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大家好，我很乐意和大家探讨fractals的相关问题。这个问题集合涵盖了fractals的各个方面，我会尽力回答您的疑问，并为您带来一些有价值的信息。
1.分形的分形
2.《冰雪奇缘》30句中英文翻译
3.分形的历史
4.土木工程常用的英语
5.麦田怪圈英文介绍
分形的分形
人们谈论分形，常常有两种含义。其一，它的实际背景是什么？其二，它的确切定义是什么？
数学家研究分形，是力图以数学方法，模拟自然界存在的、及科学研究中出现的那些看似无规律的各种现象。在过去的几十年里，分形在物理学、材料科学、地质勘探、乃至股价的预测等方面都得到了广泛的应用或密切的注意，并且由于分形的引入，使得一些学科焕发了新的活力。数学上所说的分形，是抽象的。而人们认为是分形的那些自然界的具体对象，并不是数学家所说的分形，而是不同层次近似。
1985年，曼德布罗特获得Barnard奖章。这项奖励专门颁发给那些在物理科学或者其它自然科学中有重大贡献、有重大影响的人物。在每五年一次的获奖者名单中，有爱因斯坦、费米这样一批享誉世界的科学家,可见曼德布罗特的分形研究在科学上的地位和影响。1995年应中国科学界的邀请，曼德布罗特访问中国并进行演讲。
分形图形同常见的工程图迥然不同，分形图形一般都有自相似性，这就是说如果将分形图形的局部不断放大并进行观察，将发现精细的结构，如果再放大，就会再度出现更精细的结构，可谓层出不穷，永无止境。艺术家在分形画面的不同区域涂上不同的色彩，展现在我们面前的，将会是非常美丽的画面。
几乎在曼德布罗特获得Barnard奖章的同时，以德国布来梅大学的数学家和计算机专家H.Peotgen与P.Richter等为代表，在当时最先进的计算机图形工作站上制作了大量的分形图案；J. Hubbard等人还完成了一部名为《混沌》的计算机动画。接着，印刷着分形的画册、挂历、明信片、甚至T恤衫纷纷出笼。80年代中期开始，首先在西方发达国家，接着在中国，分形逐渐成为脍炙人口的词汇，甚至连十几岁的儿童也迷上了计算机上的分形游戏。我国北京的北方工业大学计算机图形学小组于1992年完成了一部计算机动画**《相似》，这部**集中介绍了分形图形的相似性，这也是我国采用计算机数字技术完成的第一部**，获得当年**电视部颁发的科技进步奖。
更多的人陶醉于分形，并非出自科学，而是倾心于分形之美。数学上的审美很难为一般人所理解：一大堆数字、公式、符号怎么体现出来呢？然而，计算机能让数学的某些内在的美直观呈现出来，给出其形式化的表达。分形作为一类例证，为数学理论与实践中所蕴涵的美，给出了一类精彩的注记。充分反映了数学科学中的简单、和谐、统一的内涵！
一方面，从来不以科学内容本身为主题的艺术创作，也大量引用“动力系统”、“迭代逼近”、“混沌吸引子”等科学术语，进而极力采用计算机绘图手段，创造出无比神奇的作品。由这一点出发，可以说，艺术家已经开始漫步于科学领地！
另一方面，一向以严肃表情面向读者的科学著作一反常态，书名也竟然浪漫起来：《The Beauty of Fractals》(分形之美)(1986),《Fractals Everywhere》(分形处处可见),《The Algorithmic Beauty of Plants》(植物算法中的美)(1990), ….大量精美的、显示分形的科学挂图，乔装打扮，在美术馆展厅登场，接受艺术鉴赏家的评头论足，科学家也从此跨入了神圣的艺术殿堂！
分形之美，往往须经计算机的处理才能表现出来的。今天，人们可以在网络上，浏览与欣赏各种不同风格的分形作品，有的针对科学研究中要表达的一些特别的对象，有的则完全是艺术。网络天地会给你提供许多、美妙惊奇的分形图画，令你心犷神怡，也有时令你眼花缭乱。
《冰雪奇缘》30句中英文翻译
1. 文言版冰雪奇缘歌词翻译
let it go》文言文版《如释冰》The snow glows white on the mountain tonight霜辄夜白，日暮尽苍生远。
Not a footprint to be seen独游偶影江水寒。A kingdom of isolation山门内外蜃城孑然。
And it looks like I'm the queen王于冰雪定萧山。The wind is howling like this swirling storm inside风掣千刃，寒啸千载，慰我心安。
Couldn't keep it in, heaven knows I've tried身得托沧海，血以荐轩辕。Don't let them in, don't let them see勿近勿探，阴翳犹在。
Be the good girl you always have to be纲礼持之，也堪念存心善。Conceal, don't feel, don't let them know昨日无常，今时无往，Well, now they know然，尽矣说。
Let it go, let it go我如风，任去留。Can't hold it back anymore休将鸿鹄比伏囚。
Let it go, let it go我如虹，任天阔。Turn away and slam the door；且听狂澜度三秋。
I don't care what they're going to say毋言多，不敢同苟32313133353236313431303231363533e58685e5aeb931333335346131合。Let the storm rage on一霰风摊破。
The cold never bothered me anyway唯我，敢挑只身赴寒流。It's funny how some distance makes everything seem *** all啼笑远烟皆邈末，屋舍俨若蚁蝼。
And the fears that once controlled me can't get to me at all时维往矣不胜惶恐，今非彼可制我。It's time to see what I can do.To test the limits and break through适于旦夕，何以为兮。
假我之力，惊刹天地。No right, no wrong, no rules for me谁是谁非，方圆无稽。
I'm free肆意行。Let it go, let it go我如风，任去留。
I am one with the wind and sky浩荡中天气无咎。Let it go, let it go我如虹，任天阔。
You'll never see me cry初晴乍逢霁雨后。Here I stand and here I'll stay驾寒宫，划地为楼，Let the storm rage on不惧风萧索。
My power flurries through the air into the ground力拔千钧气贯地，聚息摄魄冰。My soul is spiraling in frozen fractals all around灵动珠齑腾霜起，重于游丝轻于絮。
And one thought crystallizes like an icy blast花晶盘郁撷绮思，玉宇观飞惊。I'm never going back, the past is in the past过眼翻覆往昔，何必执于归去。
Let it go, let it go我如风，任去留。And I'll rise like the break of dawn愿化羲和驱夜魔。
Let it go, let it go我如虹，任天阔。That perfect girl is gone无暇过隙便无踪。
Here I stand in the light of day驾寒宫，向阳高耸。Let the storm rage on一霰风摊破。
The cold never bothered me anyway唯我，敢挑只身赴寒流。
2. 文言版冰雪奇缘歌词翻译let it go》文言文版《如释冰》The snow glows white on the mountain tonight霜辄夜白，日暮尽苍生远。
Not a footprint to be seen独游偶影江水寒。A kingdom of isolation山门内外蜃城孑然。
And it looks like I'm the queen王于冰雪定萧山。The wind is howling like this swirling storm inside风掣千刃，寒啸千载，慰我心安。
Couldn't keep it in, heaven knows I've tried身得托沧海，血以荐轩辕。Don't let them in, don't let them see勿近勿探，阴翳犹在。
Be the good girl you always have to be纲礼持之，也堪念存心善。Conceal, don't feel, don't let them know昨日无常，今时无往，Well, now they know然，尽矣说。
Let it go, let it go我如风，任去留。Can't hold it back anymore休将鸿鹄比伏囚。
Let it go, let it go我如虹，任天阔。Turn away and slam the door；且听狂澜度三秋。
I don't care what they're going to say毋言多，不敢同苟合。Let the storm rage on一霰风摊破。
The cold never bothered me anyway唯我，敢挑只身赴寒流。It's funny how some distance makes everything seem *** all啼笑远烟皆邈末，屋舍俨若蚁蝼。
And the fears that once controlled me can't get to me at all时维往矣不胜惶恐，今非彼可制我。It's time to see what I can do.To test the limits and break through适于旦夕，何以为兮。
假我之力，惊刹天地。No right, no wrong, no rules for me谁是谁非，方圆无稽。
I'm free肆意行。Let it go, let it go我如风，任去留。
I am one with the wind and sky浩荡中天气无咎。Let it go, let it go我如虹，任天阔。
You'll never see me cry初晴乍逢霁雨后。Here I stand and here I'll stay驾寒宫，划地为楼，Let the storm rage on不惧风萧索。
My power flurries through the air into the ground力拔千钧气贯地，聚息摄魄冰。My soul is spiraling in frozen fractals all around灵动珠齑腾霜起，重于游丝轻于絮。
And one thought crystallizes like an icy blast花晶盘郁撷绮思，玉宇观飞惊。I'm never going back, the past is in the past过眼翻覆往昔，何必执于归去。
Let it go, let it go我如风，任去留。And I'll rise like the break of dawn愿化羲和驱夜魔。
Let it go, let it go我如虹，任天阔。That perfect girl is gone无暇过隙便无踪。
Here I stand in the light of day驾寒宫，向阳高耸。Let the storm rage on一霰风摊破。
The cold never bothered me anyway唯我，敢挑只身赴寒流。
3. 古文版《letitgo》歌词霜辄（zhé）夜白，日暮尽苍生远。
独游偶影江水寒。
山门内外蜃（shèn）城孑（jié）然。
王于冰雪定萧山。
风掣（chè）千刃，寒啸千载，慰我心安。
身得托沧海，血以荐轩辕。
勿近勿探，阴翳（yì）犹在。
纲礼持之，也堪念存心善。
昨日无常，今时无往，
然，尽矣说。
我如风，任去留。
休将鸿鹄（hóng hú）比伏囚。
我如虹，任天阔。
且听狂澜度三秋。
毋（wú）言多，不敢同苟合。
一霰（xiàn）风摊破。
唯我，敢挑只身赴寒流。
啼笑远烟皆邈（miǎo）末，屋舍俨（yǎn）若蚁蝼。
时维往矣不胜惶恐，今非彼可制我。
适于旦夕，何以为兮。假我之力，惊刹天地。
谁是谁非，方圆无稽。
肆意行。
我如风，任去留。
浩荡中天气无咎（jiù）。
我如虹，任天阔。
初晴乍逢霁（jì）雨后。
驾寒宫，划地为楼，
不惧风萧索。
力拔千钧气贯地，聚息摄魄冰。
灵动珠齑（jī）腾霜起，重于游丝轻于絮。
花晶盘郁撷（xié）绮（qǐ）思，玉宇观飞惊。
过眼翻覆往昔，何必执于归去。
我如风，任去留。
愿化羲和驱夜魔。
我如虹，任天阔。
无暇过隙便无踪。
驾寒宫，向阳高耸。
一霰（xiàn）风摊破。
唯我，敢挑只身赴寒流。
4. 冰雪奇缘中文歌词最低0.27元开通文库会员，查看完整内容> 原发布者：轩辕芊子 Letitgo（随它吧）冰雪奇缘主题曲Letitgo随它吧随它吧Letitgo随它吧随它吧Can'tholdyoubackanymore回头已没有办法Letitgo随它吧随它吧Letitgo随它吧随它吧Turnmybackandslamthedoor.一转身不再牵挂Thesnowblowswhiteonthemountaintonight白雪发亮铺满我的过往Notafootprinttobeseen看不到任何足迹AkingdomofisolationanditlookslikeI'mtheQueen孤立国度很荒凉我是这里的女皇Thewindishowlingliketheswirlingstorminside漫天飞霜像心里的风暴一样Couldn'tkeepitin,heavenknowsItried再也待不下去，我已尽力了Don'tletthemin,don'tletthemsee不能让他们进来，不能让他们发现Bethegoodgirl做我自己就像我的从前Youalwayshadtobe躲在现实梦境之间不被发现Well,nowtheyknow既然他们现在已经知道了Letitgo随它吧随它吧Letitgo随它吧随它吧Can'tholdyoubackanymore回头已没有办法Letitgo随它吧随它吧Letitgo随它吧随它吧Turnmybackandslamthedoor一转身不再牵挂AndhereIstand,andhereI'llstay我所立之处，将是我待的地方Letitgo随它吧随它吧Letitgo随它吧随它吧Thecoldneverbotheredmeanyway反正冰天雪地我也不怕It'sfunnyhowsomedistance保持一些距离世界变得更有趣Makeseverythingseem *** all使世间万物显得渺小AndthefearsthatoncecontrolledmeCan'tgett。
5. 冰雪奇缘中文歌词随它吧
回头已没有办法
随它吧 随它吧
一转身不再牵挂
白雪发亮 铺满我的过往
没有脚印的地方
孤立国度很荒凉
我是这里的女皇
漫天飞霜 像心里的风暴一样
只有天知道 我受过的伤
不让别人进来看见
做我自己就像我的从前
躲在现实梦境之间 不被发现
随它吧 随它吧
回头已没有办法
随它吧 随它吧
一转身不再牵挂
悬崖上 让我留下
随它吧 随它吧
反正冰天雪地我也不怕
留一点点的距离 让我跟世界分离
曾经困扰我的恐惧 消失在我回忆
夜里冰冷的空气 我终于能呼吸
我留下自己的过去 抹掉眼泪的痕迹
随它吧 随它吧
回头已没有办法
随它吧 随它吧
一转身不再牵挂
悬崖上 让我留下
随它吧 随它吧
反正冰天雪地我也不怕
封闭生活 我生命的选择
别再找我 过去已经离开我
风雪已淹没
随它吧 随它吧
回头已没有办法
随它吧 随它吧
一转身不再牵挂
悬崖上 让我留下
随它吧 随它吧
反正冰天雪地我也不怕
随它吧
楼主望采纳~
6. 《冰雪奇缘》里的所有歌词谁有The snow glows white on the mountain tonight
Not a footprint to be seen
A kingdom of isolation, and it looks like I'm the Queen
The wind is howling like the swirling storm inside
Couldn't keep it in; Heaven knows I've tried
Don't let them in, don't let them see
Be the good girl you always have to be
Conceal, don't feel, don't let them know
Well now they know
Let it go, let it go
Can't hold it back any more
Let it go, let it go
Turn away and slam the door
I don't care what they're going to say
Let the storm rage on
The cold never bothered me anyway
It's funny how some distance
Makes everything seem *** all
And the fears that once controlled me
Can't get to me at all
It's time to see what I can do
To test the limits and break through
No right, no wrong, no rules for me,
I'm free!
Let it go, let it go
I am one with the wind and sky
Let it go, let it go
You'll never see me cry
Here I stand
And here I'll stay
Let the storm rage on
My power flurries through the air into the ground
My soul is spiraling in frozen fractals all around
And one thought crystallizes like an icy blast
I'm never going back, the past is in the past
Let it go, let it go
And I'll rise like the break of dawn
Let it go, let it go
That perfect girl is gone
Here I stand
In the light of day
Let the storm rage on
The cold never bothered me anyway!
7. 求let it go文言文版制作好的歌词,歌词已有,求制作LRC歌词本人的回答已注上拼音，，谢谢！ 霜辄（zhé）夜白，日暮尽苍生远。
独游偶影江水寒。 山门内外蜃（shèn）城孑（jié）然。
王于冰雪定萧山。 风掣（chè）千刃，寒啸千载，慰我心安。
身得托沧海，血以荐轩辕。 勿近勿探，阴翳（yì）犹在。
纲礼持之，也堪念存心善。 昨日无常，今时无往， 然，尽矣说。
我如风，任去留。 休将鸿鹄（hóng hú）比伏囚。
我如虹，任天阔。 且听狂澜度三秋。
毋（wú）言多，不敢同苟合。 一霰（xiàn）风摊破。
唯我，敢挑只身赴寒流。 啼笑远烟皆邈（miǎo）末，屋舍俨（yǎn）若蚁蝼。
时维往矣不胜惶恐，今非彼可制我。 适于旦夕，何以为兮。
假我之力，惊刹天地。 谁是谁非，方圆无稽。
肆意行。 我如风，任去留。
浩荡中天气无咎（jiù）。 我如虹，任天阔。
初晴乍逢霁（jì）雨后。 驾寒宫，划地为楼， 不惧风萧索。
力拔千钧气贯地，聚息摄魄冰。 灵动珠齑（jī）腾霜起，重于游丝轻于絮。
花晶盘郁撷（xié）绮（qǐ）思，玉宇观飞惊。过眼翻覆往昔，何必执于归去。
我如风，任去留。 愿化羲和驱夜魔。
我如虹，任天阔。 无暇过隙便无踪。
驾寒宫，向阳高耸。 一霰（xiàn）风摊破。
唯我，敢挑只身赴寒流。
8. 冰雪奇缘的所有歌一、歌名：Do you want to build a snowman 演唱：Kristen Bell,Agatha Lee Monn,Katie Lopez 词：Kristen Anderson-Lopez,Robert Lopez.曲：Kristen Anderson-Lopez,Robert Lope Do you want to build a snowman？你想堆雪人吗 Come on let's go and play！来吧我们一起去玩吧 I never see you anymore，我好久没见到你了 e out the door，出来吧 it's like you've gone away你就像消失了一样 We used to be best buddies我们以前是最好的伙伴 and now we're not, I wish you would tell me why现在却变了，你能告诉我原因吗 Do you want to build a snowman？你想堆雪人吗 It doesn't have to be a snowman玩什么都可以呀 Okay,bye好吧，再见 Do you want to build a snowman？你想堆雪人吗 Or ride our bike around the halls？或在大厅里骑车 I think some pany is overdue，我觉得你早就该陪我了 I started talking to, the pictures on the walls我都开始跟墙上的画像说话了 Hang in there, Joan！简，站在那里别动哦 It gets a little lonely, all these empty rooms，这些空房子让人觉得好孤单 just watching the hours tick by只能看着时间滴滴答答地流逝 Please I know you're in there，求求你了，我知道你在里面 people are asking where you've been人们都在问你去了哪里 They say “have courage”，他们说：“要勇敢” and I'm trying to，我也在努力尝试 I'm right out here for you,just let me in我在外面等你，让我进去吧 We only have each other，我们只拥有彼此了 it's just you and me,what are we gonna do？只有你和我，我们应该怎么办 Do you want to build a snowman？你想堆个雪人吗 二、歌名：let it go 演唱：黛米·洛瓦托，伊迪娜·门泽尔 词：克里斯汀·安德森-洛佩兹，罗伯特·洛佩兹 曲：克里斯汀·安德森-洛佩兹，罗伯特·洛佩兹 Let it go 随它吧随它吧 Let it go 随它吧随它吧 Can't hold you back anymore 回头已没有办法 Let it go 随它吧随它吧 Let it go 随它吧随它吧 Turn my back and slam the door 一转身不再牵挂 The snow blows white on the mountain tonight 白雪发亮铺满我的过往 Not a footprint to be seen 看不到任何足迹 A kingdom of isolation and it looks like I'm the Queen 孤立国度很荒凉我是这里的女皇 The wind is howling like the swirling storm inside 漫天飞霜像心里的风暴一样 Couldn't keep it in, heaven knows I tried 再也待不下去 我已尽力了 Don't let them in, don't let them see不能让他们进来 不能让他们发现 Be the good girl .You always had to be做我自己就像我的从前 Conceal, don't feel Don't let them know 躲在现实梦境之间不被发现 Well, now they know 既然他们现在已经知道了 Let it go 随它吧随它吧 Let it go 随它吧随它吧 Can't hold you back anymore 回头已没有办法 扩展资料 《Let It Go》是华特迪士尼动画工作室的2013年动画**《冰雪奇缘》的主题曲，由克里斯汀·安德森-洛佩兹和罗伯特·洛佩兹作曲作词。
在**冰雪奇缘中，伊迪娜·门泽尔为主角艾莎配音并配唱，而收录于《冰雪奇缘》官方音乐带里是迪斯尼歌手黛米·洛瓦托版的《Let It Go》。2014年3月2日晚，《Let It Go》获得第86届奥斯卡最佳原创歌曲奖 ，伊迪娜·门泽尔在现场演唱了此曲 。
分形的历史
1、Stronger than a hundred men!谁人能挡寒冬至？
2.Hi, I'm Olaf and I like warm hugs.
嗨！我叫雪宝，喜欢热情的拥抱！
3.This icy force both foul and fair has a frozen heart worth mining.
不畏严寒的肆虐，一颗冰封的心等待着挖掘。
4.Split the ice apart!
掘开寒冰勇向前。
5.Strike for love And Strike for fear.
战胜恐惧求真爱。
6.Split the ice apart.And break the frozen heart.
打破寒冰。融化冰封的心。
土木工程常用的英语
在传统的几何学中，人们研究一个几何对象，总是习惯于在Euclid空间（Rn,Euclidean)对其研究和度量，其中字母n表示空间的维数，通常为整数，如n分别为1、2、3时，对应的空间为线性空间、平面空间、立体空间，在相应的空间中，我们可以测得几何对象的长度、面积、体积等。但是大约在1个世纪前，在数学领域，相继出现了一些被称为数学怪物（mathematical monsters)的东西，在传统的Euclid领域，人们无法用几何语言去表述其整体或局部性质，其中，比较著名的数学怪物包括：Von Koch曲线 此曲线在一维下测量任意段长度为无穷大（想象中，考虑到能测量原子的维度）；在二维下测量面积为零
Sierpinski三角形 此图形面积为零
Cantor集
这些数学怪物困扰数学家许多年，直至20世纪，被美国数学家Benoit B. Mandelbrot创立的分形几何学(fractal geometry)彻底解决。Mandelbrot提出：我们之所以无法用几何语言去描述这些数学怪物，是因为我们是在维数为整数的空间中，用维数同样是整数的“尺子”对其丈量、描述；而维数不应该仅仅是整数，可以是任何一个正实数；只有在几何对象对应的维数空间中，才能对该几何体进行合理的整体或局部描述。以上图的Koch曲线为例，其维数约为1.26，我们应用同样为1.26维的尺子对其进行描述，比如取该曲线前1/4段作为单位为1的尺子去丈量这个几何体，此几何体长度为4。也正是因其维数介于1维与2维之间，所以此几何体在1维下长度为无穷大，2维下面积为零。
Fractal这个词是由Mandelbrot于1975创造的，来源于拉丁文“Fractus”，其英文意思是broken，即为“不规则、支离破碎”的物体。1967年，Mandelbrot在美国《Science》杂志上发表题目为《英国的海岸线有多长》的划时代论文，标志着其分形思想萌芽的出现。1977年，Mandelbrot在巴黎出版的法文著作《Les objets fractals:forme,hasard et dimension》，1977年，在美国出版其英文版《Fractals:From,Chance,and Dimension》（《分形：形状机遇和维数》），同年，他又出版了《The Fractal Geometry of Nature》（《大自然的分形几何》），但是这三本书还未对社会和学术界造成太大的影响。直到1982年，《The Fractal Geometry of Nature》（《大自然的分形几何》）第二版才得到欧美社会的广泛关注，并迅速形成了“分形热”，此书也被分形学界视为分形“圣经”。
麦田怪圈英文介绍
土木工程 专业外语词汇大全
1. 综合类大地工程geotechnical engineering
1. 综合类反分析法back analysis method
1. 综合类基础工程foundation engineering
1. 综合类临界状态土力学critical state soil mechanics
1. 综合类数值岩土力学numerical geomechanics
1. 综合类土soil, earth
1. 综合类土动力学soil dynamics
1. 综合类土力学soil mechanics
1. 综合类岩土工程geotechnical engineering
1. 综合类应力路径stress path
1. 综合类应力路径法stress path method
2. 工程地质及勘察变质岩metamorphic rock
2. 工程地质及勘察标准冻深standard frost penetration
2. 工程地质及勘察冰川沉积glacial deposit
2. 工程地质及勘察冰积层（台）glacial deposit
2. 工程地质及勘察残积土eluvial soil, residual soil
2. 工程地质及勘察层理beding
2. 工程地质及勘察长石feldspar
2. 工程地质及勘察沉积岩sedimentary rock
2. 工程地质及勘察承压水confined water
2. 工程地质及勘察次生矿物secondary mineral
2. 工程地质及勘察地质年代geological age
2. 工程地质及勘察地质图geological map
2. 工程地质及勘察地下水groundwater
2. 工程地质及勘察断层fault
2. 工程地质及勘察断裂构造fracture structure
2. 工程地质及勘察工程地质勘察engineering geological exploration
2. 工程地质及勘察海积层（台）marine deposit
2. 工程地质及勘察海相沉积marine deposit
2. 工程地质及勘察花岗岩granite
2. 工程地质及勘察滑坡landslide
2. 工程地质及勘察化石fossil
2. 工程地质及勘察化学沉积岩chemical sedimentary rock
2. 工程地质及勘察阶地terrace
2. 工程地质及勘察节理joint
2. 工程地质及勘察解理cleavage
2. 工程地质及勘察喀斯特karst
2. 工程地质及勘察矿物硬度hardness of minerals
2. 工程地质及勘察砾岩conglomerate
2. 工程地质及勘察流滑flow slide
2. 工程地质及勘察陆相沉积continental sedimentation
2. 工程地质及勘察泥石流mud flow, debris flow
2. 工程地质及勘察年粘土矿物clay minerals
2. 工程地质及勘察凝灰岩tuff
2. 工程地质及勘察牛轭湖ox-bow lake
2. 工程地质及勘察浅成岩hypabyssal rock
2. 工程地质及勘察潜水ground water
2. 工程地质及勘察侵入岩intrusive rock
2. 工程地质及勘察取土器geotome
2. 工程地质及勘察砂岩sandstone
2. 工程地质及勘察砂嘴spit, sand spit
2. 工程地质及勘察山岩压力rock pressure
2. 工程地质及勘察深成岩plutionic rock
2. 工程地质及勘察石灰岩limestone
2. 工程地质及勘察石英quartz
2. 工程地质及勘察松散堆积物rickle
2. 工程地质及勘察围限地下水（台）confined ground water
2. 工程地质及勘察泻湖lagoon
2. 工程地质及勘察岩爆rock burst
2. 工程地质及勘察岩层产状attitude of rock
2. 工程地质及勘察岩浆岩magmatic rock, igneous rock
2. 工程地质及勘察岩脉dike, dgke
2. 工程地质及勘察岩石风化程度degree of rock weathering
2. 工程地质及勘察岩石构造structure of rock
2. 工程地质及勘察岩石结构texture of rock
2. 工程地质及勘察岩体rock mass
2. 工程地质及勘察页岩shale
2. 工程地质及勘察原生矿物primary mineral
2. 工程地质及勘察云母mica
2. 工程地质及勘察造岩矿物rock-forming mineral
2. 工程地质及勘察褶皱fold, folding
2. 工程地质及勘察钻孔柱状图bore hole columnar section
3. 土的分类饱和土saturated soil
3. 土的分类超固结土overconsolidated soil
3. 土的分类冲填土dredger fill
3. 土的分类充重塑土
3. 土的分类冻土frozen soil, tjaele
3. 土的分类非饱和土unsaturated soil
3. 土的分类分散性土dispersive soil
3. 土的分类粉土silt, mo
3. 土的分类粉质粘土silty clay
3. 土的分类高岭石kaolinite
3. 土的分类过压密土（台）overconsolidated soil
3. 土的分类红粘土red clay, adamic earth
3. 土的分类黄土loess, huangtu(China)
3. 土的分类蒙脱石montmorillonite
3. 土的分类泥炭peat, bog muck
3. 土的分类年粘土clay
3. 土的分类年粘性土cohesive soil, clayey soil
3. 土的分类膨胀土expansive soil, swelling soil
3. 土的分类欠固结粘土underconsolidated soil
3. 土的分类区域性土zonal soil
3. 土的分类人工填土fill, artificial soil
3. 土的分类软粘土soft clay, mildclay, mickle
3. 土的分类砂土sand
3. 土的分类湿陷性黄土collapsible loess, slumping loess
3. 土的分类素填土plain fill
3. 土的分类塑性图plasticity chart
3. 土的分类碎石土stone, break stone, broken stone, channery, chat, crushed sto
ne, deritus
3. 土的分类未压密土（台）underconsolidated clay
3. 土的分类无粘性土cohesionless soil, frictional soil, non-cohesive soil
3. 土的分类岩石rock
3. 土的分类伊利土illite
3. 土的分类有机质土organic soil
3. 土的分类淤泥muck, gyttja, mire, slush
3. 土的分类淤泥质土mucky soil
3. 土的分类原状土undisturbed soil
3. 土的分类杂填土miscellaneous fill
3. 土的分类正常固结土normally consolidated soil
3. 土的分类正常压密土（台）normally consolidated soil
3. 土的分类自重湿陷性黄土self weight collapse loess
4. 土的物理性质阿太堡界限Atterberg limits
4. 土的物理性质饱和度degree of saturation
4. 土的物理性质饱和密度saturated density
4. 土的物理性质饱和重度saturated unit weight
4. 土的物理性质比重specific gravity
4. 土的物理性质稠度consistency
4. 土的物理性质不均匀系数coefficient of uniformity, uniformity coefficient
4. 土的物理性质触变thixotropy
4. 土的物理性质单粒结构single-grained structure
4. 土的物理性质蜂窝结构honeycomb structure
4. 土的物理性质干重度dry unit weight
4. 土的物理性质干密度dry density
4. 土的物理性质塑性指数plasticity index
4. 土的物理性质含水量water content, moisture content
4. 土的物理性质活性指数
4. 土的物理性质级配gradation, grading
4. 土的物理性质结合水bound water, combined water, held water
4. 土的物理性质界限含水量Atterberg limits
4. 土的物理性质颗粒级配particle size distribution of soils, mechanical composi
tion of soil
4. 土的物理性质可塑性plasticity
4. 土的物理性质孔隙比void ratio
4. 土的物理性质孔隙率porosity
4. 土的物理性质粒度granularity, grainness, grainage
4. 土的物理性质粒组fraction, size fraction
4. 土的物理性质毛细管水capillary water
4. 土的物理性质密度density
4. 土的物理性质密实度compactionness
4. 土的物理性质年粘性土的灵敏度sensitivity of cohesive soil
4. 土的物理性质平均粒径mean diameter, average grain diameter
4. 土的物理性质曲率系数coefficient of curvature
4. 土的物理性质三相图block diagram, skeletal diagram, three phase diagram
4. 土的物理性质三相土tri-phase soil
4. 土的物理性质湿陷起始应力initial collapse pressure
4. 土的物理性质湿陷系数coefficient of collapsibility
4. 土的物理性质缩限shrinkage limit
4. 土的物理性质土的构造soil texture
4. 土的物理性质土的结构soil structure
4. 土的物理性质土粒相对密度specific density of solid particles
4. 土的物理性质土中气air in soil
4. 土的物理性质土中水water in soil
4. 土的物理性质团粒aggregate, cumularpharolith
4. 土的物理性质限定粒径constrained diameter
4. 土的物理性质相对密度relative density, density index
4. 土的物理性质相对压密度relative compaction, compacting factor, percent compa
ction, coefficient of compaction
4. 土的物理性质絮状结构flocculent structure
4. 土的物理性质压密系数coefficient of consolidation
4. 土的物理性质压缩性compressibility
4. 土的物理性质液限liquid limit
4. 土的物理性质液性指数liquidity index
4. 土的物理性质游离水（台）free water
4. 土的物理性质有效粒径effective diameter, effective grain size, effective siz
e
4. 土的物理性质有效密度effective density
4. 土的物理性质有效重度effective unit weight
4. 土的物理性质重力密度unit weight
4. 土的物理性质自由水free water, gravitational water, groundwater, phreatic wa
ter
4. 土的物理性质组构fabric
4. 土的物理性质最大干密度maximum dry density
4. 土的物理性质最优含水量optimum water content
5. 渗透性和渗流达西定律Darcy s law
5. 渗透性和渗流管涌piping
5. 渗透性和渗流浸润线phreatic line
5. 渗透性和渗流临界水力梯度critical hydraulic gradient
5. 渗透性和渗流流函数flow function
5. 渗透性和渗流流土flowing soil
5. 渗透性和渗流流网 flow net
5. 渗透性和渗流砂沸sand boiling
5. 渗透性和渗流渗流seepage
5. 渗透性和渗流渗流量seepage discharge
5. 渗透性和渗流渗流速度seepage velocity
5. 渗透性和渗流渗透力seepage force
5. 渗透性和渗流渗透破坏seepage failure
5. 渗透性和渗流渗透系数coefficient of permeability
5. 渗透性和渗流渗透性permeability
5. 渗透性和渗流势函数potential function
5. 渗透性和渗流水力梯度hydraulic gradient
6. 地基应力和变形变形deformation
6. 地基应力和变形变形模量modulus of deformation
6. 地基应力和变形泊松比Poisson s ratio
6. 地基应力和变形布西涅斯克解Boussinnesq s solution
6. 地基应力和变形残余变形residual deformation
6. 地基应力和变形残余孔隙水压力residual pore water pressure
6. 地基应力和变形超静孔隙水压力excess pore water pressure
6. 地基应力和变形沉降settlement
6. 地基应力和变形沉降比settlement ratio
6. 地基应力和变形次固结沉降secondary consolidation settlement
6. 地基应力和变形次固结系数coefficient of secondary consolidation
6. 地基应力和变形地基沉降的弹性力学公式elastic formula for settlement calculat
ion
6. 地基应力和变形分层总和法layerwise summation method
6. 地基应力和变形负孔隙水压力negative pore water pressure
6. 地基应力和变形附加应力superimposed stress
6. 地基应力和变形割线模量secant modulus
6. 地基应力和变形固结沉降consolidation settlement
6. 地基应力和变形规范沉降计算法settlement calculation by specification
6. 地基应力和变形回弹变形rebound deformation
6. 地基应力和变形回弹模量modulus of resilience
6. 地基应力和变形回弹系数coefficient of resilience
6. 地基应力和变形回弹指数swelling index
6. 地基应力和变形建筑物的地基变形允许值allowable settlement of building
6. 地基应力和变形剪胀dilatation
6. 地基应力和变形角点法corner-points method
6. 地基应力和变形孔隙气压力pore air pressure
6. 地基应力和变形孔隙水压力pore water pressure
6. 地基应力和变形孔隙压力系数Apore pressure parameter A
6. 地基应力和变形孔隙压力系数Bpore pressure parameter B
6. 地基应力和变形明德林解Mindlin s solution
6. 地基应力和变形纽马克感应图Newmark chart
6. 地基应力和变形切线模量tangent modulus
6. 地基应力和变形蠕变creep
6. 地基应力和变形三向变形条件下的固结沉降three-dimensional consolidation settl
ement
6. 地基应力和变形瞬时沉降immediate settlement
6. 地基应力和变形塑性变形plastic deformation
6. 地基应力和变形谈弹性变形elastic deformation
6. 地基应力和变形谈弹性模量elastic modulus
6. 地基应力和变形谈弹性平衡状态state of elastic equilibrium
6. 地基应力和变形体积变形模量volumetric deformation modulus
6. 地基应力和变形先期固结压力preconsolidation pressure
6. 地基应力和变形压缩层
6. 地基应力和变形压缩模量modulus of compressibility
6. 地基应力和变形压缩系数coefficient of compressibility
6. 地基应力和变形压缩性compressibility
6. 地基应力和变形压缩指数compression index
6. 地基应力和变形有效应力effective stress
6. 地基应力和变形自重应力self-weight stress
6. 地基应力和变形总应力total stress approach of shear strength
6. 地基应力和变形最终沉降final settlement
7. 固结巴隆固结理论Barron s consolidation theory
7. 固结比奥固结理论Biot s consolidation theory
7. 固结超固结比over-consolidation ratio
7. 固结超静孔隙水压力excess pore water pressure
7. 固结次固结secondary consolidation
7. 固结次压缩（台）secondary consolidatin
7. 固结单向度压密（台）one-dimensional consolidation
7. 固结多维固结multi-dimensional consolidation
7. 固结固结consolidation
7. 固结固结度degree of consolidation
7. 固结固结理论theory of consolidation
7. 固结固结曲线consolidation curve
7. 固结固结速率rate of consolidation
7. 固结固结系数coefficient of consolidation
7. 固结固结压力consolidation pressure
7. 固结回弹曲线rebound curve
7. 固结井径比drain spacing ratio
7. 固结井阻well resistance
7. 固结曼代尔－克雷尔效应Mandel-Cryer effect
7. 固结潜变（台）creep
7. 固结砂井sand drain
7. 固结砂井地基平均固结度average degree of consolidation of sand-drained groun
d
7. 固结时间对数拟合法logrithm of time fitting method
7. 固结时间因子time factor
7. 固结太沙基固结理论Terzaghi s consolidation theory
7. 固结太沙基－伦杜列克扩散方程Terzaghi-Rendulic diffusion equation
7. 固结先期固结压力preconsolidation pressure
7. 固结压密（台）consolidation
7. 固结压密度（台）degree of consolidation
7. 固结压缩曲线cpmpression curve
7. 固结一维固结one dimensional consolidation
7. 固结有效应力原理principle of effective stress
7. 固结预压密压力（台）preconsolidation pressure
7. 固结原始压缩曲线virgin compression curve
7. 固结再压缩曲线recompression curve
7. 固结主固结primary consolidation
7. 固结主压密（台）primary consolidation
7. 固结准固结压力pseudo-consolidation pressure
7. 固结K0固结consolidation under K0 condition
8. 抗剪强度安息角（台）angle of repose
8. 抗剪强度不排水抗剪强度undrained shear strength
8. 抗剪强度残余内摩擦角residual angle of internal friction
8. 抗剪强度残余强度residual strength
8. 抗剪强度长期强度long-term strength
8. 抗剪强度单轴抗拉强度uniaxial tension test
8. 抗剪强度动强度dynamic strength of soils
8. 抗剪强度峰值强度peak strength
8. 抗剪强度伏斯列夫参数Hvorslev parameter
8. 抗剪强度剪切应变速率shear strain rate
8. 抗剪强度抗剪强度shear strength
8. 抗剪强度抗剪强度参数shear strength parameter
8. 抗剪强度抗剪强度有效应力法effective stress approach of shear strength
8. 抗剪强度抗剪强度总应力法total stress approach of shear strength
8. 抗剪强度库仑方程Coulomb s equation
8. 抗剪强度摩尔包线Mohr s envelope
8. 抗剪强度摩尔－库仑理论Mohr-Coulomb theory
8. 抗剪强度内摩擦角angle of internal friction
8. 抗剪强度年粘聚力cohesion
8. 抗剪强度破裂角angle of rupture
8. 抗剪强度破坏准则failure criterion
8. 抗剪强度十字板抗剪强度vane strength
8. 抗剪强度无侧限抗压强度unconfined compression strength
8. 抗剪强度有效内摩擦角effective angle of internal friction
8. 抗剪强度有效粘聚力effective cohesion intercept
8. 抗剪强度有效应力破坏包线effective stress failure envelope
8. 抗剪强度有效应力强度参数effective stress strength parameter
8. 抗剪强度有效应力原理principle of effective stress
8. 抗剪强度真内摩擦角true angle internal friction
8. 抗剪强度真粘聚力true cohesion
8. 抗剪强度总应力破坏包线total stress failure envelope
8. 抗剪强度总应力强度参数total stress strength parameter
9. 本构模型本构模型constitutive model
9. 本构模型边界面模型boundary surface model
9. 本构模型层向各向同性体模型cross anisotropic model
9. 本构模型超弹性模型hyperelastic model
9. 本构模型德鲁克－普拉格准则Drucker-Prager criterion
9. 本构模型邓肯－张模型Duncan-Chang model
9. 本构模型动剪切强度
9. 本构模型非线性弹性模量nonlinear elastic model
9. 本构模型盖帽模型cap model
9. 本构模型刚塑性模型rigid plastic model
9. 本构模型割线模量secant modulus
9. 本构模型广义冯·米赛斯屈服准则extended von Mises yield criterion
9. 本构模型广义特雷斯卡屈服准则extended tresca yield criterion
9. 本构模型加工软化work softening
9. 本构模型加工硬化work hardening
9. 本构模型加工硬化定律strain harding law
9. 本构模型剑桥模型Cambridge model
9. 本构模型柯西弹性模型Cauchy elastic model
9. 本构模型拉特－邓肯模型Lade-Duncan model
9. 本构模型拉特屈服准则Lade yield criterion
9. 本构模型理想弹塑性模型ideal elastoplastic model
9. 本构模型临界状态弹塑性模型critical state elastoplastic model
9. 本构模型流变学模型rheological model
9. 本构模型流动规则flow rule
9. 本构模型摩尔－库仑屈服准则Mohr-Coulomb yield criterion
9. 本构模型内蕴时间塑性模型endochronic plastic model
9. 本构模型内蕴时间塑性理论endochronic theory
9. 本构模型年粘弹性模型viscoelastic model
9. 本构模型切线模量tangent modulus
9. 本构模型清华弹塑性模型Tsinghua elastoplastic model
9. 本构模型屈服面yield surface
9. 本构模型沈珠江三重屈服面模型Shen Zhujiang three yield surface method
9. 本构模型双参数地基模型
9. 本构模型双剪应力屈服模型twin shear stress yield criterion
9. 本构模型双曲线模型hyperbolic model
9. 本构模型松岗元－中井屈服准则Matsuoka-Nakai yield criterion
9. 本构模型塑性形变理论
9. 本构模型谈弹塑性模量矩阵elastoplastic modulus matrix
9. 本构模型谈弹塑性模型elastoplastic modulus
9. 本构模型谈弹塑性增量理论incremental elastoplastic theory
9. 本构模型谈弹性半空间地基模型elastic half-space foundation model
9. 本构模型谈弹性变形elastic deformation
9. 本构模型谈弹性模量elastic modulus
9. 本构模型谈弹性模型elastic model
9. 本构模型魏汝龙－Khosla－Wu模型Wei Rulong-Khosla-Wu model
9. 本构模型文克尔地基模型Winkler foundation model
9. 本构模型修正剑桥模型modified cambridge model
9. 本构模型准弹性模型hypoelastic model
10. 地基承载力冲剪破坏punching shear failure
10. 地基承载力次层（台）substratum
10. 地基承载力地基subgrade, ground, foundation soil
10. 地基承载力地基承载力bearing capacity of foundation soil
10. 地基承载力地基极限承载力ultimate bearing capacity of foundation soil
10. 地基承载力地基允许承载力allowable bearing capacity of foundation soil
10. 地基承载力地基稳定性stability of foundation soil
10. 地基承载力汉森地基承载力公式Hansen s ultimate bearing capacity formula
10. 地基承载力极限平衡状态state of limit equilibrium
10. 地基承载力加州承载比（美国）California Bearing Ratio
10. 地基承载力局部剪切破坏local shear failure
10. 地基承载力临塑荷载critical edge pressure
10. 地基承载力梅耶霍夫极限承载力公式Meyerhof s ultimate bearing capacity formu
la
10. 地基承载力普朗特承载力理论Prandel bearing capacity theory
10. 地基承载力斯肯普顿极限承载力公式Skempton s ultimate bearing capacity formu
la
10. 地基承载力太沙基承载力理论Terzaghi bearing capacity theory
10. 地基承载力魏锡克极限承载力公式Vesic s ultimate bearing capacity formula
10. 地基承载力整体剪切破坏general shear failure
11. 土压力被动土压力passive earth pressure
11. 土压力被动土压力系数coefficient of passive earth pressure
11. 土压力极限平衡状态state of limit equilibrium
11. 土压力静止土压力earth pressue at rest
11. 土压力静止土压力系数coefficient of earth pressur at rest
11. 土压力库仑土压力理论Coulomb s earth pressure theory
11. 土压力库尔曼图解法Culmannn construction
11. 土压力朗肯土压力理论Rankine s earth pressure theory
11. 土压力朗肯状态Rankine state
11. 土压力谈弹性平衡状态state of elastic equilibrium
11. 土压力土压力earth pressure
11. 土压力主动土压力active earth pressure
11. 土压力主动土压力系数coefficient of active earth pressure
12. 土坡稳定分析安息角（台）angle of repose
12. 土坡稳定分析毕肖普法Bishop method
12. 土坡稳定分析边坡稳定安全系数safety factor of slope
12. 土坡稳定分析不平衡推理传递法unbalanced thrust transmission method
12. 土坡稳定分析费伦纽斯条分法Fellenius method of slices
12. 土坡稳定分析库尔曼法Culmann method
12. 土坡稳定分析摩擦圆法friction circle method
12. 土坡稳定分析摩根斯坦－普拉斯法Morgenstern-Price method
12. 土坡稳定分析铅直边坡的临界高度critical height of vertical slope
12. 土坡稳定分析瑞典圆弧滑动法Swedish circle method
12. 土坡稳定分析斯宾赛法Spencer method
12. 土坡稳定分析泰勒法Taylor method
12. 土坡稳定分析条分法slice method
12. 土坡稳定分析土坡slope
12. 土坡稳定分析土坡稳定分析slope stability analysis
12. 土坡稳定分析土坡稳定极限分析法limit analysis method of slope stability
12. 土坡稳定分析土坡稳定极限平衡法limit equilibrium method of slope stability
12. 土坡稳定分析休止角angle of repose
12. 土坡稳定分析扬布普遍条分法Janbu general slice method
12. 土坡稳定分析圆弧分析法circular arc analysis
13. 土的动力性质比阻尼容量specific gravity capacity
13. 土的动力性质波的弥散特性dispersion of waves
13. 土的动力性质波速法wave velocity method
13. 土的动力性质材料阻尼material damping
13. 土的动力性质初始液化initial liquefaction
13. 土的动力性质地基固有周期natural period of soil site
13. 土的动力性质动剪切模量dynamic shear modulus of soils
13. 土的动力性质动力布西涅斯克解dynamic solution of Boussinesq
13. 土的动力性质动力放大因素dynamic magnification factor
13. 土的动力性质动力性质dynamic properties of soils
13. 土的动力性质动强度dynamic strength of soils
13. 土的动力性质骨架波akeleton waves in soils
13. 土的动力性质几何阻尼geometric damping
13. 土的动力性质抗液化强度liquefaction stress
13. 土的动力性质孔隙流体波fluid wave in soil
13. 土的动力性质损耗角loss angle
13. 土的动力性质往返活动性reciprocating activity
13. 土的动力性质无量纲频率dimensionless frequency
13. 土的动力性质液化liquefaction
13. 土的动力性质液化势评价evaluation of liquefaction potential
13. 土的动力性质液化应力比stress ratio of liquefaction
13. 土的动力性质应力波stress waves in soils
13. 土的动力性质振陷dynamic settlement
13. 土的动力性质阻尼damping of soil
13. 土的动力性质阻尼比damping ratio
14. 挡土墙挡土墙retaining wall
14. 挡土墙挡土墙排水设施
14. 挡土墙挡土墙稳定性stability of retaining wall
14. 挡土墙垛式挡土墙
14. 挡土墙扶垛式挡土墙counterfort retaining wall
14. 挡土墙后垛墙（台）counterfort retaining wall
14. 挡土墙基础墙foundation wall
14. 挡土墙加筋土挡墙r
Crop circles are patterns created by the flattening of crops such as wheat, barley, rye, or corn. The term crop circle entered the Oxford Dictionary in 1990.
Self-described pranksters Doug Bower and Dave Chorley claimed to have started the crop circle phenomenon in 1978.[1] Their work is continued by other groups of crop circle makers such as the circlemakers arts collective founded by John Lundberg in the early 1990s.[2]
It has been claimed that evidence suggesting these formations are caused by some force other than humans is found in hundreds of photographs of bent or warped growth nodes. Biophysicist W. C. Levengood's Crop Circle Reports are an example of claimed evidence and research gathered that attempts to show that these types of crop circles with these type of node-warping are clearly not man-made, and that they are not simply snapped and broken from impact or crushing, but by some intense focus of energy such as microwaves or spinning plasma vortex as concluded by Levengood.[3]
While it has been suggested that ball lightning and vortices in the wind might rarely produce isolated indentations in crops, neither is capable of the complex and often delicate patterns seen in more elaborate crop circles.
History
1678 pamphlet on the "Mowing-Devil"The earliest recorded image resembling a crop circle is depicted in an English woodcut pamphlet published in 1678 called the "Mowing-Devil". The image depicts a demon with a scythe mowing [4] an oval design in a field of oats. The pamphlet's text reads as follows:
Being a True Relation of a Farmer, who Bargaining with a Poor Mower, about the Cutting down Three Half Acres of Oats, upon the Mower's asking too much, the Farmer swore "That the Devil should Mow it, rather than He." And so it fell out, that that very Night, the Crop of Oats shew'd as if it had been all of a Flame, but next Morning appear'd so neatly Mow'd by the Devil, or some Infernal Spirit, that no Mortal Man was able to do the like.
Also, How the said Oats ly now in the Field, and the Owner has not Power to fetch them away.
A more recent historical report of crop circles was published in Nature, volume 22, pp. 290–291, 29 July 1880, and republished in the January 2000 issue of the Journal of Meteorology.[5] It describes the 1880 investigations by amateur scientist John Rand Capron:
"The storms about this part of Western Surrey have been lately local and violent, and the effects produced in some instances curious. Visiting a neighbour's farm on Wednesday evening (21st), we found a field of standing wheat considerably knocked about, not as an entirety, but in patches forming, as viewed from a distance, circular spots....I could not trace locally any circumstances accounting for the peculiar forms of the patches in the field, nor indicating whether it was wind or rain, or both combined, which had caused them, beyond the general evidence everywhere of heavy rainfall. They were suggestive to me of some cyclonic wind action,..."[6]
There are also many other anecdotal accounts of crop circles in Ufology literature that predate the modern crop circle phenomena, though some cases involve crops which were cut or burnt, rather than flattened.[7][8]
A crop circle in the form of a Triskelion[edit] Patterns
Early examples of crop circles were usually simple circular patterns of various sizes. After some years, more complex geometric patterns emerged. In addition to circle designs based on sacred geometry, some of the later formations, those occurring after 2000, are based on other principles, including fractals. Many crop circles now have fine intricate detail, regular symmetry and careful composition. Elements of three-dimensionality have been introduced, and some crop circles appear to be inspired by animals or religious symbols.[9]
[edit] Creators
In 1991, two men from Southampton, England, announced that they had conceived the idea as a prank at a pub near Winchester, Hampshire, during an evening in 1976. Inspired by the 1966 Tully Saucer Nests,[10] Doug Bower and Dave Chorley made their crop circles using planks, rope, hats and wire as their only tools: using a four-foot-long plank attached to a rope, they easily created circles eight feet in diameter. The two men were able to make a 40-foot (12 m) circle in 15 minutes.
The pair became frustrated when their work did not receive significant publicity, so in 1981, they created a circle in Matterley Bowl, a natural amphitheatre just outside Winchester, Hampshire—an area surrounded by roads from which a clear view of the field is available to drivers passing by. Their designs were at first simple circles. When newspapers claimed that the circles could easily be explained by natural phenomena, Bower and Chorley made more complex patterns. A simple wire with a loop, hanging down from a cap—the loop positioned over one eye—could be used to focus on a landmark to aid in the creation of straight lines. Later designs of crop circles became increasingly complicated.
Bower's wife had become suspicious of him, noticing high levels of mileage in their car. Eventually, fearing that his wife suspected him of adultery, Bower confessed to her, and subsequently, he and Chorley informed a British national newspaper. Chorley died in 1996, and Doug Bower has made crop circles as recently as 2004. Bower has said that, had it not been for his wife's suspicions, he would have taken the secret to his deathbed, never revealing that it was a hoax.[11]
Circlemakers.org, a group of crop circle makers founded by John Lundberg, have demonstrated that making what self-appointed cereologist experts state are "unfakeable" crop circles is possible. On more than one occasion, such cereologists have claimed that a crop circle was "genuine" when in fact the people making the circle had previously been filmed making the circle.[12]
A crop circle in SwitzerlandScientific American published an article by Matt Ridley,[13] who started making crop circles in northern England in 1991. He wrote about how easy it is to develop techniques using simple tools that can easily fool later observers. He reported on "expert" sources such as the Wall Street Journal who had been easily fooled and mused about why people want to believe supernatural explanations for phenomena that are not yet explained. Methods to create a crop circle are now well documented on the Internet.[14]
On the night of July 11–12, 1992, a crop-circle making competition, for a prize of several thousand UK pounds (partly funded by the Arthur Koestler Foundation), was held in Berkshire. The winning entry was produced by three helicopter engineers, using rope, PVC pipe, a trestle and a ladder. Another competitor used a small garden roller, a plank and some rope.
In 1992 Hungarian youths Gábor Takács and Róbert Dallos, both then 17, were the first people to be legally charged after creating a crop circle. Takács and Dallos, of the St. Stephen Agricultural Technicum, a high school in Hungary specializing in agriculture, created a 36-meter diameter crop circle in a wheat field near Székesfehérvár, 43 miles (69 km) southwest of Budapest, on June 8, 1992. On September 3, the pair appeared on Hungarian TV and exposed the circle as a hoax, showing photos of the field before and after the circle was made. As a result, Aranykalász Co., the owners of the land, sued the youngsters for 630,000 HUF (approximately $3000 USD) in damages. The presiding judge ruled that the students were only responsible for the damage caused in the 36-meter diameter circle, amounting to about 6,000 HUF (approximately $30 USD), and that 99% of the damage to the crops was caused by the thousands of visitors who flocked to Székesfehérvár following the media's promotion of the circle. The fine was eventually paid by the TV show, as were the students' legal fees.[citation needed]
好了，关于“fractals”的话题就讲到这里了。希望大家能够通过我的讲解对“fractals”有更全面、深入的了解，并且能够在今后的工作中更好地运用所学知识。
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