Is the spiral effect psychological?

The author had the pleasure to discuss the topic via e-mail with Branko Grünbaum in his 87th year. During this correspondence, the question arose whether a spiral structure (given a certain definition of it) could be recognized automatically or whether “to some extent, at least, the spiral effect is psychological”, as Grünbaum and Shephard had conjectured in 1987 ("Tilings and Patterns", exercise section of Chapter 9.5). In this paper, an algorithm for automatic detection of such a tiling’s spiral structure and its first implementation results will be discussed. Finally, the definitions for several types of spiral tilings will be refined based on this investigation.