令人称奇的自然分形图案.doc

令人称奇的自然分形图案.doc令人称奇的自然分形图案
海洋贝类、螺旋星系再到人类肺部的结构,混沌的模型无处不在
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From sea shells and spiral galaxies to the structure of human lungs, the patterns of chaos are all around us.
从海洋贝类、螺旋星系再到人类肺部的结构,混沌的模型无处不在。
Fractals are patterns formed from chaotic equations and contain self-similar patterns plexity increasing with magnification. If you divide a fractal pattern into parts you get a nearly identical reduced-size copy of the whole.
分形是从混沌方程形成的一系列图形,包含不断放大的复杂自相似图案。如果将一个分形图案分为几个部分,那么每一小块都和整体形状完全一样。
The mathematical beauty of fractals is that plexity is formed with relatively simple equations. By iterating or repeating fractal-generating equations many times, random outputs create beautiful patterns that are unique, yet recognizable.
分形的数学之美在于可以从相对简单的方程推导出无限复杂的系统。通过多次迭代或重复分形生成方程,随机输出就可以产生独特且可识别的美丽图案。
We have pulled together some of the most stunning natural examples we could find of fractals on our .
地球上也存在一些自然生成的分形图形,下面我们将从中挑出一些最美丽的图案,以飨读者。
Above:
Romanesco oli
罗马花椰菜(Romanesco oli)
This variant form of cauliflower is the ultimate fractal vegetable. Its pattern is a natural representation of the i or golden spiral, a logarithmic spiral where every quarter turn is farther from the origin by a factor of phi, the golden ratio.
这种花椰菜的变种形式是一种极限分形蔬菜。它的图案是斐波纳契(i)黄金螺旋的自然呈现形式,在这个对数螺旋中,每一个直角转弯与起始点的距离都被Φ值所约束,Φ值即黄金分割率。
Image: Flickr/.
图片来源:Flickr/.
Salt Flats
盐滩(Salt Flats)
The San Francisco Bay salt flats pictured above have been used mercial salt production for over a century.
上图中的旧金山湾(San Francisco Bay)盐滩曾经出产了将近一个世纪之久的商品盐。
Below, an image from the largest salt flat in the world, Salar de Uyuni, located in southern Bolivia. The encrusted salt shows a remarkably consistent but random pattern, a characteristic of fractals.
下图展示了世界上最大的盐滩,即位于玻利维亚南部的乌尤尼岩沼(Salar de Uyuni)。结痂的盐层展现出一种非常一致的随机图案模式,这就是分形的特征。
Images: 1) Flickr/Tolka Rover. 2) Flickr/Mike D. Green.
图片来源:1)Flickr/Tolka Rover   2)Flickr/Mike D. Green
Ammonite Sutures
菊石缝合线(Ammonite Sutures)
Extinct for 65 milli