A hexagonal graphical user interface (GUI) is provided in which a user interface is rendered including one or more primary icons, each of the one or more primary icons comprising a hexagon and representing an initial state. In the GUI, responsive to the selection of a first icon from the primary icons, one or more secondary icons are displayed, where each of the secondary icons is a hexagon and positioned in the user interface in a hexagonal tiling (hextille) arrangement with respect to at least one of the first icon or another one of the secondary icons, and where each of the secondary icons represents additional states subsequent to the initial state along valid paths from the initial state.