Local and recognizable hexagonal picture languages

In this paper we introduce hexagonal Wang tiles, local hexagonal picture languages, and recognizable hexagonal picture languages. We use hexagonal Wang tiles to introduce hexagonal Wang systems(HWS), a formalism to recognize hexagonal picture languages. It is noticed that the family of hexagonal picture languages defined by hexagonal Wang systems coincides with the family of hexagonal picture languages recognized by hexagonal tiling system. Similar to hv-domino systems, we define xyz-domino systems and prove that recognizable picture languages are characterized as projections of xyz-local picture languages. We also consider hexagonal pictures over one letter alphabet.