Determining Parastichy Numbers Using Discrete Fourier Transforms

Riichirou Negishi¹*, Kumiko Sekiguchi¹, Yuichi Totsuka² and Masaya Uchida¹

¹Saitama Institute of Technology, 1690 Fussaiji, Fukaya, Saitama 369-0293, Japan
²Global Software Co. Ltd., 3-11-10 Kenpuku, Honjo, Saitama 367-0044, Japan
*E-mail address: negishi@sit.ac.jp

(Received September 21, 2017; Accepted October 31, 2017)

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.

Keywords: Parastichy Number, Fibonacci Number, Fourier Transform, Sunflower Seeds, Pineapple Ramenta