On Spiral Structures in Tilings

In this paper, the existence of spiral structure in certain types of tilings is investigated. Following a question posed by Branko Grünbaum, it is demonstrated that all Archimedean tilings can be partitioned in a spiral like manner thereby fulfilling a definition given in 2017 for this visual effect. Furthermore, to show that this is not possible for every arbitrary periodic tiling, non “spirable” examples are constructed in the sense of this definition. Lastly, an intuitive result for one-armed spirals is established: one-armed spirals and periodic tilings cannot coexist.