In[]:=
dragun[t_]:=piecewiserecursivefractal[t,Identity,Piecewise[{{{1},0<=#<=1/2},{{2},1/2<=#<=1}},{}]&,{2*#&,2*(1-#)&},{(1+I)*#/2&,(I-1)*#/2+1&}]
In[]:=
piecewiserecursivefractal[x_,f_,which_,iters_,fns_]:=piecewiserecursivefractal[x,g_,which,iters,fns]=((piecewiserecursivefractal[x,h_,which,iters,fns]:=Block[{y},y/.Solve[f[y]==h[y],y]]);Union@@((fns[[#]]/@piecewiserecursivefractal[iters[[#]][x],Composition[f,fns[[#]]],which,iters,fns])&/@which[x]))
In[]:=
dragun[1/3]
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+
1
5
2
5
In[]:=
dragun/@Range[0,1,1/77]
In[]:=
ComplexListPlot[Flatten[%]]
Out[]=
In[]:=
ComplexListPlot[Flatten[dragun/@Range[0,1,1/2^10]]]
Out[]=
