Enumeration of double square tiles

I'm currently writing the chapter of my thesis on double square tiles and I needed to go back about two years ago to play with some files that allowed me to generate double square using a brute-force approach and some unproven assumptions.

Here's a GIF picture with a table containing all the prime double square tiles of perimeter at most 48 and up to isometries (reflections and rotations) found by the algorithm, which seems to enumerate exactly all of them.

In the next days, I intend to implement efficiently the algorithm described in [1] to enumerate all double square tiles and compare the outputs.