An alternative representation of Fractal Gene Regulatory Networks facilitating analysis and interpretation

This paper introduces a new representation of Fractal Gene Regulatory Networks (FGRNs) that facilitates analysis and interpretation of their internal mechanisms. FGRNs are demonstrated to be useful tools in solving some problems but because of the complex nature of using the fractal proteins, an FGRN solution is difficult to analyze hindering an understanding of its functionality. The new representation uses a mathematical network-oriented perspective and clarifies the role of fractals in the running FGRNs. The underlying network structure and the transfer functions of the nodes are derived from the model and make reductions in the computational costs of the solutions. As a case study, FGRNs are evolved as distributed controllers based on sensor information for a modular snake robot and the solutions are analyzed and interpreted using the proposed network-oriented representation. The analysis reveals that the underlying control strategy is a simple linear equation where the modules have the access to the proper sensors. The more complex solutions are generated by the evolved FGRN controllers where the access of the modules to the sensory information is more restricted. The underlying effective parts of the networks are demonstrated and analyzed for the controllers in the both cases.