Is the spiral effect psychological?

TL;DR

This paper presents an algorithm for automatically detecting spiral structures in tilings, investigates whether the spiral effect is perceptually psychological or structurally detectable, and refines definitions of spiral tilings.

Contribution

It introduces a novel algorithm for automatic spiral structure detection in tilings and refines the classification of spiral tilings based on empirical results.

Findings

The algorithm successfully detects spiral structures in various tilings.

The study suggests that some spiral effects can be recognized automatically, challenging the idea that they are purely psychological.

Refined definitions for different types of spiral tilings based on detection results.

Abstract

In 2017 a definition of spiral tilings was given, thereby answering a question posed by Gr\"unbaum and Shephard in the late 1970s. The author had the pleasure to discuss the topic via e-mail with Branko Gr\"unbaum 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 Gr\"unbaum and Shephard had conjectured in 1987 (see exercise section of chapter 9.5 in "Tilings and Patterns"). 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 are refined based on this investigation.