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本文提出分形图形生成的一种新方法。采用分数维布朗运动来合成分形图形，分数维布朗运动用一种新的方法──递归空间滤波来获得。由分数维布朗运动的功率谱确定其二维成形滤波器的频率响应，然后采用以一维原形滤波器加旋转变换的方法来设计具有圆对称和指数衰减频率响应的成形滤波器。用成形滤波器对高斯分布的白色过程滤波，便可以得到具有期望分数维的布朗运动分形图形。
This paper presents a new method of fractal graphics generation. Fractional Brownian motion is used to synthesize fractal graphics. Fractional Brownian motion is obtained using a new method, called recursive spatial filtering. The frequency response of the two-dimensional shaping filter is determined by the power spectrum of fractional Brownian motion, and then a shaping filter with circularly symmetric and exponential decaying frequency response is designed by using one-dimensional original filter plus rotational transformation. By using the shaping filter to filter the white process of Gaussian distribution, the Brownian motion fractal graph with the desired fractal dimension can be obtained.