Draw a set of circles on a grid (2d plane)

Question

I'm trying to draw a set of 64 disks on a grid 8x8. Like this figure:

I have so far:

I want to automate this task with a for loop for example, I dont know. See my code, this is brutal force code, one line for each disk

\documentclass{article} 
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}[scale=3]
\draw[step=.5cm,gray,very thin] (-2.0,-2.0) grid (2.0,2.0);
\draw (-1.75,1.75) circle (0.15cm);
\draw (-1.25,1.75) circle (0.15cm);
\draw (-0.75,1.75) circle (0.15cm);
\draw (-0.25,1.75) circle (0.15cm);
\draw (0.25,1.75) circle (0.15cm);
\draw (0.75,1.75) circle (0.15cm);
\draw (1.25,1.75) circle (0.15cm);
\draw (1.75,1.75) circle (0.15cm);
\end{tikzpicture}
\end{document}

Answer 1

This is quite easy if you look a bit into the manual. At the end of Page 901 of the pgfmanual verion 3.0.1a, you find a similar pattern of circles as pointed out by @Symbol1. The remaining tiks and labels are basic easy sruff.

\documentclass[tikz,border=5pt]{standalone} 
\usetikzlibrary{calc}
\begin{document}

\begin{tikzpicture}[line width=.7pt, outer sep=0pt]
\foreach \x in {1,...,8}
  \foreach \y in {1,...,8}
    \draw [fill=red](\x,\y) circle (0.3cm);
\node [minimum size=8.2cm,draw](o) at (4.5,4.5){};

\node at (o.north) [above]{$N=64, \eta=0.3$};
\node at (o.south) [below=1em]{eixo x};
\node at (o.west)  [left=2.5em,rotate=90]{eixo y};

\foreach \i  in {0,0.2,0.4,0.6,0.8,1.0}{
  \draw ($(o.south west)!\i!(o.south east)$)node[below]{\i}--++(0,2mm);
  \draw ($(o.south west)!\i!(o.north west)$)node[left]{\i}--++(2mm,0);
}
\end{tikzpicture}
\end{document}