In this paper, we propose an explicit time-stepping scheme for the pattern formation in reaction–diffusion systems on evolving surfaces. The proposed numerical method is based on a simple discretization scheme of Laplace–Beltrami operator over triangulated surface. On the static and evolving domains, we perform various numerical experiments for effect of domain growth and pattern formations. The computational results demonstrate that our proposed method can simulate pattern formation in reaction–diffusion systems on evolving surfaces. The actual zebra skin pattern and computational results are compared. In the computational results, we can observe different pattern formations on the evolving surface with specific rotation speed.

在本文中，我们提出了一个明确的时间步长方案，用于在不断变化的表面上的反应扩散系统中形成图案。所提出的数值方法是基于三角表面上Laplace-Beltrami算子的简单离散化方案。在静态和不断变化的域上，我们对域生长和图案形成的影响进行了各种数值实验。计算结果表明，我们提出的方法可以模拟在不断变化的表面上反应扩散系统中的图案形成。比较了实际的斑马皮模式和计算结果。在计算结果中，我们可以观察到在特定转速下不断变化的表面上形成的不同图案。