2017/01/04 by Pau Atela, Atela, Pau, Christophe Golé +1
Agricultural and Biological Sciences · #37 #92 #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Plant Diversity and Evolution #Plant Molecular Biology Research #Plant nutrient uptake and metabolism #Tissues and Organs (q-bio.TO)
paper · pdf · doi:10.48550/arxiv.1701.01361
openalex publication_date 2017/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study properties of phyllotactic and rhombic tilings on the cylin- der. These are discrete sets of points that generalize cylindrical lattices. Rhombic tilings appear as periodic orbits of a discrete dynamical system S that models plant pattern formation by stacking disks of equal radius on the cylinder. This system has the advantage of allowing several disks at the same level, and thus multi-jugate config- urations. We provide partial results toward proving that the attractor for S is entirely composed of rhombic tilings and is a strongly normally attracting branched manifold and conjecture that this attractor persists topologically in nearby systems. A key tool in understanding the geometry of tilings and the dynamics of S is the concept of pri- mordia front, which is a closed ring of tangent disks around the cylinder. We show how fronts determine the dynamics, including transitions of parastichy numbers, and might explain the Fibonacci number of petals often encountered in compositae.