Synthesis of tiled patterns using factor graphs

Patterns with pleasing structure are common in art, video games, and virtual worlds. We describe a method for synthesizing new patterns of tiles on a regular grid that are similar in appearance to a set of example patterns. Exemplars are used both to specify valid tile arrangements and to emphasize multi-tile structures. We model a pattern as a probabilistic graphical model called a factor graph. Factors represent the hard logical constraints between tiles, the soft statistical relationships that determine style, and the local dependencies between tiles at neighboring sites. We describe a simple method for learning factor functions from a small exemplar. We then synthesize new patterns through a stochastic search method that is inspired by MC-SAT. Efficient synthesis is challenging because of the combination of hard and soft constraints. Our synthesis algorithm, called BlockSS, scales linearly with the number of tiles and the hardness of the problem. We use our technique to model building facades, cities, and decorative patterns.