We study two chemical models for pattern formation in growing plant tips. For hemisphere radius and parameter values together optimal for spherical surface harmonic patterns of index l = 3, the Brusselator model gives an 84% probability of dichotomous branching pattern and 16% of annular pattern, while the hyperchirality model gives 88% probability of dichotomous branching and 12% of annular pattern.

neurocomputation involves discrete signals communicated along fixed transmission lines between discrete computational elements. This concept is shown to be inadequate to account for invariance in recognition, as well as for the holistic global aspects of perception identified by Gestalt theory. A Harmonic Resonance theory is presented as an alternative paradigm of neurocomputation, that exhibits both the property of invariance, and the emergent Gestalt properties of perception, not as special mechanisms contrived to achieve those properties, but as natural properties of the resonance itself.

Definition of the Subject

Mesa-type patterns in the one-dimensional

Abstract. In this work the existence of a global attractor for the solution semiflow of the coupled two-cell Brusselator model equations is proved. A grouping estimation method and a new decomposition approach are introduced to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of fourvariable reaction-diffusion systems with cubic autocatalytic nonlinearity and with linear coupling. It is also proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. 1.