Help:=proc(): print(` DT(T,a,b,i,eps), Trees(k) `): end:
with(plots):
#plots a binary tree T with vertex at y=i and using a<=x<=b
#such that the left child gets the left territory for i+1
#and the right child ...
DT:=proc(T,a,b,i,eps) local v,pic,pic1,pic2:

v:={[(a+b)/2,i]}:

pic:=plot(v,style=point,axes=none):

if T={} then
 RETURN(NULL):
fi:

pic1:=DT(T[1],a,(a+b)/2-eps,i+1,eps):

pic2:=DT(T[2],(a+b)/2+eps,b,i+1,eps):

pic:=pic,pic1,pic2:


if T[1]<>{} then
 pic:=pic,plot([v[1], [(a+(a+b)/2-eps)/2  ,i+1] ] ):
fi:


if T[2]<>{} then
 pic:=pic,plot([v[1], [((a+b)/2+eps+b)/2  ,i+1] ] ):
fi:

RETURN(pic):

end:




#the set of all binary trees of depth <=k
Trees:=proc(k) local S,t1,t2:

if k=0 then 
 RETURN({ {} }):
fi:

S:=Trees(k-1):

{seq(seq( [ t1,t2 ], t1 in S),t2 in S),{}}:

end: