Fibonacci direct product variation tilings

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