Fractals, Vol. 11, Supplementary Issue (February 2003) 233–241 ❢ c World Scientific Publishing Company MULTILINEAL RANDOM PATTERNS EVOLVING SUBDIFFUSIVELY IN SQUARE LATTICE ADAM GADOMSKI Institute of Mathematics and Physics, University of Technology and Agriculture, PL-85796 Bydgoszcz, Poland Abstract Stochastic multiline evolution in square lattice is studied. It turns out that the emerging patterns evolve subdiffusively, which is characterized by the 1 4 exponent. Possible origin of such a slow behavior is discussed, and some elucidation, supporting the small fractional value is given. A notion of (dynamic) phase transition concept may sometimes help in understanding the presented random kinetic behavior. 1. INTRODUCTION Retrospective view towards history of statistical physics shows that simple models are really worth developing. As a certain quite “out-of-date” general example, traced back to the twenties, the Ising model should be mentioned. A slightly younger “toy” model, known to almost everyone, appears to be the percolation model. After the era of applying the computer and its very capacities had emerged, they both have been visibly put forward, and stand nowadays for basis of many applications in microelectronics, materials engineering and technology, chemical processing, etc. Other examples of simple statistical-physical models can undoubtedly be the growth models, intensively explored since the early eighties, or even earlier. On the list of those models one can mostly find the following simple “computer- aided” phenomena, like e.g. diffusion-limited aggregation (first invented by Witten and Sander in 1981), and its variations; ballistic growth; Eden cluster formation or chemical reaction-limited growth. One has also to mention a large class of models, that may be named deposition models. They led to formation of random deposits on a plane (line), 233