Geometrical study of phyllotactic patterns by Bernoulli spiral lattices. (12th July 2017)

• Record Type: Journal Article
• Authors: Sushida, Takamichi; Yamagishi, Yoshikazu
• Other Names: INOUE Y. guestEditor.; AKIYAMA M. guestEditor.
• Is Part Of: Development growth and differentiation. Volume 59:Number 5(2017)
• Page Start: 379
• Page End: 387
• Publication Date: 2017-07-12
• Subjects: Bernoulli spiral lattice -- continued fraction -- disk packing -- phyllotaxis -- Voronoi tiling; Embryology -- Periodicals; Developmental biology -- Periodicals; Growth -- Periodicals; 574.3
• DOI: 10.1111/dgd.12378
• Languages: English
• ISSNs: 0012-1592

Abstract

Abstract : Geometrical studies of phyllotactic patterns deal with the centric or cylindrical models produced by ideal lattices. van Iterson (Mathematische und mikroskopisch – anatomische Studien über Blattstellungen nebst Betrachtungen über den Schalenbau der Miliolinen, Verlag von Gustav Fischer, Jena, 1907) suggested a centric model representing ideal phyllotactic patterns as disk packings of Bernoulli spiral lattices and presented a phase diagram now called Van Iterson's diagram explaining the bifurcation processes of their combinatorial structures. Geometrical properties on disk packings were shown by Rothen & Koch (J. Phys France, 50(13), 1603‐1621, 1989). In contrast, as another centric model, we organized a mathematical framework of Voronoi tilings of Bernoulli spiral lattices and showed mathematically that the phase diagram of a Voronoi tiling is graph‐theoretically dual to Van Iterson's diagram. This paper gives a review of two centric models for disk packings and Voronoi tilings of Bernoulli spiral lattices. Abstract : Geometrical studies of phyllotactic patterns deal with the centric or cylindrical models produced by ideal lattices. This paper gives a review of two centric models for disk packings and Voronoi tilings of Bernoulli spiral lattices.