Spirograph patterns ...

makePoints[n_]  :=  
        Table[{Cos[t], Sin[t]}, {t, 2  Pi/n, 2 Pi, 2 Pi/n}] // 
          N;

    init[n_] := 
        Module[{}, 
picture = {}; 
points = makePoints[n];
];

    addLayer[s_] := 
        Module[{n, skipList}, 
n = 
            Length[points]; 
skipList  =  
            Table[points[[1 +  Mod[i s, n]]], {i, 0, 
                n}]; 
AppendTo[picture, 
            Line[skipList]];
];

    setColor[r_, g_, b_] := 
        AppendTo[picture, RGBColor[r, g, b]];

    showIt := 
        Show[Graphics[picture], AspectRatio -> 1, 
          ImageSize -> {400, 
              400}];


    init[19];

    setColor[0, 1, 0];

    addLayer[9];

    setColor[1, 0, 0];

    addLayer[7];

    setColor[0, 0, 1];

    addLayer[3];

    showIt;

m = 37;
init[m];
Do[ 
setColor[Mod[i*m/3, m]/m, Mod[i*m/4, m]/m, 
          Mod[i*m/5, m]/m]; 
addLayer[
          i];
, {i, (m - 1)/2, 
          3, -1}];
showIt;