Generative models for pictures tiled by triangles
The problem of generation of triangle-tiled pictures that are two-dimensional figures tiled by isosceles right triangles of the same size, is investigated. Grammars called context-free triangle-tiled picture grammars (CF-ttPG) that generate such figures making use of context-free type rules, are proposed. The special case that all rules of such a grammar are regular, is studied. In the framework of membrane computing which is a biologically inspired computability model, generation of triangle-tiled pictures by rules of a CF-ttPG is considered. The picture language of rectangular hollow frames which cannot be generated by any CF-ttPG, can be generated by a specific type of P system with two membranes.
triangle-tiled picture picture grammar rectangular hollow frame p system picture generation by grammars context-free grammar figure decomposed by triangles