LETTER TO THE EDITOR Random space-f3ling-tiling: fractal properties and kinetics

Abstnet. A kinetic version of random Apollonian packing model is intraduced. In this model, droplets nucleate spontaneously, gmw at a uniform rate and stop growing upon collisions. The fr;iaal dimension, Df of the pow, space is found m be equal to Df = d(l- expp- (2d+z-2) / (d + 2)1), a result which is confirmed exactly in ID and numerically in m.. Pattern formation processes are numerous and include, e.g., diffusion-limited aggregation, dendritic growth, dielectric breakdown, solidification of supercooled liquids, growing and coalescing droplets [I-31. These moving-boundary problems are easy to formulate but extremely difficult to solve. Given the importance and complexity of 'non-equilibrium pattern fonhtion processes, it is interesting to investigate models which are ainenatile to theoretical analysis but nevertheless may mimic some features of pattern formation phenomena occurring in nature. In the present study, we descnk~one such model which is exactly soluble in one dimension and tractable on a mean-field level in arbitrary dimension d. Based on the kinetic description, we then deduce geometric properties of arising patterns including the fractal dimension of the pore space. There are a number of pattern formation models in which the spacefilling pattems ar