Generation of Checkered Patterns and Their Variations by Making Use of Eulerian Graph Features

A variety of pictures of checkered pattern graphics appear on the Internet. However, rarely seen is how those graphics were produced. This paper shows various checkered patterns and their variations generated automatically by a computer program, making use of features of Eulerian Graph. Given a line drawing of binary images, the procedure extracts contours of the line figures. The contours in turn form a set of contour cycles of the regions surrounded by the original lines of the figures, which are supposed to form an Eulerian Circuit. The drawing can be various combinations of closed lines -- circles, rectangles, ellipses, any of closed drawings. Bi-partitioning the contours into partitions (X, Y), filling inside the regions of X and Y, the procedure outputs the checkered patterns or their likes. Various patterns were successfully produced in a number of experiments as well as demonstrating that the algorithm is very robust and that some of the patterns are aesthetic. Since the checkered patterns are used in the Emblem of Tokyo Olympic 2020, it is timely to do the demonstration about the design of checkered patterns and their relations with computer programs and mathematics.