This work uses the concepts and tools of complexity theory to examine the effect of logical thinking and two cognitive styles, such as, the degree of field dependence/independence and the convergent/divergent thinking on students' understanding of the structure of matter. Students were categorized according to the model they adopted for the structure of matter: continuous or particulate. This categorical variable was then analysed by the random walk approach in order to search for power law correlations in the rank-ordered psychometric scores. In addition, the random walk method was applied to students' three misconceptions on this matter. Moreover, elements of complexity theory in relation to the present method are given. The results provide empirical evidence for the effect of these variables on students' understanding of the structure of matter. Interpretations of the results are provided and implications for teaching are discussed. (Contains 4 figures.)