Symmetric Venn Diagrams in the Plane: The Art of Assigning a Binary Bit String Code to Planar Regions Using Curves

Abstract

The authors discuss artwork created by assigning a binary string code with length 11 to each of 211 = 2,048 planar regions formed intersection of 11 rotations of a single simple closed curve over 360/11 degrees. The goal of this process is to create the maximum number of connected regions, exactly one for each of the 2,048 different binary strings with length 11. The difficulty in this process lies in finding a suitable curve. The authors briefly describe the methods of finding these complicated curves and show how colors can be assigned to regions representing orbits of shifts of binary strings, thus creating unusual images.