Determining Parastichy Numbers Using Discrete Fourier Transforms

Abstract

We report a practical method to assign parastichy numbers to spiral patterns formed by sunflower seeds and pineapple ramenta using a discrete Fourier transform. We designed various simulation models of sunflower seeds and pineapple ramenta and simulated their point patterns. The parastichy numbers can be directly and accurately assigned using the discrete Fourier transform method to analyze point patterns even when the parastichy numbers contain a divergence angle that results in two or more generalized Fibonacci numbers. The presented method can be applied to extract the structural features of any spiral pattern.

Isolating phyllotactic patterns embedded in the secondary growth of sweet cherry (Prunus avium L.) using magnetic resonance imaging

“…This is even possible if the features are difficult to discern by eye, or embedded internally within extensive secondary growth. With larger sets of node locations, Fourier Methods could further automate the process of finding parastichy numbers [33,34]. Isolating features in mature specimens can lead to insights regarding the developmental history of a plant, which is crucial to manipulate plant forms in a directed way and mechanistically understand the origins of morphology.…”

Determining Parastichy Pairs for Florets and Seeds on Sunflowers

“…Zhang (2021) designed their own model to study gerbera's inflorescences and successfully generated the Pp. Negishi et al (2017) applied Discrete Fourier Transform (DFT) to a simulation with arbitrarily divergence angles and found that the Pp becomes generalized Fibonacci numbers. So far, most of researches on Pp about sunflowers have fo- cused on the relationship related to the Fibonacci number, and yet so few applications of sunflowers' Pp have been explored.…”