【精彩圖集】令人稱(chēng)奇的自然分形圖案.doc

【精彩圖集】令人稱(chēng)奇的自然分形圖案從海洋貝類(lèi)、螺旋星系再到人類(lèi)肺部的結(jié)構(gòu)，混沌的模型無(wú)處不在。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. 分形是從混沌方程形成的一系列圖形，包含不斷放大的復(fù)雜自相似圖案。如果將一個(gè)分形圖案分為幾個(gè)部分，那么每一小塊都和整體形狀完全一樣。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.分形的數(shù)學(xué)之美在于可以從相對(duì)簡(jiǎn)單的方程推導(dǎo)出無(wú)限復(fù)雜的系統(tǒng)。通過(guò)多次迭代或重復(fù)分形生成方程，隨機(jī)輸出就可以產(chǎn)生獨(dú)特且可識(shí)別的美麗圖案。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圖形，下面我們將從中挑出一些最美麗的圖案，以饗讀者。Above:Romanesco Broccoli羅馬花椰菜（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.這種花椰菜的變種形式是一種極限分形蔬菜。它的圖案是斐波納契（Fibonacci）黃金螺旋的自然呈現(xiàn)形式，在這個(gè)對(duì)數(shù)螺旋中，每一個(gè)直角轉(zhuǎn)彎與起始點(diǎn)的距離都被值所約束，值即黃金分割率。Image: Flickr/Tin.G.圖片來(lái)源：Flickr/Tin.G.Salt Flats鹽灘（Salt Flats）The San Francisco Bay salt flats pictured above have been used for commercial salt production for over a century.上圖中的舊金山灣（San Francisco Bay）鹽灘曾經(jīng)出產(chǎn)了將近一個(gè)世紀(jì)之久的商品鹽。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.下圖展示了世界上最大的鹽灘，即位于玻利維亞南部的烏尤尼巖沼（Salar de Uyuni）。結(jié)痂的鹽層展現(xiàn)出一種非常一致的隨機(jī)圖案模式，這就是分形的特征。Images: 1) Flickr/Tolka Rover. 2) Flickr/Mike D. Green.圖片來(lái)源：1）Flickr/Tolka Rover 2）Flickr/Mike D. GreenAmmonite Sutures菊石縫合線(xiàn)（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.已經(jīng)滅絕了6500萬(wàn)年之久的菊石是一種帶有多室螺旋狀外殼的海洋頭足類(lèi)動(dòng)物，其小室之間的阻隔即縫合線(xiàn)就是一種復(fù)雜的分形曲線(xiàn)。斯蒂芬杰古爾德（Stephen Jay Gould）曾以菊石縫合線(xiàn)隨時(shí)間的復(fù)雜性來(lái)論證不存在向著更高復(fù)雜性方向發(fā)展的進(jìn)化驅(qū)動(dòng)力，人類(lèi)的出現(xiàn)是一個(gè)“壯麗的偶然”，在宇宙中獨(dú)一無(wú)二。The shells of ammonites also grow as a logarithmic spiral, a pattern that appears often in nature, as with romanesco broccoli.和羅馬花椰菜一樣，菊石外殼也會(huì)按照對(duì)數(shù)螺旋的方式生長(zhǎng)，這種生長(zhǎng)模式在自然界中頗為常見(jiàn)。Ammonites also inspired this cathedral staircase in Barcelona, Spain.西班牙巴塞羅那一處教堂樓梯的設(shè)計(jì)靈感就來(lái)自于菊石。Images: 1) Flickr/cobalt123. 2) Flickr/Didier.bier. 3) Flickr/Edgley Cesar圖片來(lái)源：1）Flickr/cobalt123 2）Flickr/Didier.bier 3）Flickr/Edgley CesarMountains山脈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.地質(zhì)構(gòu)造作用力向上抬升地殼，侵蝕再將地殼撕得支離破碎，山脈從此形成，同時(shí)也產(chǎn)生了分形圖案。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.上圖是喜馬拉雅山脈（Himalayan Mountains）的高空?qǐng)D像，地球上許多最高的山峰都集中在這一帶。造山運(yùn)動(dòng)始于7000萬(wàn)年前，隨著印度板塊和歐亞大陸板塊的不斷碰撞，喜馬拉雅山脈還在被抬升。Image: NASA/GSFC/JPL, MISR Team.圖片來(lái)源：NASA/戈達(dá)德航天中心/噴氣推進(jìn)實(shí)驗(yàn)室，多角度輻射成像光譜儀小組（MISR Team）Ferns蕨類(lèi)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 Barnsleys Fern formula ultimately produce a unique fern-shaped object.蕨類(lèi)植物是最常見(jiàn)的自相似集合，這意味著不管放大或縮小多少倍，它們的圖案都可以進(jìn)行數(shù)學(xué)上的推導(dǎo)和重現(xiàn)。這種蕨類(lèi)圖形被稱(chēng)為巴恩斯利蕨，是以首創(chuàng)者邁克爾巴恩斯利（Michael Barnsley）的名字命名的，用于描述這種分形圖形的數(shù)學(xué)公式第一次表明，雖然混度遵循建立在非線(xiàn)性迭代方程上的確定規(guī)則，但它天生無(wú)法預(yù)測(cè)。換句話(huà)說(shuō)，就是重復(fù)利用巴恩斯利蕨類(lèi)公式所產(chǎn)生的隨機(jī)數(shù)可以形成一個(gè)蕨類(lèi)形狀的獨(dú)特物體。Images: 1) Flickr/cobalt123. 2) Flickr/CatDancing.圖片來(lái)源：1）Flickr/cobalt123 2）Flickr/CatDancingClouds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.上圖中的海洋層云（stratus clouds）圖是水文氣象衛(wèi)星（Aqua satellite）在遠(yuǎn)離非洲海岸的大西洋上所拍攝的照片，圖中分形狀的云彩圖案被一系列的對(duì)角線(xiàn)槽所擾亂。據(jù)NASA地球大觀（NASA Earth Observatory）網(wǎng)站介紹，在連續(xù)的成云區(qū)看到如此醒目的分界線(xiàn)特別不同尋常，科學(xué)家還在尋找出現(xiàn)分界線(xiàn)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 Krmn cloud streets, for the late fluid dynamicist Theodore von Krmn.下圖展示的是長(zhǎng)達(dá)320公里的云旋（cloud vortex），NASA的相關(guān)記錄顯示，這是有史以來(lái)所拍攝到的最長(zhǎng)云旋隊(duì)列。為了紀(jì)念已故的流體動(dòng)力學(xué)家西奧多馮卡門(mén)（Theodore von Krmn），這些云旋也被稱(chēng)為馮卡門(mén)云街（von Krmn 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.當(dāng)?shù)痛沟脑茖颖粛u嶼一類(lèi)的物體所阻礙時(shí)就會(huì)形成云街，飛機(jī)在飛行時(shí)機(jī)翼后方的氣流也會(huì)形成類(lèi)似的漩渦。Images: 1) Jeff Schmaltz/MODIS Land Rapid Response Team/NASA. 2) NASA.圖片來(lái)源：1）Jeff Schmaltz/MODIS地面快速反應(yīng)部隊(duì)（MODIS Land Rapid Response Team）/NASA 2）NASALeaves樹(shù)葉Many plants follow simple recursive formulas in generating their branching shapes and leaf patterns.很多植物在生成分枝形狀和葉片圖案時(shí)遵循簡(jiǎn)單的遞歸法則。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.具有諷刺意味的是，沿著主干道、次級(jí)干道和三級(jí)道路的森林砍伐模式也形成了相似的圖案，下面這幅照片拍攝的是巴西西部朗多尼亞州（Rondonia）的森林砍伐，朗多尼亞州是亞馬遜森林被砍伐最多的地區(qū)之一。Images: 1) Flickr/ CatDancing. 2) NASA.圖片來(lái)源：1）Flickr/ CatDancing 2）NASACanyons峽谷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.上面這幅大峽谷（ Grand Canyon）的偽彩色照片展示了科羅拉多河（Colorado River）幾百萬(wàn)年的沖刷所形成的分形圖案，圖中的紅色是植被區(qū)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.下面這幅偽彩色照片拍攝的是亞利桑那州的謝伊峽谷國(guó)家保護(hù)區(qū)（Canyon de Chelly National Monument），美國(guó)國(guó)家公園管理局（National Park Service）宣稱(chēng)該峽谷保護(hù)區(qū)是北美地區(qū)最長(zhǎng)的連續(xù)人居景觀之一。Images: 1) GeoEye/Space Imaging. 2) NASA.圖片來(lái)源：1）GeoEye/Space Imaging 2）NASALightning閃電The path lightning takes is formed step by step as it moves towards the ground, turning air into plasma.當(dāng)閃電沖向地面將空氣變?yōu)榈入x子體時(shí)，它所經(jīng)歷的路徑是逐步形成的。Images: 1) Flickr/thefost. 2) Flickr/Brujo+.圖片來(lái)源：1）Flickr/thefost 2）Flickr/Brujo+.Peacock Feathers孔雀羽毛Peacocks attract mates with the repeating patterns in their plumage.孔雀通過(guò)展現(xiàn)羽毛上的重復(fù)圖案吸引異性前來(lái)交配。Images: 1) Flickr/Digimist. 2) Flickr/Maia C.圖片來(lái)源：1）Flickr/Digimist 2）Flickr/Maia CSnowflakes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 desc