How can I make a diagram with lots of colored circles?

Question

How can I make a diagram like you see below?

It may be very interesting question. It is obvious that green dots are pseudo-random inside greater disc, but the proportion of red, blue and yellow ones is unclear. — Przemysław Scherwentke, Jun 12, 2016 at 7:00
@PrzemysławScherwentke, the only important thing is that there is a big group of normal dots (all the same) and a smaller group of special dots (different from the normal dots and also different from eachother), but the exact numbers or placement is not so important. Each picture shows a different distribution of the dots, so it would be better if the numbers do not vary as in the example picture. — hkBst, Jun 12, 2016 at 7:34
As a starting point you can probably be helped by tex.stackexchange.com/questions/286755. — StefanH, Jun 12, 2016 at 9:40

Community · Accepted Answer · 2017-04-13 12:34:46Z

This is a nice job for JLDiaz's Poisson disk sampling algorithm, because that's a more "pleasant looking" distribution than independently distributed points.

Inclusion

\documentclass{article}
\usepackage{tikz}
\usepackage{poisson}
\begin{document}
\edef\mylist{\poissonpointslist{5}{5}{0.3}{20}} % Generate a 5x5 field of points
\begin{tikzpicture}
    \begin{scope}
     \clip (2.5,2.5) circle [radius=2.5];
     \foreach \x/\y [count=\i] in \mylist {
        \pgfmathparse{(\x-2.5)^2+(\y-2.5)^2} % Calculate the point's distance from the centre
        \ifdim\pgfmathresult pt < 5.75pt % Only draw if the full point fits in the circle

            \pgfmathparse{int(mod(\i,15))} % We'll make groups of fifteen: 1 cyan, 1 orange, 1 yellow, 12 grey
            \ifnum\pgfmathresult=0
                \fill [cyan] (\x,\y) circle (0.1);
            \else
                \ifnum\pgfmathresult=1
                    \fill [orange] (\x,\y) circle (0.1);
                \else
                    \ifnum\pgfmathresult=2
                        \fill [yellow] (\x,\y) circle (0.1);
                    \else
                        \fill [black!70] (\x,\y) circle (0.1);
                    \fi
                \fi
            \fi
        \fi
     }
     \end{scope}
     \draw[very thick] (2.5,2.5) circle [radius=2.5];
\end{tikzpicture}
\end{document}

Exclusion:

\documentclass{article}
\usepackage{tikz}
\usepackage{poisson}
\begin{document}
\edef\mylist{\poissonpointslist{5.5}{5.5}{0.3}{20}} % Generate a 5x5 field of points
\begin{tikzpicture}
    \begin{scope}
     \foreach \x/\y [count=\i] in \mylist {
        \pgfmathsetmacro\radius{(\x-2.75)^2+(\y-2.75)^2} % Calculate the point's distance from the centre
        \ifdim\radius pt > 6.75pt
            \ifdim\radius pt < 8pt
                \pgfmathparse{int(mod(\i,3))}
                \ifnum\pgfmathresult=0
                    \fill [cyan] (\x,\y) circle (0.1);
                \else
                    \ifnum\pgfmathresult=1
                        \fill [orange] (\x,\y) circle (0.1);
                    \else
                        \ifnum\pgfmathresult=2
                            \fill [yellow] (\x,\y) circle (0.1);
                        \fi
                    \fi
                \fi
            \fi
        \else
            \ifdim\radius pt < 5.75pt
                \fill [black!70] (\x,\y) circle (0.1);
            \fi
        \fi
     }
     \end{scope}
     \draw[very thick] (2.75,2.75) circle [radius=2.5];
\end{tikzpicture}
\end{document}

Bernard · Accepted Answer · 2016-06-12 21:46:10Z

You can do that with the \psRandom command from pstricks-add, which distributes random points within a rectangular frame (defined by the coordinates of opposite vertices) and clips these points within an arbitrary closed curve.

\documentclass[x11names,  border=3pt]{standalone}
\usepackage{pstricks-add}
\usepackage{auto-pst-pdf}

\begin{document}

\begin{pspicture}
\sffamily\bfseries
\psset{unit=1.5cm, randomPoints=400, labelsep=1.25}
\begin{psmatrix}[rowsep=4cm, colsep=5cm]%{c}
 & \psRandom[dotsize=3pt,  linecolor=OliveDrab3](-1,-1)(1,1){\pscircle(0,0){1}}
\psRandom[dotsize=3pt, color,  randomPoints=160](-1,-1)(1,1){\pscircle(0,0){1}}\\%
%%%
\psRandom[dotsize=3pt,  linecolor=OliveDrab3](-1,-1)(1,1){\pscircle(0,0){1}}
\psRandom[dotsize=3pt, color,  randomPoints=160](-1,-1)(1,1){\psRing[linestyle=none](0,0){1.}{1.5}}
\hspace*{-1}
 &
\psRandom[dotsize=3pt,  linecolor=OliveDrab3](-1,-1)(1,1){\pscircle(0,0){1}}
\psRandom[dotsize=3pt,  color,  randomPoints=160](0,-2)(2,0){\pscircle(1.25,-0.8){0.4}}
 &
\psRandom[dotsize=3pt,  linecolor=OliveDrab3](-1,-1)(1,1){\pscircle(0,0){1}}
\pscircle[fillstyle=solid,  fillcolor=white](0.4,-0.25){0.4}
\psRandom[dotsize=3pt,  color,  randomPoints=160](0,-2)(2,0){\pscircle(0.4,-0.25){0.4}}
%%%
\nput{-90}{1,2}{Inclusion}
\nput{-90}{2,1}{Exclusion}
\nput{-90}{2,2}{Segregation}
\nput{-90}{2,3}{Integration}
\end{psmatrix}
\end{pspicture}

\end{document}

Not that it is super-interesting, but "random within a rectangle THEN clipped by some curve" is not the same as "random within some curve". — Matsmath, Jun 12, 2016 at 22:41
As long as it's a uniform distribution… And I guess it's easier to program. Of course,inside a circle, we could use polar coordinates — Bernard, Jun 12, 2016 at 22:53
@Matsmath I was wondering how does one define "random within some curve"? — Maesumi, Jun 14, 2016 at 19:08

StefanH · Accepted Answer · 2016-06-12 21:33:39Z

Here is a solution using Tikz also. I have separated it in four files. The idea is the same in all figures. I start with random positions and then decide the color of the circle depending on its distance from origin. Circles on the borders are not printed.

Inclusion:

\documentclass[tikz,border=5]{standalone}
\begin{document}
\begin{tikzpicture}[x=1pt,y=1pt,
  declare function={
    vecdist(\ax,\ay,\bx,\by)=sqrt((\ax-\bx)^2+(\ay-\by)^2);
  }]
  \def\R{40}
  \def\whitecol{white}
  \pgfmathdeclarerandomlist{color}{{red}{blue}{yellow}{green}{green}{green}}
  %
  \foreach \x in {1,...,200}
  {
    \pgfmathrandominteger{\px}{-49}{49}
    \pgfmathrandominteger{\py}{-49}{49}
    \pgfmathrandomitem{\c}{color}
    \pgfmathparse{ifthenelse(vecdist(\px,\py,0,0)<\R-1,"\c","\whitecol"}
    \let\c\pgfmathresult
    %
    \ifx\c\whitecol\else\draw[fill,\c] (\px,\py) circle (1);\fi
  };
  \draw(-50,-50) rectangle (50,50);
  \draw(0,0) circle (\R);
\end{tikzpicture}
\end{document}

Exclusion:

\documentclass[tikz,border=5]{standalone}
\begin{document}
\begin{tikzpicture}[x=1pt,y=1pt,
  declare function={
    vecdist(\ax,\ay,\bx,\by)=sqrt((\ax-\bx)^2+(\ay-\by)^2);
  }]
  \def\R{40}
  \def\whitecol{white}
  \pgfmathdeclarerandomlist{color}{{red}{blue}{yellow}}
  %
  \foreach \x in {1,...,300}
  {
    \pgfmathrandominteger{\px}{-49}{49}
    \pgfmathrandominteger{\py}{-49}{49}
    \pgfmathrandomitem{\c}{color}
    \pgfmathparse{ifthenelse(vecdist(\px,\py,0,0)<\R+1,%
      ifthenelse(vecdist(\px,\py,0,0)<\R-1,"green","\whitecol"),%
      "\c"}
    \let\c\pgfmathresult
    %
    \ifx\c\whitecol\else\draw[fill,\c] (\px,\py) circle (1);\fi
  };
  \draw(-50,-50) rectangle (50,50);
  \draw(0,0) circle (\R);
\end{tikzpicture}
\end{document}

Segregation:

\documentclass[tikz,border=5]{standalone}
\begin{document}
\begin{tikzpicture}[x=1pt,y=1pt,
  declare function={
    vecdist(\ax,\ay,\bx,\by)=sqrt((\ax-\bx)^2+(\ay-\by)^2);
  }]
  \def\R{40}
  \def\r{10}
  \def\whitecol{white}
  \pgfmathdeclarerandomlist{color}{{red}{blue}{yellow}}
  %
  \foreach \x in {1,...,200}
  {
    \pgfmathrandominteger{\px}{-49}{49}
    \pgfmathrandominteger{\py}{-49}{49}
    \pgfmathparse{ifthenelse(vecdist(\px,\py,0,0)<\R-1,"green","\whitecol"}
    \let\c\pgfmathresult
    %
    \ifx\c\whitecol\else\draw[fill,\c] (\px,\py) circle (1);\fi
  };
  \foreach \x in {1,...,50}
  {
    \pgfmathrandominteger{\px}{40}{60}
    \pgfmathrandominteger{\py}{-40}{-20}
    \pgfmathrandomitem{\c}{color}
    \pgfmathparse{ifthenelse(vecdist(\px,\py,50,-30)<\r-1,"\c","\whitecol"}
    \let\c\pgfmathresult
    %
    \ifx\c\whitecol\else\draw[fill,\c] (\px,\py) circle (1);\fi
  };
  \draw(-50,-50) rectangle (70,50);
  \draw(0,0) circle (\R);
  \draw(50,-30) circle (\r);
\end{tikzpicture}
\end{document}

Integration:

\documentclass[tikz,border=5]{standalone}
\begin{document}
\begin{tikzpicture}[x=1pt,y=1pt,
  declare function={
    vecdist(\ax,\ay,\bx,\by)=sqrt((\ax-\bx)^2+(\ay-\by)^2);
  }]
  \def\R{40}
  \def\r{10}
  \def\whitecol{white}
  \pgfmathdeclarerandomlist{color}{{red}{blue}{yellow}}
  %
  \foreach \x in {1,...,300}
  {
    \pgfmathrandominteger{\px}{-49}{49}
    \pgfmathrandominteger{\py}{-49}{49}
    \pgfmathrandomitem{\c}{color}
    \pgfmathparse{vecdist(\px,\py,0,0)}\let\pdist\pgfmathresult
    \pgfmathparse{ifthenelse(vecdist(\px,\py,0,0)<\R-1,%
      ifthenelse(vecdist(\px,\py,10,-10)<\r-1,"\c",%
      ifthenelse(vecdist(\px,\py,10,-10)<\r+1,"\whitecol","green")),%
      "white")}
    \let\c\pgfmathresult
    %
    \ifx\c\whitecol\else\draw[fill,\c] (\px,\py) circle (1);\fi
  };
  \draw(-50,-50) rectangle (50,50);
  \draw(0,0) circle (\R);
  \draw(10,-10) circle (\r);
\end{tikzpicture}
\end{document}

And the result as pictures.

You might be interested in the veclen function (which does what your vecdist function does but only “better”). — Qrrbrbirlbel, Jun 12, 2016 at 22:22
@Qrrbrbirlbel, Great, I will try it. I was looking for something like it but the Tikz-manual is quite extensive (>1000 pages) and it was easier to write myself. — StefanH, Jun 13, 2016 at 11:02

Thruston · Accepted Answer · 2016-06-13 10:32:34Z

Here's a version in Metapost using a variation of my slightly clunky implementation of Poisson Disc Sampling.

Please forgive the length of the code. If anything is unclear, please comment and I'll add some explanation. The reference for the algorithm that I used is https://www.jasondavies.com/poisson-disc/ .

prologues := 3;
outputtemplate := "%j%c.eps";

% is point "p" inside cyclic path "ring" ?
vardef inside(expr p, ring) = 
  save t, count, test_line;
  count := 0;
  path test_line;
  test_line = p -- (infinity, ypart p);
  for i = 1 upto length ring:
     t := xpart (subpath(i-1,i) of ring intersectiontimes test_line);
     if ((0 <= t) and (t<1)): count := count + 1; fi
  endfor
  odd(count)
enddef;
% Find m pairs inside "shape" using Poisson Disc 
% Sampling with radius "r" and trial placements "k".
% Smaller "r" and larger "k" are slower.
% The number of points returned "m" depends on the size of the
% shape and the sampling radius chosen.  
vardef find_pds_pairs(expr shape, r, k) =
    save w, h, diagonal, cellsize, imax, jmax, m, n, far_enough_away, 
         a, p, g, random, temp, trial, xx, yy, ii, jj, output;
    numeric w, h, cellsize, imax, jmax, g[], m, n; 
    pair diagonal;
    diagonal = urcorner shape - llcorner shape;
    w = xpart diagonal;
    h = ypart diagonal;
    cell_size := r/sqrt(2);

    imax := floor(w/cell_size);
    jmax := floor(h/cell_size);
    for i = -1 upto 1+imax:
      for j = -1 upto 1+jmax:
        g[i][j] := -1;
      endfor
    endfor

    z0 = center shape;
    g[floor(x0/cell_size)][floor(y0/cell_size)] := 0; 
    m := 0; % index of marks made
    n := 0; % index of active points
    a[n] = m;
    boolean far_enough_away;
    pair p[];
    forever:
      exitif n<0;
      % shuffle a[0..n]
      for i=n step -1 until 0:
        random := floor uniformdeviate i;
        temp := a[i]; a[i] := a[random]; a[random] := temp;
      endfor
      % now a[n] is our random point
      trial := 0;
      forever:
         % find a trial point
         trial := trial+1;
         exitif trial>k;
         p0 := z[a[n]];
         p[trial] := p0 shifted (r+uniformdeviate r,0) rotatedabout(p0,uniformdeviate 360);
         xx := xpart p[trial];
         yy := ypart p[trial];
         % test it if it is inside the shape
         if inside(p[trial], shape):
             ii := floor(xx/cell_size);
             jj := floor(yy/cell_size);
             far_enough_away := true;
             for i=ii-1 upto ii+1:
               for j=jj-1 upto jj+1:
                 if known g[i][j]:
                    if (g[i][j] > -1):
                       if (x[g[i][j]] - xx) ++ (y[g[i][j]] - yy) < r:
                          far_enough_away := false;
                       fi
                    fi
                 fi
               endfor
             endfor
         else:
           far_enough_away := false;
         fi
         exitif far_enough_away;
      endfor

      if far_enough_away:
        m := m+1;
        n := n+1;
        z[m] = p[trial];
        a[n] := m;
        g[ii][jj] := m;
      else:
        n := n-1; % ie remove a[n] from next shuffle
      fi
    endfor
    % now we have the "m" points we need, so return the number
    m
enddef;


beginfig(1);

color apple, sky, crimson, mustard;
apple   = 1/256(140,184,48);
sky     = 1/256(84,152,239);
crimson = 1/256(180,60,50);
mustard = 1/256(238,208,26);

path C, c, dot; 
C = fullcircle scaled 64;
c = fullcircle scaled 21;
dot = fullcircle scaled 4.2;

picture big_mono, big_mixed, small_multi;

randomseed := 2021.30977;

M := find_pds_pairs(c scaled 16/21, 5, 20);
small_multi = image(
    fill c withcolor background;
    for i=0 upto M:
       r := i mod 3;
       fill dot shifted z[i] 
            withcolor if r=0: sky elseif r=1: crimson else: mustard fi;
    endfor
    draw c;
    );

clearxy;
M := find_pds_pairs(C scaled 59/64, 8, 20);
big_mono = image(
    for i=0 upto M:
        fill dot shifted z[i] withcolor apple;
    endfor
    draw C withpen pencircle scaled 1;
);

big_mixed = image(
    for i=0 upto M:
       fill dot shifted z[i] withcolor 
         if     (i=3) or (i=10) or (i=19): sky 
         elseif (i=7) or (i=14) or (i=24): crimson 
         elseif (i=2) or (i=16) or (i=29): mustard
         else: apple
         fi;
    endfor
    draw C withpen pencircle scaled 1;
);

defaultfont := "phvr8r";
picture type[];

type0 = image(
   draw big_mixed;
   label("Inclusion", (0,-42));
);

type1 = image(
   draw big_mono;
   draw small_multi shifted 48 right rotated -20;
   label("Segregation", (0,-52));
);

type2 = image(
   draw big_mono;
   draw small_multi shifted 16 right rotated -20;
   label("Integration", (0,-52));
);

type3 = image(
   draw big_mono;
   for t=1/3 step 1/3 until 8:
      r := uniformdeviate 1;
      fill dot shifted point t of (C scaled (1.1 + abs(0.1 normaldeviate)))
               withcolor if r < 1/3: crimson elseif r < 2/3: sky else: mustard fi;
   endfor
   label("Exclusion", (0,-52));
); 

draw type0;
draw type1 shifted 96 down;
draw type2 shifted 96 down shifted 108 right;
draw type3 shifted 96 down shifted 108 left;

%
endfig;
end.

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