Lonely Runner Conjecture

circ = 1; rad = circ/(2 \[Pi]); nRunners = 5;
rList[t_] := {1 t, 2 t, 4 t, 8 t, 9.6 t, 21 t, 31 t, 33 t}[[1 ;; nRunners]]

dist[d\[Theta]_, circ_] := 
  N[circ/2 (TriangleWave[(d\[Theta] - \[Pi]/2)/(2 \[Pi])] + 1)/2]
minDist[runnerList_, circ_] :=
 Table[
  runner = runnerList[[i]];
  other = DeleteCases[runnerList, runner];
  Min[dist[Abs[runner - other], circ]],
  {i, 1, nRunners}
  ]

colorList = Table[ColorData[97, "ColorList"][[i]], {i, 1, 10}];
colorListLighter = Table[Lighter[ColorData[97, "ColorList"][[i]], 0.7], {i, 1, 10}];

Manipulate[
 {Graphics[
    {
     White, EdgeForm[Black],
     Disk[{0, 0}, rad + 0.005 (nRunners + 3)],
     Disk[{0, 0}, rad - 0.005*3],
     Table[
      {
       If[(minDist[rList[tmax], circ][[i]]) >= 1/nRunners,
        colorList[[i]] = colorListLighter[[i]],
        White
        ],
       Thickness[0.01], 
       Circle[{0, 0}, 
        rad + 0.005 i, {rList[tmax][[i]] - (2 \[Pi])/nRunners, 
         rList[tmax][[i]] + (2 \[Pi])/nRunners}]
       }
      , {i, 1, nRunners}
      ],
     Table[
      {
       If[(minDist[rList[tmax], circ][[i]]) >= 1/nRunners,
        colorList[[i]] = colorListLighter[[i]],
        colorList[[i]]
        ], PointSize[0.05], 
       Point[(rad + 0.005 i) {Cos[rList[tmax][[i]]], 
          Sin[rList[tmax][[i]]]}]
       }
      , {i, 1, nRunners}
      ],
     {Black, Text[Style[ToString[nRunners], 14, Italic], {0, 0}]}
     },
    PlotRange -> rad + 0.005 (nRunners + 3) + 0.01
    ]}[[1]],
 {tmax, 0.00001, 3, .00001}]