LABYRINTHINE PATTERNS IN A SELF-AVOIDING GROWING STRING

We propose a model of a self-avoiding growing string with excluded vol ume effects. In this model, the string develops to form a complex shap e like a labyrinth. We find simple dynamical scaling relations for sev eral characteristic quantities, including the radius of gyration and r adius of curvature. Detailed numerical calculations show that there ar e two length scales and one time scale characterizing the shape transf ormations of the growing string.