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 l...

Let G be a planar embedded 2-connected graph. Then the vertices of its resonance graph R(G) are the 1-factors of G, two 1-factors being adjacent whenever their symmetric difference is a bounded face of G. For a class of graphs containing the chemically important catacondensed benzenoid graphs we show that the resonance graphs are median. In particular, if G belongs to this class, R(G) has an is...

The interplay between local constraints and global structure of mathematical and physical systems is both subtle and important. The macroscopic physical properties of a system depend heavily on its global symmetries, but these are often difficult to predict given only information about local interactions between the components. A rich history of work on tilings of the Euclidean plane and higher...

Two-dimensional (2-D) spatially varying convolutional filters for three-dimensional (3-D) depth extrapolation are efficiently designed and implemented by using McClellan transformations. Although efficient, McClellan transformations only approximate circularly symmetric depth extrapolation filters. The accuracy of the extrapolation filters can be increased only at an increase in the computation...