Applying Accumulation

CL[k_,n_,alpha_]:=Accumulate[z=1;
Table[z=k*E^(#[[i]]I)z,
{i,n}]]&/@Tuples[{-alpha,alpha},n];
GCL=Function[{k,n,alpha},
Graphics[Table[{ColorData["CherryTones"][i/4],
Rotate[BSplineCurve@Transpose@{Re@#,
Im@#}&/@CL[k,n,alpha],i*Pi/2]},{i,4}],
ImageSize->400,Background->Lighter[Gray,.7]]];
{GCL[.7,10,Pi/4],GCL[.8,8,Pi/6]}