Abstract
Problem of pattern formation in stochastic processes with long-range correlations is of great importance. In particular, many regularities are often found in the emergent patterns, offering a possibility of classification of the underlying processes. Here we study numerically and analytically paths traced by many ants simultaneously waking on a plane. The process is is defined by constant speed of each ant with reflection from the previously existing paths. We simulate the process with different ant densities and monitor the emergence of paths (real-time visualization of the process is available). The quantitative analysis of these patterns in terms of statistical probability distributions and time series is found to be in a good agreement with the analytical predictions.
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