Turing patterns can be used to reproduce biological skin patterns. However, the similarity between the reproduced Turing pattern and the actual skin pattern has not been evaluated quantitatively and has only been determined visually. We propose a method for quantitatively evaluating the similarity between the pattern reproduced by the Turing pattern and biological skin patterns using persistent homology, which is a topological data analysis method. Persistent homology can quantitatively extract the structural information of the pattern, allowing an analysis that focuses only on the structure of the biological skin pattern without being affected by variation in the pattern due to individual differences. The experiment tested the effectiveness of persistent homology analysis on multiple Turing patterns generated by varying the parameters of the Gray–Scott model. We used real images of Scomber japonicus as the organisms represented by Turing patterns, and the similarity between the real images and Turing patterns was calculated using persistent homology. The results confirmed the tendency for a high degree of similarity between real images of several S. japonicus and the Turing patterns generated with certain parameters. These results suggest that persistent homology can be used to quantitatively evaluate the reproducibility of Turing patterns.

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