A Bing Link in a torus consists of two tori linked in a chain in the interior of the torus. A Whitehead link in a torus consists a single torus in the interior linked to itself in a particular way. By alternating these constructions, one can produce certain Cantor sets in R^3 that are non standard, but have simply connected complement. We will state conditions on the number of each type of link needed to guarantee that a Cantor Set is obtained in the limit.