The Mathematical Biology of Diatoms

10Pattern Formation in Diatoma vulgaris Colonies: Observations and Description by a Lindenmayer-System

Thomas Harbich

Independent Researcher, Am Brüdenrain, Weissach im Tal, Germany

Abstract

The araphid diatom Diatoma vulgaris forms zig-zag-shaped colonies whose structures change spatially and temporally with cell divisions. To describe pattern formation, a notation of possible divisions is introduced, based on four symbols, which enables analysis of observations. The observed processes provide evidence for an asymmetry with respect to the mirroring on the transapical plane. An extension of the symbols by elements that consider this asymmetry allows description of colony morphogenesis by a non-deterministic Lindenmayer system with only two basic elements and one parameter. The space of possible patterns is strongly reduced by the observed production rules tenuis and their temporal distribution. Sections on the chain in which divisions occur synchronously show characteristic chain formations and transitional states between them. Considering only deterministic processes, patterns of the formed structures can be derived at the level of connections, which are frequently encountered and represent a confirmation of the theory. In addition, they have implications for the curvature of filamentous colonies. This is discussed in the context of evolutionary advantage.

Keywords: Colony structure, Diatoma vulgaris, Lindenmayer system, pattern formation

10.1 Introduction

Diatoms form a class ...