Visual Methods for Representing Flow Space with Vector Fields (Short Paper)

The issue of human mobility has been a focal point of research among numerous scholars in the field of geography for decades. Among them, the visualization of origin-destination (OD) data is an important branch of geographic flow studies. In this paper, we vectorize and represent immigration flows using OD flow data of U.S. immigrants in the year 2000, constructing an immigration space. Through data validation, it is confirmed that the vector field satisfies the Gauss’s theorem and is irrotational, demonstrating that the field can be derived from a potential and that the field is uniquely determined by the potential. Scalar potential fields are inferred from the vector field, providing a more intuitive and convenient description of the underlying flow patterns in geographical interaction matrices. Additionally, this paper employs potential fields and applies a density-equalizing areal cartogram to reconstruct the global representation of functional space, constructing cartogram maps based on potential magnitudes.