Pointillism via Linear Programming

Pointillism is a painting technique in which the painter does nothing but place dots of paint on the canvas. Up close, a pointillist painting can appear to be completely abstract, a mass of dots. But from afar, the dots can wondrously merge into a realistic representation of the subject-a face, perhaps, or, as in Georges-Pierre Seurat's A Sunday on La Grande Jatte-1884, a group of Parisians relaxing in a park on a sunny afternoon (oil on canvas, 1884-86, Art Institute of Chicago).

We describe how to use linear programming to construct a pointillist portrait. Our goal is an effect similar to that achieved by Seurat: We'd like our portrait to be a meaningless (but aesthetically pleasing) jumble when looked at closely, but recognizable (and even subtle) when viewed from a distance. To simplify the exposition, we focus on the construction of a black-and-white portrait (though in the final section, we do add color).

For other examples of "Opt Art"-art produced with the aid of mathematical optimization techniques-see Bosch [2002], Bosch [2003], and Bosch and Herman [2004].