Constructed nested triangles as thus:

> restart;

> t:=evalf(Pi/3):

> m:=[[0,0],[1,0],[cos(t),sin(t)],[0,0]]:

> w:=[]:

> t:=0.1:

> for k to 20 do w:=[op(w),m]:sm:=[m[2],m[3],m[1],m[2]]:m:=(1-t)*m+t*sm:od:

> plot(w,color=black,scaling=constrained,axes=none);

>