This communication provides an illustration for the use of computer simulations in human immunology. When traditional experiments are impossible, unethical, or unfeasible, in silico modeling procedures may help to fill the gaps in our knowledge of an immune system response to a pathogen. In our study, we define terms and properties of modeled entities: "a clonotype", its distribution, and rank-frequency summaries, and describe properties associated with each of these three clonotype-related entities. We simulate a multistage dynamic process of an immune memory response to influenza. We believe that illustrated properties of fractality and self-similarity might arise due to the following process. The memory T cells operate in a complex environment of shifting pathogen concentrations, increasing and then decreasing inflammatory signals, and multiple interactions with other immune cells and their infected targets. Therefore, a fractal structure to such a population would represent an optimization in terms of percolation into immune/inflammatory space.