Construction of weavings in the plane

This work develops, in graph‐theoretic terms, a methodology for systematically constructing weavings of overlapping nets derived from 2‐colorings of the plane. From a 2‐coloring, two disjoint simple, connected graphs called nets are constructed. The union of these nets forms an overlapping net, and a weaving map is defined on the intersection points of the overlapping net to form a weaving. Furthermore, a procedure is given for the construction of mixed overlapping nets and for deriving weavings from them. A method for constructing weavings of (mixed) overlapping nets in the plane is discussed.