Modulation effect with global ambiguity in 2-dimensional random walk

Here, we developed a two-dimensional multi-agent random walk algorithm. In our algorithm, agents interact with each other and change their directional rules by locally detecting moving directions of other agents. In addition to that, we introduced modulation effects in which agents controlled rule-intervals depending on number of local other agents. We show that modulation effects which introduce global ambiguity play a crucial role in establishing optimal random walk by checking the slope value (μ), depending on the density of agents. We set a modulation-added model and non-modulation model. The latter is control model. In case of non-modulation model, the slope values (μ) highly depend on the density of agents. However, in case of modulation-added model, the slope values (μ) are flexible and independent of the density of agents.