令人称奇的自然分形图案

来源:百度文库 编辑:神马文学网 时间:2024/03/28 16:58:27

来源Earth\'s Most Stunning Natural Fractal Patterns | Wired Science | Wiredcom
译者Lineker

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 of complexity 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 infinite complexity 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 planet.

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 Broccoli

罗马花椰菜(Romanesco Broccoli)

This variant form of cauliflower is the ultimate fractal vegetable. Its pattern is a natural representation of the Fibonacci 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(Fibonacci)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/Tin.G.

图片来源:Flickr/Tin.G.

Salt Flats

盐滩(Salt Flats)

The San Francisco Bay salt flats pictured above have been used for commercial 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 million years, ammonites were marine cephalopods that built chambered spiral shells. The walls between these chambers, called sutures, were complex fractal curves. Stephen Jay Gould used the complexity of ammonite sutures over time to argue that there is no evolutionary drive toward greater complexity and that we are a "glorious accident," alone in the universe.

已经灭绝了6500万年之久的菊石是一种带有多室螺旋状外壳的海洋头足类动物,其小室之间的阻隔即缝合线就是一种复杂的分形曲线。斯蒂芬·杰·古尔德(Stephen Jay Gould)曾以菊石缝合线随时间的复杂性来论证不存在向着更高复杂性方向发展的进化驱动力,人类的出现是一个“壮丽的偶然”,在宇宙中独一无二。

The shells of ammonites also grow as a logarithmic spiral, a pattern that appears often in nature, as with romanesco broccoli.

和罗马花椰菜一样,菊石外壳也会按照对数螺旋的方式生长,这种生长模式在自然界中颇为常见。

Ammonites also inspired this cathedral staircase in Barcelona, Spain.

西班牙巴塞罗那一处教堂楼梯的设计灵感就来自于菊石。

Images: 1) Flickr/cobalt123. 2) Flickr/Didier.bier. 3) Flickr/Edgley Cesar

图片来源:1)Flickr/cobalt123   2)Flickr/Didier.bier   3)Flickr/Edgley Cesar

Mountains

山脉

Mountains are the result of tectonic forces pushing the crust upward and erosion tearing some of that crust down. The resulting pattern is a fractal.

地质构造作用力向上抬升地壳,侵蚀再将地壳撕得支离破碎,山脉从此形成,同时也产生了分形图案。

Above is an image of the Himalayan Mountains, home to many of the tallest peaks on Earth. The Himalayas are still being uplifted by the collision of India with the Eurasian plate, which began about 70 million years ago.

上图是喜马拉雅山脉(Himalayan Mountains)的高空图像,地球上许多最高的山峰都集中在这一带。造山运动始于7000万年前,随着印度板块和欧亚大陆板块的不断碰撞,喜马拉雅山脉还在被抬升。

Image: NASA/GSFC/JPL, MISR Team.

图片来源:NASA/戈达德航天中心/喷气推进实验室,多角度辐射成像光谱仪小组(MISR Team)

Ferns

蕨类植物(Ferns)

Ferns are a common example of a self-similar set, meaning that their pattern can be mathematically generated and reproduced at any magnification or reduction. The mathematical formula that describes ferns, named after Michael Barnsley, was one of the first to show that chaos is inherently unpredictable yet generally follows deterministic rules based on nonlinear iterative equations. In other words, random numbers generated over and over using Barnsley's Fern formula ultimately produce a unique fern-shaped object.

蕨类植物是最常见的自相似集合,这意味着不管放大或缩小多少倍,它们的图案都可以进行数学上的推导和重现。这种蕨类图形被称为巴恩斯利蕨,是以首创者迈克尔·巴恩斯利(Michael Barnsley)的名字命名的,用于描述这种分形图形的数学公式第一次表明,虽然混度遵循建立在非线性迭代方程上的确定规则,但它天生无法预测。换句话说,就是重复利用巴恩斯利蕨类公式所产生的随机数可以形成一个蕨类形状的独特物体。

Images: 1) Flickr/cobalt123. 2) Flickr/CatDancing.

图片来源:1)Flickr/cobalt123   2)Flickr/CatDancing

Clouds

云彩

The marine stratus clouds above were photographed by the Aqua satellite over the South Atlantic Ocean, off the west coast of Africa. A fractal cloud pattern is interrupted by a series of diagonal grooves. According the NASA Earth Observatory, it is highly unusual to see such a sharp boundary in a continual cloud formation such as this, and scientists have yet to explain how it could form.

上图中的海洋层云(stratus clouds)图是水文气象卫星(Aqua satellite)在远离非洲海岸的大西洋上所拍摄的照片,图中分形状的云彩图案被一系列的对角线槽所扰乱。据NASA地球大观(NASA Earth Observatory)网站介绍,在连续的成云区看到如此醒目的分界线特别不同寻常,科学家还在寻找出现分界线的真正原因。

Below, the 200-mile long series of cloud vortexes is perhaps the longest of these formations ever photographed, according to NASA. These cloud vortexes are also called von Kármán cloud streets, for the late fluid dynamicist Theodore von Kármán.

下图展示的是长达320公里的云旋(cloud vortex),NASA的相关记录显示,这是有史以来所拍摄到的最长云旋队列。为了纪念已故的流体动力学家西奥多·冯·卡门(Theodore von Kármán),这些云旋也被称为冯·卡门云街(von Kármán cloud streets)。

Cloud streets form when low-lying clouds are interrupted by an object such as an island. Similar patterns occur in the wind flow downstream of airplane wings.

当低垂的云层被岛屿一类的物体所阻碍时就会形成云街,飞机在飞行时机翼后方的气流也会形成类似的漩涡。

Images: 1) Jeff Schmaltz/MODIS Land Rapid Response Team/NASA. 2) NASA.

图片来源:1)Jeff Schmaltz/MODIS地面快速反应部队(MODIS Land Rapid Response Team)/NASA   2)NASA

Leaves

树叶

Many plants follow simple recursive formulas in generating their branching shapes and leaf patterns.

很多植物在生成分枝形状和叶片图案时遵循简单的递归法则。

Ironically, deforestation patterns that occur along primary, secondary and tertiary roadways form a similar pattern, like that pictured below from the state of Rondonia in western Brazil, one of the most deforested regions of the Amazon.

具有讽刺意味的是,沿着主干道、次级干道和三级道路的森林砍伐模式也形成了相似的图案,下面这幅照片拍摄的是巴西西部朗多尼亚州(Rondonia)的森林砍伐,朗多尼亚州是亚马逊森林被砍伐最多的地区之一。

Images: 1) Flickr/ CatDancing. 2) NASA.

图片来源:1)Flickr/ CatDancing   2)NASA

Canyons

峡谷

This false-color image above, of the Grand Canyon, displays the fractal pattern created by the Colorado River over millions of years. Red indicates areas of vegetation in the image.

上面这幅大峡谷( Grand Canyon)的伪彩色照片展示了科罗拉多河(Colorado River)几百万年的冲刷所形成的分形图案,图中的红色是植被区域。

Blow, a false-color image of Canyon de Chelly National Monument in Arizona. The National Park Service calls it one of the longest continually inhabited landscapes in North America.

下面这幅伪彩色照片拍摄的是亚利桑那州的谢伊峡谷国家保护区(Canyon de Chelly National Monument),美国国家公园管理局(National Park Service)宣称该峡谷保护区是北美地区最长的连续人居景观之一。

Images: 1) GeoEye/Space Imaging. 2) NASA.

图片来源:1)GeoEye/Space Imaging   2)NASA

Lightning

闪电

The path lightning takes is formed step by step as it moves towards the ground, turning air into plasma.

当闪电冲向地面将空气变为等离子体时,它所经历的路径是逐步形成的。

Images: 1) Flickr/thefost. 2) Flickr/Brujo+.

图片来源:1)Flickr/thefost   2)Flickr/Brujo+.

Peacock Feathers

孔雀羽毛

Peacocks attract mates with the repeating patterns in their plumage.

孔雀通过展现羽毛上的重复图案吸引异性前来交配。

Images: 1) Flickr/Digimist. 2) Flickr/Maia C.

图片来源:1)Flickr/Digimist   2)Flickr/Maia C

Snowflakes

雪花

Crystallizing water forms repeating patterns in snowflakes and on frosty surfaces. The patterns have inspired claims about the power of consciousness to affect matter, as well as one of the first described fractal curves, the Koch snowflake.

雪花和结霜表面的冰晶会形成重复图案。这些图案启发人们去思考意识的力量是如何影响物质的,另外在这些图案中科赫雪花(Koch snowflake)也是第一种被详细描述的分形曲线。

Images: 1) Flickr/mommamia. 2) Flickr/monteregina.

图片来源:1)Flickr/mommamia   2)Flickr/monteregina

Waterfall

瀑布

Similar to canyons, a combination of rock irregularity and gravity produces repeating patterns as water flows over the side of a sharp ledge.

和峡谷类似,瀑布水流在流经陡峭的岩架面时,不规则岩石和重力的协同作用会产生重复图案。

Image: Flickr/catdancing

图片来源:Flickr/catdancing

River Delta

河流三角洲

The Yukon River branches into thousands of distributary channels as it drains into the Bering Sea off the coast of Alaska. The river is flowing right to left in the image, with the Bering Sea visible in the far left side of the image.

育空河(Yukon River)流入白令海(Bering Sea )之前,在阿拉斯加海岸附近形成数千条分流河道。图中河流的流向是自右至左,最左边的白令海清晰可见。

Image: NASA.

图片来源:NASA