Iterated Averaging of Polygon Vertices
Proceedings of Bridges 2021: Mathematics, Art, Music, Architecture, Culture
Pages 197–204
Regular Papers
Abstract
This work examines artwork generated from the problem of repeatedly averaging together the vertices of a polygon, constructing new polygons with each iteration. Rather than investigate the final state, I’m interested in the aesthetics of intermediate states. I discuss several extensions of the fundamental process, including variations on the vertices averaged, the type of average used, and the initial polygon. Considerations for creating final images and example images using these concepts are presented.