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。

A new method for generation of fractal Images is presented in this paper. To synthesize fractal Images, fractional Brownian motions are used which are obtained by a new means-recursive space filtering. The power spectrum of fractional Brownian motion can be used to determine the frequency-response of the two-dimensional shaping filter of fractional Brownian motion, then the shaping filter whose frequency response is circularly symmetric and exponentially decaying can be designed using a method based on one-dimensional prototype filter and rotation transforms. The fractional Brownian motion based fractal Image with desired fractional dimension can be generated by applying its shaping filter to a Gaussian distributed white process.