- (1.1,1);
  \node[] at (1.15,0.5) {1};
  
  \draw[<->] (-0.05,1-\cellsize) -- (-0.05,1);
  \node[anchor=east] at (-0.05,1-\cellsize/2) {$N^{-1/2}$};
\end{tikzpicture}
