Think carefully about the procedure below that I was reminded of recently. It revisits again the technique called recursion and builds up a particular pleasing pattern of squares:

TO BEAVER :B
PU HOME PD
SQUARE :SIDE :B
SQ :B/2
END

TO SQUARE :SIDE :B
IF :SIDE <:B [STOP]
REPEAT 4 [FD :SIDE SQUARE :SIDE/2 :B LT 90]
END

Try SQUARE 60 6 or SQUARE 60 2 or......

In a more direct geometrical sense:

Some Danish teachers at a conference this summer, who had worked at the July problem showed me what other tilings they had found using only two differently sized equilateral triangles.

They were particularly excited by the stars - so central to their designs. You might like to produce an elegant program to replicate these.