Needle crystal formation in two dimensions

A simple model (based on conformal mapping) is constructed to simulate the two-dimensional growth of needle crystals growing out regularly from a common point. The resulting patterns are very similar to those which were obtained by other methods. The radius of gyration exponent beta is measured and found to be in the range 0.58-0.65, independent of the number of needles (n). It is shown that for large patterns, beta asymptotically approaches a value of 2/3. To compare the patterns with the DLA aggregates, the average slope ( alpha ) was measured for the density-density correlation function plotted logarithmically (log r to log C(r)). The relation between alpha and beta , which is characteristic of DLA fractal aggregates, is satisfied only in the case n = 8.