Generative models for pictures tiled by triangles
نویسندگان
چکیده
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 (CFttPG) 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. Key-words: picture generation by grammars, context-free grammar, picture grammar, triangle-tiled picture, P system, figure decomposed by triangles, rectangular hollow frame.
منابع مشابه
Triangle Tiling I: the tile is similar to ABC or has a right angle
An N-tiling of triangle ABC by triangle T is a way of writing ABC as a union of N triangles congruent to T , overlapping only at their boundaries. The triangle T is the “tile”. The tile may or may not be similar to ABC. This paper is the first of four papers, which together seek a complete characterization of the triples (ABC,N, T ) such that ABC can be N-tiled by T . In this paper, we consider...
متن کاملTile rewriting grammars and picture languages
Tile Rewriting Grammars (TRG) are a new model for defining picture languages. A rewriting rule changes a homogeneous rectangular subpicture into a isometric one tiled with specified tiles. Derivation and language generation with TRG rules are similar to contextfree grammars. A normal form and some closure properties are presented. We prove this model has greater generative capacity than the Til...
متن کاملTilings with noncongruent triangles
We solve a problem of R. Nandakumar by proving that there is no tiling of the plane with pairwise noncongruent triangles of equal area and equal perimeter. We also show that no convex polygon with more than three sides can be tiled with finitely many triangles such that no pair of them share a full side.
متن کاملTiling triangle ABC with congruent triangles similar to ABC
We investigate the problem of cutting a triangle ABC into N congruent triangles (the “tiles”), each of which is similar to ABC. The more general problem when the tile is not similar to ABC is not treated in this paper; see [1]. We give a complete characterization of the numbers N for which some triangle ABC can be tiled by N tiles similar to ABC, and also a complete characterization of the numb...
متن کاملEmergence of Euclidean geometrical intuitions in hierarchical generative models
In this study, we aim to understand the origins of human intuitions about Euclidean geometry by simulating geometric concepts acquisition with unsupervised learning in hierarchical generative models. Specifically, we build a deep neural network that learns a hierarchical generative model of sensory inputs. The results show that hidden layer activities can support the categorization of different...
متن کامل