\documentclass[a4]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{amsmath,amsfonts,amssymb}
\usepackage{graphicx}
\usepackage[usenames,dvipsnames]{xcolor}
%\usepackage{tikz}

\usepackage{pgfplots}
\usepackage{tikz,animate}
\usepackage{pgfplots}
\usetikzlibrary{shapes.arrows}
\usetikzlibrary{arrows.meta}

\usetikzlibrary{calc,patterns,angles,quotes}
\begin{document}
\pagestyle{empty}


\begin{tikzpicture}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Left upper 2-cluster
%%%%%%%%%%%%%%%%%%

%\draw[thick,fill=green,opacity=0.50] (-3.8-0.3,2.0-0.5) circle (0.65);
%\draw[thick,fill=blue,opacity=1.00] (-3.8-0.3,+2.0-0.5) circle (0.4);


%\draw[thick,fill=Cyan,opacity=0.50] (-2.6-0.3,1.9-0.5) circle (0.65);
%\draw[thick,fill=blue,opacity=1.00] (-2.6-0.3,1.9-0.5) circle (0.4);


\draw[thick,fill=Cyan,opacity=0.50] (-3.35,0.95) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-3.35, 0.95) circle (0.4);


\draw[thick,fill=Cyan,opacity=0.50] (-4.4,0.6) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-4.4,0.6) circle (0.4);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Left lower 2-cluster
%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (-3.2,-3.1) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-3.2,-3.1) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] (-4.3,-3.1) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-4.3,-3.1) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Middle upper 4-cluster
%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (-0.8, 1.6) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-0.8, 1.6) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 0.3, 1.4) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 0.3, 1.4) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 1.2, 1.7) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 1.2, 1.7) circle (0.4);

\draw[thick,fill=blue,opacity=1.00] ( 0.3, 1.4) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 2.35, 1.5) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 2.35, 1.5) circle (0.4);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Right upper 3-cluster
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] ( 4.05, 1.65) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 4.05, 1.65) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 5.15, 1.25) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 5.15, 1.25) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 4.9, 0.45) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 4.9, 0.45) circle (0.4);

\draw[thick,fill=blue,opacity=1.00] ( 5.15, 1.25) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% a 4-cluster
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\draw[thick,fill=Cyan,opacity=0.50] ( -2.4-0.5, -1.25) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( -2.4-0.5, -1.25) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( -1.75-0.5, -0.7) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( -1.75-0.5, -0.7) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( -1.5-0.5, -1.85) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( -1.5-0.5, -1.85) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( -1.0-0.5, -0.3) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( -1.0-0.5, -0.3) circle (0.4);

\draw[thick,fill=blue,opacity=1.00] ( -2.4-0.5, -1.25) circle (0.4);

\draw[thick,fill=blue,opacity=1.00] ( -1.75-0.5, -0.7) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% a 2 cluster
%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] ( 0.2, -0.15) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 0.2, -0.15) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 0.5, -1.0) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 0.5, -1.0) circle (0.4);

\draw[thick,fill=blue,opacity=1.00] ( 0.2, -0.15) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% a 2-cluster
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] ( 3.2, -0.35) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 3.2, -0.35) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 2.2, -0.85) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 2.2, -0.85) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  Lower left 3-cluster
%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] ( -2.5, -4.65) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( -2.5, -4.65) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( -3.1, -5.75) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( -3.1, -5.75) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( -2.0, -5.65) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( -2.0, -5.65) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  Middle lower 3-cluster
%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] ( -0.2, -3.15) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( -0.2, -3.15) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 0.2, -3.95) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 0.2, -3.95) circle (0.4);

\draw[thick,fill=blue,opacity=1.00] ( -0.2, -3.15) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 0.6, -5.0) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 0.6, -5.0) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  lower right 4-cluster
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] ( 2.6, -3.1) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 2.6, -3.1) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 3.7, -3.0) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 3.7, -3.0) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 2.7, -4.1) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 2.7, -4.1) circle (0.4);

\draw[thick,fill=blue,opacity=1.00] ( 2.6, -3.1) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 3.8, -4.0) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 3.8, -4.0) circle (0.4);

\draw[thick,fill=blue,opacity=1.00] ( 3.7, -3.0) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%
%  a 2-cluster
%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] ( 3.0, -6.0) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 3.0, -6.0) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 4.1, -5.7) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 4.1, -5.7) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a 2-cluster
%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] ( 5.5, -2.9) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 5.5, -2.9) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] ( 5.0, -1.8) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] ( 5.0, -1.8) circle (0.4);


\end{tikzpicture}


\end{document}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (-1.4,3.2) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-1.4,3.2) circle (0.4);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (-0.8,1.8) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-0.8,1.8) circle (0.4);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (0.8,2.8) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (0.8,2.8) circle (0.4);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (1.9,3.9) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (1.9,3.9) circle (0.4);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (2.9,2.1) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (2.9,2.1) circle (0.4);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (4.1,3.1) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (4.1,3.1) circle (0.4);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Panel b) 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (-3.5,-2.0) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-3.5,-2.0) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (-2.5,-0.0) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-2.5,0.0) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (-1.5,-1.5) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-1.5,-1.5) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] (-0.8,-0.6) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-0.8,-0.6) circle (0.4);

\draw[thick,black!50] (-1.5,-1.5) circle (0.65);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\draw[thick,fill=Cyan,opacity=0.50] (0.5,-1.9) circle (0.65);
%\draw[thick,fill=blue,opacity=1.00] (0.5,-1.9) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (0.7,-0.3) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (0.7,-0.3) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (2.7,-0.6) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (2.7,-0.6) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\draw[thick,fill=Cyan,opacity=0.50] (3.8,-1.8) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (3.8,-1.8) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Panel c) 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (-3.5,-6.0) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-3.5,-6.0) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] (-3.0,-5.0) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-3.0,-5.0) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] (-2.41,-5.92) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-2.41,-5.92) circle (0.4);

\draw[thick,black!50,opacity=0.50] (-3.5,-6.0) circle (0.65);
\draw[thick,black!50,opacity=0.50] (-3.0,-5.0) circle (0.65);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (-1.5,-4.0) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-1.5,-4.0) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] (-1.2,-5.1) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-1.2,-5.1) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] (-0.9,-6.2) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (-0.9,-6.2) circle (0.4);

\draw[thick,black!50,opacity=0.50] (-1.5,-4.0) circle (0.65);
\draw[thick,black!50,opacity=0.50] (-0.9,-6.2) circle (0.65);
\draw[thick,black!50,opacity=0.50] (-1.2,-5.1) circle (0.65);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (0.5,-4.3) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (0.5,-4.3) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (0.8,-5.8) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (0.8,-5.8) circle (0.4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[thick,fill=Cyan,opacity=0.50] (2.8,-4.4) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (2.8,-4.4) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] (3.9,-4.6) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (3.9,-4.6) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] (2.7,-5.6) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (2.7,-5.6) circle (0.4);

\draw[thick,fill=Cyan,opacity=0.50] (3.8,-5.8) circle (0.65);
\draw[thick,fill=blue,opacity=1.00] (3.8,-5.8) circle (0.4);

\draw[thick,black!50,opacity=0.50] (2.8,-4.4) circle (0.65);
\draw[thick,black!50,opacity=0.50] (3.9,-4.6) circle (0.65);
\draw[thick,black!50,opacity=0.50] (2.7,-5.6) circle (0.65);



\begin{tikzpicture}
% z- axis
\draw[->, thin] (0,-5) -- (0,2);
% upper circle

\draw[->,thick, red] (0,0) -- (-0.866025,0.5);
\draw (-0.75,0.2) node [text=red]{ $R_1$};
\draw[-,thin] (-2.5,0) -- (1.8,0);
\draw[thick] (0,-3) circle (1.5);
\draw[thick, blue] (0,-1.29167) circle (0.817559);
\draw[thin, blue] (-2,-1.29167) -- (1.8,-1.29167);
\draw[-,thin] (-2.5,-3) -- (1.8,-3);
\draw[->,thin] (-2.3,-1.4) -- (-2.3,0);
\draw[->, thin] (-2.3,-1.9) -- (-2.3,-3);
\draw (-2.3,-1.65) node [text]{$a$};
\draw[->, thin,blue] (-2.0,-0.4) -- (-2.0, 0.0);
\draw[->, thin,blue] (-2.0,-0.8) -- (-2.0, -1.29167);
\draw (-1.9, -0.6) node [text=blue]{$a_1$};
\draw[->, thin, blue] (-2.0, - 2.0) -- (-2.0,-1.29167) ;
\draw[->, thin, blue] (-2.0, -2.4) -- (-2.0, -3.0);
\draw (-1.9,-2.2) node [text=blue]{$a_2$};
\draw (2.0, -1.0) node [text=blue]{$M$};
\draw (0.2, 1.2) node [text]{$A$};
\draw (0.2, 0.2) node [text]{$B$};
\draw (0.2, -0.3) node [text]{$C$};
\draw (0.2, -0.8) node [text]{\small $D$};
\draw (0.2, -1.15) node [text]{\small $E$};
\draw (0.2, -1.4) node [text]{\tiny $F$};
\end{tikzpicture}


\begin{tikzpicture}
\draw[->, ultra thick] (-1,0) -- (2.5,0);
\draw (2.5,-0.5) node {\Large $x$};
\draw[->, ultra thick] (0,-2.5) -- (0,1);
\draw (-0.5,1) node {\Large $z$};
\draw[-,ultra thick, blue] (0,0) -- (1,-2);
\draw[thick, blue,fill=blue] (1,-2) circle  (0.2);
\draw (1.6,-2.2) node [text=blue]{\Large $m$};
\draw[->,,thick] (0,-1.5) arc[radius=1.2, start angle=270, end angle=300];
%\draw[-,,thick] (-2.,-1.25) arc[radius=2.25, start angle=210, end angle=330];
\draw[thick] (0,0) circle (2.25);
\draw [->, ultra thick, red] (1.5,-0.5) -- (1.5,-1.5);
\draw (0.8,-1.0) node [text=blue]{\Large $l$};
\draw (1.8,-1.0) node [text=red]{\Large $g$};
%pic [draw, ->,''$\varphi$'', angle eccentricity=5.5] {angle =(0,-2) -- (0,0) -- (1,-2)};
\end{tikzpicture}






