We define a mathematical formalism based on the concept of an ''open dynamical system'' and show how it can be used to model embodied cognition. This formalism extends classical dynamical systems theory by distinguishing a ''total system'' (which models an agent in an environment) and an ''agent system'' (which models an agent by itself), and it includes… (More)
We present a rigorous mathematical analysis of a discrete dynamical system modeling plant pattern formation. In this model, based on the work of physicists Douady and Couder, fixed points are the spiral or he-lical lattices often occurring in plants. The frequent occurrence of the Fibonacci sequence in the number of visible spirals is explained by the… (More)
This article presents new methods for the geometrical analysis of phyllotactic patterns and their comparison with patterns produced by simple, discrete dynamical systems. We introduce the concept of ontogenetic graph as a parsimonious and mech-anistically relevant representation of a pattern. The ontogenetic graph is extracted from the local geometry of the… (More)
A simple kinematic model for the trajectories of Listeria monocytogenes is generalized to a dy-namical system rich enough to exhibit the resonant Hopf bifurcation structure of excitable media and simple enough to be studied geometrically. It is shown how L. monocytogenes trajectories and meandering spiral waves are organized by the same type of attracting… (More)
A geometric invariant for the study of planar curves and its application to spiral tip meander.
In recent years computer models have become increasingly important in providing insights into the developmental process of plants. The study of phyllotactic patterns provides a good example of this. Despite the huge diversity of plant forms there are only a few ways in which plant organs such as leaves, florets, scales, etc. are arranged along a plant stem.… (More)
The calculation of divergence angles between primordia in a plant apex depends on the point used as the center of the apex. In mathematically ideal phyllotactic patterns, the center is well defined but there has not been a precise definition for the center of naturally occurring phyllotactic patterns. A few techniques have been proposed for estimating the… (More)