Asymptotic analysis and random sampling of digitally convex polyominoes

Abstract

Recent work of Brlek et al. gives a characterization of digitally convex polyominoes using combinatorics on words. From this work, we derive a combinatorial symbolic description of digitally convex polyominoes and use it to analyze their limit properties and build a uniform sampler. Experimentally, our sampler shows a limit shape for large digitally convex polyominoes. © 2013 Springer-Verlag Berlin Heidelberg.