  The direct product of two Fibonacci tilings can be described as a genuine
stone inflation rule with four prototiles. This rule admits various
modifications, which lead to 48 different inflation rules, known as the direct
product variations. They all result in tilings that are measure-theoretically
isomorphic by the Halmos--von Neumann theorem. They can be described as cut and
project sets with characteristic windows in a two-dimensional Euclidean
internal space. Here, we analyse and classify them further, in particular with
respect to topological conjugacy.
