gTangle: a grammar for the procedural generation of tangle patterns

Tangles are a form of structured pen-and-ink 2D art characterized by repeating, recursive patterns. We present a method to procedurally generate tangle drawings, seen as recursively split sets of arbitrary 2D polygons with holes, with anisotropic and non-stationary features. We formally model tangles with group grammars, an extension of set grammars, that explicitly handles the grouping of shapes necessary to represent tangle repetitions. We introduce a small set of expressive geometric and grouping operators, showing that they can respectively express complex tangles patterns and sub-pattern distributions, with relatively simple grammars. We also show how users can control tangle generation in an interactive and intuitive way. Throughout the paper, we show how group grammars can, in few tens of seconds, produce a wide variety of patterns that would take artists hours of tedious and time-consuming work. We then validated both the quality of the generated tangles and the efficiency of the control provided to the users with a user study, run with both expert and non-expert users.