Emergence of Diverse Epidermal Patterns via the Integration of the Turing Pattern Model with the Majority Voting Model

Abstract

Animal skin patterns are increasingly explained using the Turing pattern model proposed by Alan Turing. The Turing model, a self-organizing model, can produce spotted or striped patterns. However, several animal patterns exist that do not correspond to these patterns. For example, the body patterns of the ornamental carp Nishiki goi produced in Japan vary randomly among individuals. Therefore, predicting the pattern of offspring is difficult based on the parent fish. Such a randomly formed pattern could be explained using a majority voting model. This model is a type of cellular automaton model that counts the surrounding states and transitions to high-number states. Nevertheless, the utility of these two models in explaining fish patterns remains unclear. Interestingly, the patterns generated by these two models can be detected among very closely related species. It is difficult to think that completely different epidermal formation mechanisms are used among species of the same family. Therefore, there may be a basic model that can produce both patterns. Herein, the Turing pattern and majority voting method are represented using cellular automata, and the possibility of integrating these two methods is examined. This integrated model is equivalent to both models when the parameters are adjusted. Although this integrated model is extremely simple, it can produce more varied patterns than either one of the individual models. However, further research is warranted to determine whether this model is consistent with the mechanisms involved in the formation of animal fish patterns from a biological perspective.

Keywords

• Turing pattern
• majority voting model
• cellular automata
• animal skin patterns
• reaction–diffusion equation