The book A New Kind of Science [1] suggests a multiway system that uses complex numbers, which this Demonstration implements with a variety of multiway mappings.

A graph is constructed from a multiway system by connecting a point with its images under the maps.

When only is in the function, the starting point is taken from the 2D slider. When both and are in the function, then starts at 0 and is the value taken from the 2D slider.