Avoiding Approximate Squares

As is well-known, Axel Thue constructed an infinite word over a 3-letter alphabet that contains no squares, that is, no nonempty subwords of the form xx. In this paper we consider a variation on this problem, where we try to avoid approximate squares, that is, subwords of the form xx ' where vertical bar x vertical bar = vertical bar x vertical bar ' and x and x ' are "nearly" identical.