pursuitString[
   k_] := (Quiet@
      ToExpression[
       "Clear[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,A,B,\
F,G,H,J,L,M,P,Q,R,S,T,U,V,W,X,Y,Z,\[Alpha],\[Beta],\[Gamma],\[Delta],\
\[CurlyEpsilon],\[Zeta],\[Eta],\[Theta],\[Iota],\[Kappa],\[Lambda],\
\[Chi],\[Nu],\[Xi],\[Omicron],\[Rho],\[Sigma],\[Tau],\[Upsilon],\
\[CurlyPhi],\[Chi],\[Psi],\[Omega],\[CapitalAlpha],\[CapitalBeta],\
\[CapitalGamma],\[CapitalDelta],\[CapitalEpsilon],\[CapitalZeta],\
\[CapitalEta],\[CapitalTheta],\[CapitalIota],\[CapitalKappa],\
\[CapitalLambda],\[CapitalMu],\[CapitalNu],\[CapitalXi],\
\[CapitalOmicron],\[CapitalPi],\[CapitalRho],\[CapitalSigma],\
\[CapitalTau],\[CapitalUpsilon],\[CapitalPhi],\[CapitalChi],\
\[CapitalPsi],\[CapitalOmega],midpt,newpt,scale,plots,li,abs];\
\[IndentingNewLine]midpt[pc_,pd_]:=(Tr/@Thread@{pc,pd})/2;\
\[IndentingNewLine]newpt[pa_,pc_,pd_]:=Module[{pb,pnew,xnew,ynew,pab},\
\[IndentingNewLine]pb=midpt[pc,pd];\[IndentingNewLine]pab={pb[[1]]-pa[\
[1]],pb[[2]]-pa[[2]]};\[IndentingNewLine]xnew=If[pab[[1]]\[Equal]0,pa[\
[1]],Sign[pab[[1]]] \
1/Sqrt[1+(pa[[2]]-pb[[2]])^2/(pa[[1]]-pb[[1]])^2]+pa[[1]]];\
\[IndentingNewLine]ynew=If[pab[[1]]\[Equal]0,pa[[2]]+Sign[pab[[2]]] \
1,pa[[2]]+(xnew-pa[[1]]) \
#[[2]]/#[[1]]&@pab];\[IndentingNewLine]pnew=If[EuclideanDistance[pa,\
pb]<EuclideanDistance[pa,{xnew,ynew}],pb,{xnew,ynew}]];\
\[IndentingNewLine]abs[li_]:=Module[{a,b,c,d,e,f,g},\
\[IndentingNewLine]a={Min@#,Max@#}&@li[[All,1]];\[IndentingNewLine]b={\
Min@#,Max@#}&@li[[All,2]];\[IndentingNewLine]c=Abs[Differences@a];\
\[IndentingNewLine]d=Abs[Differences@b];\[IndentingNewLine]e=Max@{c,d}\
/2;f=1.5;g=f*e;\[IndentingNewLine]{{#-g,#+g}&@Mean@a,{#-g,#+g}&@Mean@\
b}];\[Zeta]=" <> ToString[#] <> ";scale=\[Zeta];" <> "{" <> 
        StringDrop[
         StringJoin@
          Thread[{("a" <> ToString[#] & /@ Range@#), 
            Array["," &, #]}], -1] <> "}" <> 
        "=scale*N@RandomSample[CirclePoints[\[Zeta]],\[Zeta]];plots=\
With[{\[Rho]=(*Hue[#]&/@Table[CDF[NormalDistribution[0,1],x],{x,-#,#,(\
2#)/25.}]&[2]*)Array[Black&," <> ToString[#] <> 
        "],\[Eta]=4,\[Theta]=3,\[Iota]=5,\[Kappa]=0},Flatten[{\
Graphics[{PointSize[.02]," <> 
        StringDrop[
         StringDrop[(",Nest[Lighter,\[Rho][[1]],\[Eta]],Line[{" <> 
               ToString[#[[1]]] <> ",midpt[" <> ToString[#[[2]]] <> 
               "," <> ToString[#[[3]]] <> "]}],Line[{" <> 
               ToString[#[[2]]] <> "," <> ToString[#[[3]]] <> 
               "}],Circle[" <> ToString[#[[1]]] <> 
               ",1],\[IndentingNewLine]Nest[Lighter,\[Rho][[1]],\
\[Theta]],Point@" <> ToString[#[[1]]] <> 
               ", Nest[Lighter,\[Rho][[1]],\[Iota]],Point@midpt[" <> 
               ToString[#[[2]]] <> "," <> ToString[#[[3]]] <> 
               "], Nest[Lighter,\[Rho][[1]],\[Kappa]],Point@newpt[" <>
                ToString[#[[1]]] <> "," <> ToString[#[[2]]] <> "," <> 
               ToString[#[[3]]] <> "]," & /@ (Partition[
               "a" <> ToString[#] & /@ Flatten[{Range@#, Range@2}], 3,
                1])), -1] <> ",Frame\[Rule]True}],(" <> "{" <> 
          StringDrop[
           
           StringJoin@
            Thread[{("b" <> ToString[#] & /@ Range@#), 
              Array["," &, #]}], -1] <> "}" <> 
          "=Chop/@N/@Quiet[li=Module[{li},li=" <> "{" <> 
          StringDrop[
           StringJoin@
            Thread[{("a" <> ToString[#] & /@ Range@#), 
              Array["," &, #]}], -1], 1] <> "}" <> 
        ";newpt[#[[1]],#[[2]],#[[3]]]&/@Thread@{li,RotateLeft[li,1],\
RotateLeft[li,2]}]];" <> "{" <> 
        StringDrop[
         StringJoin@
          Thread[{("a" <> ToString[#] & /@ Range@#), 
            Array["," &, #]}], -1] <> "}" <>
        "=" <> "{" <> 
        StringDrop[
         StringJoin@
          Thread[{("b" <> ToString[#] & /@ Range@#), 
            Array["," &, #]}], -1] <> "}" <> ";" <> 
        "Quiet[Graphics[{PointSize[.02]," <> 
        StringDrop[(",Nest[Lighter,\[Rho][[1]],\[Eta]],Line[{" <> 
             ToString[#[[1]]] <> ",midpt[" <> ToString[#[[2]]] <> 
             "," <> ToString[#[[3]]] <> "]}],Line[{" <> 
             ToString[#[[2]]] <> "," <> ToString[#[[3]]] <> 
             "}],Circle[" <> ToString[#[[1]]] <> 
             ",1],\[IndentingNewLine]Nest[Lighter,\[Rho][[1]],\[Theta]\
],Point@" <> ToString[#[[1]]] <> 
             ", Nest[Lighter,\[Rho][[1]],\[Iota]],Point@midpt[" <> 
             ToString[#[[2]]] <> "," <> ToString[#[[3]]] <> 
             "], Nest[Lighter,\[Rho][[1]],\[Kappa]],Point@newpt[" <> 
             ToString[#[[1]]] <> "," <> ToString[#[[2]]] <> "," <> 
             ToString[#[[3]]] <> "]," & /@ (Partition[
             "a" <> ToString[#] & /@ Flatten[{Range@#, Range@2}], 3, 
             1])), -1] <> 
        "},PlotRange\[Rule]abs@li,Frame\[Rule]True]])&/@Range[Floor[\
\[Zeta] Sqrt[\[Zeta]]]]}]];\[IndentingNewLine]Manipulate[Show[plots[[\
var]],Frame\[Rule]True],{var,1,Length@plots,1,AnimationRate\[Rule]10}]\
"] &[k]);

(*eg implementation for any k: pursuitString[20]*)