Trees

obj0={Line[{{0,0},{0,1}}]};k=.7;T[obj_,t_]:=obj/.Line[{u_,v_}]:>Sequence[Line[{v,v+k*(({{Cos[t], Sin[t]}, {-Sin[t], Cos[t]}})).(v-u)}],Line[{v,v+k*(({{Cos[t], -Sin[t]}, {Sin[t], Cos[t]}})).(v-u)}]];newobj=NestList[T[#,Pi/3]&,obj0,11];Show[Graphics[newobj],PlotRange->All,AspectRatio->Automatic]

matRotace[t_]:=(({{Cos[t], Sin[t]}, {-Sin[t], Cos[t]}}))
disk[hue_,fi0_,t_]:=Graphics[{Opacity[0.9],Hue[hue],Disk[matRotace[t].{Cos[fi0],Sin[fi0]},0.3]},PlotRange->{{-2,2},{-2,2}}];
Manipulate[
Show[disk[0,+0.5,t],disk[0.76,-0.5,-t]]
,{t,0,2Pi}];

(*Manipulate[
Show[disk[hue,+0.5,0]]
,{hue,0,1}]*)

ClearAll[newLines]
line0={{0,0},{1,0}};
newLines[{u_List,v_List},k_,t_]:=Module[{smer},smer=v-u;{{v,v+k*(matRotace[t].smer)},{v,v+k*(matRotace[-t].smer)}}];
Graphics[{Line[line0],Line/@newLines[line0,1,(Pi/4)]}];

NestList[f,x0,3]

zmnoz[{cary:{{{_,_},{_,_}}..},k_?NumericQ,t_?NumericQ,iter_Integer}]:=Module[{dalsiCary},dalsiCary=Flatten[newLines[#,k,t]&/@cary,1];{dalsiCary,k,t,iter+1}]
zmnoz[{newLines[line0,1,(Pi/4)],0.5,0.1,1}]

newLines[line0,1,(Pi/4)]