Applying the Dynamics of Circle Maps to Phyllotactic Patterns

Scott Hotton


An important characteristic of plant patterns is the angle between consecutive organs along the shoot. This is known as the divergence angle and its value is often nearly constant on an individual plant. This creates a lattice pattern for the collection of plant organs. When plant shoots are not round the divergence angles become more variable and the lattice pattern displays crystal like dislocations.

In this talk I will present a family of dynamical systems which models plant development. These dynamical systems are based on an inhibitory theory of plant organ formation and they are able to reproduce the regular and irregular patterns seen in plants. A constant divergence angle corresponds to a pure rotation on an attracting invariant circle. The more variable divergence angles of elliptical systems corresponds to a diffeomorphism on an attractive invariant circle. It is easy to compare the regular patterns produced by the model and the regular patterns in plants. I will explain how the theory of circle maps can be used to make a quantitative comparison between the irregular patterns of the model and the irregular patterns in actual plants.


  • To proceed to the next page in the talk click on
  • >
    in the box above.
  • To go to the previous page click on
  • <
    in the box above.
  • Every page of this talk is listed in the table of contents
  • Clicking on any entry in the table of contents will take you to the page that the entry refers to.
  • To go to the table of contents click on
  • *
    in the box above.