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利用描述可激发介质中波的传播的二维反应扩散方程，首次研究了一类规则分形网络：谢尔宾斯基地毯（SG）上斑图（pattern）的形成．随着控制参量的变化，SG上可以有湍流、螺旋波，以及辫状波等多种形式的斑图；与规则体系比较，分形体系的受限扩散使得复杂斑图的形成受到抑制．在合适的控制参量区内，还发现存在“结构诱导”的脉冲波的周期激发现象以及辫状波向螺旋波、湍流的跃迁．
Using a two-dimensional reaction-diffusion equation that describes the propagation of waves in an excitable medium, a class of regular fractal networks is studied for the first time: the formation of patterns on the sherbinski carpet (SG). With the change of control parameters, turbulent flow, spiral wave and braided wave can be used on SG. Compared with the regular system, the restricted diffusion of fractal system can restrain the formation of complex speckle. In the appropriate control parameter region, it is also found that there is a phenomenon of “structure-induced” periodic excitation of pulsed waves and the transition of braided waves to spiral waves and turbulence.