SHAPE TRANSFORMATION OF A GROWING STRING IN A PLANE

We propose a model of a string which grows at a constant rate and stud y the characteristic properties of shape transformations. Numerical ca lculations show that the string grown from a straight line comes to as sume a complex shape confined in a small region in which we can observ e a characteristic length. From a statistical point of view, we can sa y that the string with the complex shape is an assembly of many arcs w hose mean radius is approximately equal to the characteristic length. The radius varies, depending on several parameters, but the curvature histogram can be modified to a unique form by rescaling the length sca le. This means that all solutions in our model of a growing string are statistically equivalent. The scaling properties and several other qu antities which characterize the system are also studied.