The Buckethandle can be created by drawing semicircles joining the points of the Cantor Middle-Thirds Set
in the above presented manner. It is homeomorphic to the inverse limit space of the Tent Map f(x)=1-|2x-1| (or if one prefers the Logistic Map g(x)=4x(1-x)).
This is the inverse limit space arising from the inverse sequence
with a single bondig map of the form f(x)=4 λ x(1-x) where λ
is a little to the right from the value
¼ (1+ √ 6 )
≈ 0.86237 .