Power law distribution of frequencies of characters in dreams explained by random walk on semantic network

Abstract

In an individual’s dreams some characters occur more frequently than others.  In dream series of five individuals, character frequencies follow a power law probability distribution, a distribution often found for contact with people in waking life.  Knowing the form of the distribution is important for statistical considerations, because a power law distribution is highly skewed.  The form also constrains explanations of how characters are generated in dreams.  Character generation is analogous to naming people in a verbal fluency task.  We explain the power law with an established model for this task, a random walk on an individual’s semantic memory for people and their associations.  We demonstrate with simulations that a random walk on such a network can produce a power law character frequency distribution, whether the random walk is self-avoiding or not and whether the network is connected or not.