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法国数学家B.B.Mandelbrot创立的“分形几何学”(fractal geometry)已广泛应用于众多领域。分形(Fractal)与分维(fractal dimension)是科学家们近十年的热门话题,无论在物理学、化学、生物学、生理学,还是在地球科学、冶金技术及材料科学等,均能见到分形理论的辉煌成果。分形是指具有自相似性的几何对象。所谓自相似性是指局部与整体在形态、功能和信息等方面具有统计意义上的相似性,适当地放大或缩小分形对象的几何尺寸,整个结构并不改变。研究分形的几何学称为分形几何学。定量描述分形的参数就是分维。
The “fractal geometry” created by French mathematician B.B. Mandelbrot has been widely used in many fields. Fractal and fractal dimension are hot topics for scientists in the past decade. Fractals can be seen in physics, chemistry, biology, physiology, earth science, metallurgy and material science. The brilliant achievements of the theory. Fractals refer to geometric objects that have self-similarity. The so-called self-similarity means that the locality and the whole have statistical similarities in terms of form, function, and information, and appropriately enlarge or reduce the geometric size of the fractal object, and the entire structure does not change. The geometry of the study fractal is called fractal geometry. Quantitative description of fractal parameters is fractal dimension.