Scaling and fractal formation in persistence

The spatial distribution of unvisited/persistent sites in 1D A+A-->0 model is studied numerically. Over length scales smaller than a cut-off xi(t) sim ilar to t(z), the set of unvisited sites is found to be a fractal. The frac tal dimension d(f), dynamical exponent z and persistence exponent a are rel ated through z(1 - d(f)) = theta. The observed values of d(f) and z are fou nd to be sensitive to the initial density of particles. We argue that this may be due to the existence of two competing length scales, and discuss the possibility of a crossover at late times.