Generation of biological pattern and form.

We propose two models for pattern formation in early embryogenesis. The first deals with patterns in motile mesenchymal cells; the second treats patterns in epithelial sheets. In the mesenchymal model, cells exert tractions which deform the extracellular matrix within which they move. This in turn affects their motion. The model field equations are formulated and analysed, and applied to two widely studied phenomena: skin-organ primordia for feather and scale patterns, and the development of cartilage patterns in limb bone formation. The model for epithelial pattern formation consists of viscoelastic field equations with a calcium-controlled contraction trigger. Preliminary analysis is presented which demonstrates the existence of travelling wave solutions.