Plotting points around two circles using tikz

Question

I am looking to place points around two circles like this:

Using tikz I can draw for example the two circles but how can I either i)plot small circles like \fill (x,y) circle[radius=3pt]; on the given circles or ii)around the circle. I can't find each point satisfying the equation for a large number of points as this would be very time consuming. Thanks

Answer 1

Quick and dirty with pgfplots, plotting cos(x)+random number against sin(x)+random number.

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
  cycle list={
    only marks,mark=*,fill=red,draw=black,mark size=1pt\\
    only marks,mark=*,fill=cyan,draw=black,mark size=1pt\\
  },
  domain=0:360,
  samples=500,
  title={N=500,\dots},
  grid,
  axis equal
]

\addplot ({(0.5+0.07*rand)*cos(x)},{(0.5+0.07*rand)*sin(x)});
\addplot ({(1+0.1*rand)*cos(x)},{(1+0.1*rand)*sin(x)});

\end{axis}
\end{tikzpicture}
\end{document}