Scatter Diagramm (Färbung der einzelnen Felder nach Häufigkeit)

\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{statistics}
\usepackage{luacode}
\begin{luacode*}
-- Initialize the random number generator according to
-- http://lua-users.org/wiki/MathLibraryTutorial
math.randomseed( tonumber(tostring(os.time()):reverse():sub(1,6)) )

-- standard Box-Muller transform
-- https://en.wikipedia.org/wiki/Box-Muller_transform
function gauss_random(mu, sigma)
   -- State variables
   local generate = false
   local z0 = 0.0
   local z1 = 0.0

   -- Parameters
   mu = mu or 0.0
   sigma = sigma or 1.0

   function random()
      generate = not generate

      if (not generate) then
         return z1*sigma + mu;
      end

      local u1, u2
      repeat
         u1 = math.random()
         u2 = math.random()
      until ( u1 > 1e-16 )

      z0 = math.sqrt(-2.0 * math.log(u1)) * math.cos(2*math.pi * u2)
      z1 = math.sqrt(-2.0 * math.log(u1)) * math.sin(2*math.pi * u2)
      return z0*sigma + mu
   end

   return random
end

function generate(N)
   local tab = {}
   local gauss = gauss_random()
   for i = 1, N do
      tab[i] = { x = gauss(), y = gauss() }
   end
   return tab
end

function generate_table(tab)
   tex.sprint("{\r")
   tex.sprint("x y z\r")
   for i = 1, #tab do
      tex.sprint(tab[i].x .. " " .. tab[i].y .. " 0\r")
   end
   tex.sprint("}")
end

function generate_hist(tab,xmin,xmax,Nx,ymin,ymax,Ny)
   local xstep = (xmax - xmin) / (Nx-1)
   local ystep = (ymax - ymin) / (Ny-1)

   tex.sprint("{\r")
   tex.sprint("x y z\r")
   for x = xmin,xmax,xstep do
      for y = ymin,ymax,ystep do
         local bins = 0
         for i = 1,#tab do
            if (x-xstep/2 <= tab[i].x and tab[i].x < x+xstep/2) and 
               (y-ystep/2 <= tab[i].y and tab[i].y < y+ystep/2) then
               bins = bins + 1
            end
         end
         tex.sprint(x .. " " .. y .. " " .. bins .. "\r")
      end
      tex.sprint("\r")
   end
   tex.sprint("}")

end
\end{luacode*}
\newcommand\generatetable[5]{%
  \directlua{tab = generate(#1)}
  \expandafter\pgfplotstableread\directlua{generate_table(tab)}#4
  \expandafter\pgfplotstableread\directlua{generate_hist(tab,#2,#3)}#5
}
\begin{document}
\generatetable{400}{-4,4,10}{-4,4,10}\pointtable\histtable
\begin{tikzpicture}
  \begin{axis}
    \addplot[
      matrix plot,mesh/rows=10,mesh/cols=10,
      point meta=explicit,
      shader=faceted,colormap/cool
    ] table[meta=z] {\histtable};
    \addplot[only marks,mark=o] table {\pointtable};
  \end{axis}
\end{tikzpicture}
\end{document}