Reaction-diffusion systems which have reaction term satisfying f(-q) = -f(q) tend strongly to form striped patterns. Haken’s slaving principle is used to derive differential equations for unstable mode amplitudes close to the Turing instability. This connects a dynamical symmetry to pattern selection, with possible relevance to biological and chemical pattern-forming phenomena.

We present a technique for the analysis of pattern formation by a class of models for the formation of ocular dominance stripes in the striate cortex of some mammals. The method, which employs the adiabatic approximation to derive a set of ordinary differential equations for patterning modes, has been successfully applied to reaction-diffusion models for striped patterns [1]. Models of ocular dominance stripes have been studied [2,3] by computation, or by linearization of the model equations. These techniques do not provide (...) a rationale for the origin of the stripes. We show here that stripe formation is a non-linear property of the models. Our analysis indicates that stripe selection is closely linked to a property in the dynamics of the models which arises from a symmetry between ipsilateral and contralateral synapses to the visual cortex of a given hemisphere. (shrink)

Explores the theories of the development of shape and size in living organisms and offers an exposition of the kinetic theory of shape.

Two general features of metameric patterning in Drosophilaare considered: (1) maintenance of a constant number of metameres (segments or parasegments) in the face of variation in length of the embryo; (2) expression of pattern by on‐off switchings of particular genes, with only three or four rows of cells to each element of pattern. For each of these features, the general strategic question is raised: could reaction‐diffusion theory account for this? In both cases, it is answered affirmatively. For the second feature, (...) this review contains some hitherto unpublished computer simulations by one of us (K. Y. T.), illustrating that a reaction‐diffusion mechanism can be transformed into a patterned switching mechanism by nothing more than compartmenting of the diffusion region. For the scale of three compartments to one pattern repeat unit (representing three rows of cells to a segment) the switching pattern predicted by computation is two‐off to one‐on. This resembles the pattern of expression of the engrailed gene, posteriorly localized in each segment. (shrink)