From what I have understood so far,
a design patent is a form of legal protection granted to the ornamental design of a functional item. Design patents are a type of industrial design right.
a utility patent is a patent that covers the creation of a new or improved — and useful — product, process or machine. A utility patent, also known as a “patent for invention,” prohibits other individuals or companies from making, using or selling the invention without authorization.
In the case of data visualization, the whole point of the visualization is to make a dataset consumable. To me, this is in sync with the utility definition (as it is a method of consuming data). However, it achieves this by using graphical (ornamental) design.
Basically, with data visualization, it seems like the ornamental design is the utility.
In this case, if I were to invent a new kind of data visualization, what type of patent would it be.