Point Density Heat Map with TikZ

Question

I have a set of data points in a two dimensional space and would like to create a density heat map of the points that looks smooth, similar to the picture below which I produced in MATLAB. Darker regions have a higher concentration of points and vice verse. How can this be done with TikZ?

Answer 1

Here is my best attempt so far:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{fadings}
\begin{document}
\pgfdeclarelayer{foreground}
\pgfsetlayers{main,foreground}
\tikzfading[name=fade out, inner color=transparent!70, outer color=transparent!100]
\begin{tikzpicture}
\newcommand{\heat}[2]{%
  \fill[black,path fading=fade out] (#1,#2) circle (1);
  \begin{pgfonlayer}{foreground}
    \node at (#1,#2) {+};
  \end{pgfonlayer}
}
\foreach \i in {0,...,200}{%
  \pgfmathsetmacro\x{rnd*10}
  \pgfmathsetmacro\y{rnd*10}
  \heat{\x}{\y};
}
\end{tikzpicture}
\end{document}