Recurrence Tables

z[n_]:=Exp[I*Pi*n*2^0.3]; L={{0,0}};
Do[L=Append[L,{Re[L[[i,1]]+I*L[[i,2]]+z[i]],
Im[L[[i,1]]+I*L[[i,2]]+z[i]]}],{i,250}];
Graphics[Table[{Hue[i/250],
Line[{L[[i]],L[[i+1]]}]},{i,250}],
ImageSize->500,Background->RGBColor["silver"]]