\documentclass[a4paper, 12pt]{article}

% a nice font
\usepackage{kpfonts}

% basic text stuff
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}

\usepackage{tikz} % main tikz package

% for a nicer colorscheme
\input{colors.tex}

% some functions to generate random numbers from StackExchange
% (see https://tex.stackexchange.com/a/148133)
\makeatletter
\pgfmathdeclarefunction{invgauss}{2}{%
  \pgfmathln{#1}% <- might need parsing
  \pgfmathmultiply@{\pgfmathresult}{-2}%
  \pgfmathsqrt@{\pgfmathresult}%
  \let\@radius=\pgfmathresult%
  \pgfmathmultiply{6.28318531}{#2}% <- might need parsing
  \pgfmathdeg@{\pgfmathresult}%
  \pgfmathcos@{\pgfmathresult}%
  \pgfmathmultiply@{\pgfmathresult}{\@radius}%
}

\pgfmathdeclarefunction{randnormal}{0}{%
  \pgfmathrnd@
  \ifdim\pgfmathresult pt=0.0pt\relax%
    \def\pgfmathresult{0.00001}%
  \fi%
  \let\@tmp=\pgfmathresult%
  \pgfmathrnd@%
  \ifdim\pgfmathresult pt=0.0pt\relax%
    \def\pgfmathresult{0.00001}%
  \fi
  \pgfmathinvgauss@{\pgfmathresult}{\@tmp}%
}
\makeatother


\begin{document}
    \begin{tikzpicture}
        \pgfmathsetseed{123} % set the seed for reproducible documents

        \draw[fill=gray!30, line width=5pt, draw=white]
            plot[smooth, samples=100, domain=0:2] (\x,\x * \x) -| (-1,0) -- cycle;
        \draw[fill=brokengrey!30, line width=5pt, draw=white]
            plot[smooth, samples=100, domain=0:1.5] (\x,\x * \x) -| (4,0) -- cycle;
        \draw[fill=brokenwhite!30, line width=5pt, draw=white]
            plot[smooth, samples=100, domain=1.5:2] (\x,\x * \x) -| (4,1.5*1.5) -- cycle;

        \node (l1) at (-0.5,3.5) {$\mathcal L_1$};
        \node (l2) at (3.5,3.5) {$\mathcal L_2$};
        \node (l2) at (3.5,0.5) {$\mathcal L_3$};

        \foreach \i in {0,...,10} {
          \fill [opacity=0.8] (0.5+randnormal/3, 2.5+randnormal/4) circle (0.05);
          \fill [opacity=0.8] (3+randnormal/5, 2.9+randnormal/5) circle (0.05);
          \fill [opacity=0.8] (1.9+randnormal/4, 1+randnormal/5) circle (0.05);
          \fill [opacity=0.8] (0.2+randnormal/5, 0.8+randnormal/4) circle (0.05);
        }

        \draw [ultra thick, red, densely dashed]
            plot [smooth cycle, tension=1] coordinates {(0,2) (1,1.8) (1.2,3) (0,2.8)};
        \node[red] (c3) at (-0.7,2.5) {$\mathcal C_3$};

        \draw [ultra thick, blue, densely dashed]
            plot [smooth cycle, tension=1] coordinates {(2.5,2.8) (3.7,2.5) (3,3.5)};
        \node[blue] (c1) at (2.2,3.5) {$\mathcal C_1$};

        \draw [ultra thick, orange, densely dashed]
            plot [smooth cycle, tension=1] coordinates {(-0.5,0.3) (2.5, 0.3) (2,1.8) (1,1.2) (0, 1.3)};
        \node[orange] (c2) at (2.9,1.5) {$\mathcal C_2$};
    \end{tikzpicture}
\end{document}