n=4;
alpha=1/3 N[Pi];
Needs["Statistics`DescriptiveStatistics`"];
p:=Module[{},{w={v,l,v,l,v,l,v,l,v,l,v,l,v};
    g[x_]:=x/.v->{v,l,v,r,r,v,l,v}//Flatten;
    t=Nest[g,w,n];
    winkel=CumulativeSums[t/.{l->1,r->-1,v->0}];
    schritt=t/.{l->0,r->0,v->1};
    bewegung=CumulativeSums[schritt E^(alpha I winkel)];
    bild1=ListPlot[Transpose[{Re[bewegung],Im[bewegung]}],
         PlotJoined->True,AspectRatio->Automatic,
         Axes->False,
         DisplayFunction->Identity]
         }];
Do[{p;abb[n]=bild1},{n,0,3}];
abbarray=GraphicsArray[{{abb[0],abb[1]},{abb[2],abb[3]}}];
bild=Show[abbarray,DisplayFunction->$DisplayFunction,
     ImageSize->{400,300}];