This tiling represents a hyperbolic kaleidoscope of 4 mirrors meeting as edges of a square, with eight squares around every vertex.
This symmetry by orbifold notation is called (*4444) with 4 order-4 mirror intersections.
In Coxeter notation can be represented as [1+,8,8,1+], (*4444 orbifold) removing two of three mirrors (passing through the square center) in the [8,8] symmetry.
The *4444 symmetry can be doubled by bisecting the fundamental domain (square) by a mirror, creating *884 symmetry.
This bicolored square tiling shows the even/odd reflective fundamental square domains of this symmetry.