escape[points_, pt_, n_, incr_] := 
 First[MaximalBy[pt + # & /@ (incr*CirclePoints[n]), 
   Min[EuclideanDistance[First[Nearest[points][#]], #], 
     EuclideanDistance[#, 
       RegionNearest[
         RegionBoundary[
          Circle[{pt[[1]], pt[[2]]}, incr](*Rectangle[{-#,-#},{#,#}]&[
          3]*)]][#]] &] &]]; 
escape[points_, pt_, incr_] := escape[points, pt, 40, incr];
escape[points_, pt_] := escape[points, pt, 40, .2];
newptRadius[pa_, pb_, time_, incr_] := 
  Module[{pnew, xnew, ynew, pab, radius, dist}, 
   dist = EuclideanDistance[pa, pb];
   radius = If[dist >= incr, incr, dist];
   pab = {pb[[1]] - pa[[1]], pb[[2]] - pa[[2]]};
   xnew = 
    If[pab[[1]] == 0, pa[[1]], 
     Sign[pab[[1]]] radius/
        Sqrt[1 + (pa[[2]] - pb[[2]])^2/(pa[[1]] - pb[[1]])^2] + 
      pa[[1]]];
   ynew = 
    If[pab[[1]] == 0, pa[[2]] + Sign[pab[[2]]] radius, 
     pa[[2]] + (xnew - pa[[1]]) #[[2]]/#[[1]] &@pab];
   pnew = {xnew, ynew}];
newptRadius[pa_, pb_, time_] := newptRadius[pa, pb, time, .1];
npr[n_, e_, incr_] := newptRadius[#, e, 1, incr] & /@ n;
pursuitlattice[startpoint_, latticelist_, escapeespeed_, iterations_, 
   incriment_] := Module[{},
   NestList[{npr[#[[1]], #[[2]], incriment], 
      escape[#[[1]], #[[2]], 
       escapeespeed *incriment]} &, {latticelist, startpoint}, 
    iterations]];
escapeedist[calculationlist_] := 
  EuclideanDistance[#[[1]], #[[2]]] & /@ 
   Thread[{calculationlist[[All, 2]], 
     First /@ 
      Table[Nearest[calculationlist[[All, 1]][[t]], 
        calculationlist[[All, 2]][[t]]], {t, 
        Length@calculationlist}]}];
vectorplot[t_, m_, n_] := Module[{list},
   list = 
    Thread[Table[Part[pl[[All, 1]][[a]], #], {a, t - m, t, 1}]] &@
     Flatten[Position[pl[[All, 1]][[t]], #] & /@ 
       Nearest[pl[[All, 1]][[t]], pl[[All, 2]][[t]], 20]]; 
   Graphics[{Nest[Lighter, Red, 3], 
     Line[Table[pl[[All, 2]][[a]], {a, t - n, t, 1}]], 
     PointSize[.02], Red, Point[pl[[All, 2]][[t]]],
      Nest[Lighter, Red, 3], 
     Point[Table[pl[[All, 2]][[a]], {a, t - n, t - 1, 1}]], 
     Nest[Lighter, Blue, 3], Point[list[[All, m + 1]]], Line /@ list},
     Frame -> True]];
vectorplot[t_] := vectorplot[t, 1, 4];
straightline[max_, maxa_] := Module[{},
   tables2 = Table[{4 t, .5}, {t, 0, max, .1}];
   tables1 = 
    FoldList[newptRadius[#, tables2[[#2]], #2] &, #, 
       Range[Floor[max/.1]]] & /@ 
     Flatten[Table[{a, b}, {a, 0, maxa}, {b, 0, 1}], 1];
   ed1 = EuclideanDistance[#, #2] & @@@ Drop[#, -10] &@
     Thread@{Take[tables2, Length@tables1], 
       Table[Nearest[tables1[[t]], tables2[[t]]][[1]], {t, 
         Length@tables1}]};
   Show[ListLinePlot[{Thread@{Range[Length@ed1], ed1}, 
      Thread@{Range[Length@ed1][[4 ;; -1 ;; 4]], 
        ed1[[4 ;; -1 ;; 4]]}}], 
    Plot[{, 1/(x/9 + 13)}, {x, 0, Length@ed1}]]];
straightline[] := straightline[50, 50];
(**)
(*pl = pursuitlattice[{-1.95, 1.55}, 
    Flatten[Table[{a, b}, {a, -20, 50}, {b, -10, 30}], 1], 4, 
    250, .1]; // Timing*)
(*ListLinePlot[pl[[All, 2]], AspectRatio -> Automatic]*)
(*ListPlot[Last@pl[[All, 1]], AspectRatio -> Automatic, PlotRange -> All]*)
(*ed = escapeedist[pl];{ListLinePlot[ed],Min[ed]}*)
(*vectorplot[198]*)
(*Animate[ListPlot[{#, {#2}} & @@ pl[[pt]], AspectRatio -> Automatic, 
  Axes -> False, PlotStyle -> {{Pink, PointSize[.01]}, {RGBColor[.3, .5, .7], 
     PointSize[.01]}}, PlotRange -> {{10, 25}, {5, 10}}], {{pt, 200}, 
  200, 250, 1}, AnimationRate -> 5]*)
  (*straightline[]*)
  (*Animate[Show[ListPlot[Flatten[{#[[pt]]}&/@tables1,1],PlotStyle\
\[Rule]{Pink,PointSize[.01]}],ListPlot[{tables2[[pt]]}]],{{pt,1},1,\
Floor[40/.1],1},AnimationRate\[Rule]5]*)