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@BrianWeinstein
Last active August 16, 2019 06:53
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nc = 15; nr = 3;
cx = Table[ToExpression[StringJoin["cx", ToString[i]]], {i, 1, nc}];
cy = Table[ToExpression[StringJoin["cy", ToString[i]]], {i, 1, nc}];
rx = Table[ToExpression[StringJoin["rx", ToString[i]]], {i, 1, nr}];
ry = Table[ToExpression[StringJoin["ry", ToString[i]]], {i, 1, nr}];
coordList = Flatten[{Transpose[{cx, cy}], Transpose[{rx, ry}]}];
cspeed = 1;
rspeed = 1.1;
eqns = Flatten[
{Table[
{{Derivative[1][cx[[i]]][t], Derivative[1][cy[[i]]][t]} ==
cspeed*Normalize[Sum[{rx[[j]][t] - cx[[i]][t], ry[[j]][t] - cy[[i]][t]}/((cx[[i]][t] - rx[[j]][t])^2 +
(cy[[i]][t] - ry[[j]][t])^2), {j, 1, nr}]],
cx[[i]][0] == RandomReal[{-30, 30}],
cy[[i]][0] == RandomReal[{-30, 30}]
},
{i, 1, nc}
],
Table[
{{Derivative[1][rx[[i]]][t], Derivative[1][ry[[i]]][t]} ==
rspeed*Normalize[Sum[{rx[[i]][t] - cx[[j]][t], ry[[i]][t] - cy[[j]][t]}/((cx[[j]][t] - rx[[i]][t])^2 +
(cy[[j]][t] - ry[[i]][t])^2), {j, 1, nc}]],
rx[[i]][0] == RandomReal[{-5, 5}],
ry[[i]][0] == RandomReal[{-5, 5}]
},
{i, 1, nr}
]
}
];
soln = NDSolve[eqns, coordList, {t, 0, 200}, MaxSteps -> 200000, PrecisionGoal -> 2][[1]];
coordListFn[t_] := Flatten[Table[{coordList[[i]][t], coordList[[i + 1]][t]}, {i, 1, 2*(nc + nr), 2}]]
cops[t_] := Evaluate[coordListFn[t][[1 ;; 2*nc]] /. soln[[1 ;; 2*nc]]]
robbers[t_] := Evaluate[coordListFn[t][[2*nc + 1 ;; 2*(nc + nr)]] /. soln[[2*nc + 1 ;; 2*(nc + nr)]]]
Manipulate[
Show[
ParametricPlot[
{cops[t], robbers[t]}, {t, 0, tmax},
PlotRange -> All, PlotStyle -> {Darker[Red], {Darker[Green]}}
],
ListPlot[
{Partition[cops[0], 2], Partition[robbers[0], 2], Partition[cops[tmax], 2], Partition[robbers[tmax], 2]},
PlotStyle -> {Directive[PointSize[Medium], Black], Directive[PointSize[Medium], Black], Darker[Red], Darker[Green]}
],
Axes -> False
],
{tmax, 0.001, 200, 1.5}
]
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