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It is well-known that reaction–diffusion systems are used to describe the patte formation models. In this paper, we will investigate the patte formation generated by the fractional reaction–diffusion systems. We first explore the mathematical mechanism of the patte by applying the linear stability analysis for the fractional Gierer–Meinhardt system. Then, an efficient high-precision numerical scheme is used in the numerical simulation. The proposed method is based on an exponential time differencing Runge–Kutta method in temporal direction and a Fourier spectral method in spatial direction. This method has the advantages of high precision, better stability, and less storage. Numerical simulations show that the system control parameters and fractional order exponent have decisive infl uence on the generation of pattes. Our numerical results verify our theoretical results.