Locked Links

Described here is a pattern generated by a program which draws “locked links”. The links are always regular polygons and they are “locked” together by weaving their edges over and under each other. This is best illustrated in Fig. 1. Input to the program which generates the locked links includes the total number of sides for the polygon in the center of each figure. Even numbered inputs provide figures with two separate intertwined links, each with half the number of sides originally requested. Odd numbered inputs generate a single link with the input number of sides that intertwines with itself, basically forming a knot. Figure 1 contains examples for initial inputs of 3, 4, 5, 6, and 8 sides. Other inputs to the program include the length of a side of the polygon in the center of the figure, thickness of a link, center of the figure, and angle at which to begin drawing. The program is an intense exercise in algebra and trigonometry but is actually quite compact when completed. (My version is about 100 lines of code.)…