Bicolored tilings and the Scott map

We define bicolored tilings as a disk with a collection of smooth curves with a coloring map on the tiles that these curves delimit. Using two transformations, we define an equivalence on tilings. We then define the Scott map which creates a bijection between a generalised version of Postnikov diagrams and bicolored tilings, preserving equivalences, and mapping the geometric exchange of a diagram to an edge flip in a tiling.