“这是一个分形问题，”马库斯说。
这里有几个可供下载的分形几何软件。
There are several fractal geometry software programs available for download.
分形几何在土壤学中的应用及其展望。
Application of Fractal Geometry in Pedology and its Prosptects.
质量是分形的。
花椰菜中的天然不规则分形(Fractal)。
希望将分形艺术的美分享给每一个人！
I wish I could share the beautiful fractal art with everyone!
典型的例子包括图形处理、强力搜索、分形和粒子模拟。
Classic examples include graphics processing, brute-force searching, fractals, and particle simulations.
电子计算机图形显示协助了人们推开分形几何的大门。
Computer graphics to help people open the door to fractal geometry.
当你实现你自己的改变时，想象自己是一个分形图形中的一个初始形状。
As you embrace your change, picture yourself as the initial shape in a fractal image.
分形几何的出现扩展了我们对建筑的维度与比例的传统认识。
The appearance of fractal geometry extended our former understanding about dimension and scale of architecture.
初步研究结果表明，用分形几何解释某些岩土问题是十分有效的。
The result of study shows that applying the fractal geometry to explain some problems in geotechnology is very effective.
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。
Fractals are patterns formed from chaotic equations and contain self-similar patterns of complexity increasing with magnification.
分形艺术也是近年来世界流行的艺术形式，是科学与艺术完美的结合。
Fractal art is an artistic form, much in fashion in recent years, as well as the perfect combination of science and arts.
把一个分形放大，你会看到更多的复杂性和重复性。这张图片被称为“海马尾巴”。
Zooming in on a fractal reveals ever-increasing complexity and repetition. This section is known as a "seahorse tail."
曼德尔勃特集合给图像设计师带来了许多乐趣。这里有几个可供下载的分形几何软件。
Graphic designers have lots of fun with the Mandelbrot set. There are several fractal geometry software programs available for download.
有些人喜爱分形艺术，这本身就是一类形式、颜色、细节与光线非常多变的艺术作品。
Same goes for the fractal art which itself is a very diversified form of artwork in terms of forms, colors, details and lights.
结果表明，在高中数学课程中开设“分形几何”这一选修专题不但必要而且可行。
The results show that setting fractal geometry as a selected topic at high school is not only necessary but also feasible.
分形理论作为一种描述客观世界的几何工具，在短短的时间内已成功应用于许多学科。
As a mathematic tool of modeling natural geometry, fractal theory has been found wide applications in varied fields with great success.
主要由轻质混凝土预制系统来建造，形状来自于埃塞俄比亚当地传统纺织物的分形图案。
It was built using a lightweight concrete prefab system, and the shapes come from a traditional Ethiopian fractal pattern commonly found in the local fabrics.
这个悬臂结构只有一端固定；所谓分形，就是指能够分叉成多个部分的结构，每个子结构与母结构是大体近似的。
A cantilevered beam is anchored at only one end; a fractal is a shape that can be split into parts, each of which is a smaller, though sometimes not exact, copy of the larger structure.
运用分形理论，不仅可以定性，而且可以定量地分析系统的运动状态，从而实现对复杂机械系统的故障诊断。
Used with fractal theory, the running state of the system can be analyzed not qualitatively but also quantitatively, and then the faults of complex machinery system can be diagnosed.
由于它们在所有的尺度上都呈现相似，分形经常被认为具有无限的复杂度（非正式的表述）” （Wikipedia）。
Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms)" (Wikipedia).
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。
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.
数学上的分形（fractals）是一种非常复杂的几何形状，这正是医生所要关注的，它是协助医生区分健康的细胞形态和癌变的一个重要特征。
The mathematics of fractals – very complex geometric shapes – is just what the doctor ordered, helping to capture the difference between the shape of a healthy cell and a cancerous one.
通过使用新的分析技术，埃雷兹·李伯曼和他的同事发现，基因组片段紧密地构成了一个“分形球”（译注：想象一下由面条揉成的球），尽管基因组片段相互扭曲纠缠，但它们之间却没有节点（译注：也就是面条球里的每根面条都不相交）。
Using new analytic techniques, Erez Lieberman and colleagues found that the genome is packed into what’s called a “fractal globule”—despite being intensely twisted, the string of genes never knots.
研究人员随后将X射线的光束收窄，使其只有十分之一毫米宽，这时他们发现，碎片形的区域只出现在射线照射的地方。
The researchers then narrowed down the X-ray beam so that it was just a tenth of a millimetre across and found that the fractal-like regions occurred only where the beam struck the sample.
在统计学中，风险管理的标准方法是基于“钟形曲线”（或曰正态分布）的，绝大多数结果分布在中间，极端情况十分罕见。
The standard statistical approach to risk management is based on a “bell curve” or normal distribution, in which most results are in the middle and extremes are rare.
在统计学中，风险管理的标准方法是基于“钟形曲线”（或曰正态分布）的，绝大多数结果分布在中间，极端情况十分罕见。
The standard statistical approach to risk management is based on a “bell curve” or normal distribution, in which most results are in the middle and extremes are rare.
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