Question

能有高手帮我翻译一下这段吗？我是新人，谢谢！最好不要机器翻译的哦，谢谢

分形几何
普通几何学研究的对象，一般都具有整数的维数。比如，零维的点、一维的线、二维的面、三维的立体、乃至四维的时空。最近十几年的，产生了新兴的分形几何学，空间具有不一定是整数的维，而存在一个分数维数，这是几何学的新突破，引起了数学家和自然科学者的极大关注。
分形几何的产生
客观自然界中许多事物，具有自相似的“层次”结构，在理想情况下，甚至具有无穷层次。适当的放大或缩小几何尺寸，整个结构并不改变。不少复杂的物理现象，背后就是反映着这类层次结构的分形几何学。
客观事物有它自己的特征长度，要用恰当的尺度去测量。用尺来测量万里长城，嫌太短；用尺来测量大肠杆菌，又嫌太长。从而产生了特征长度。还有的事物没有特征尺度，就必须同时考虑从小到大的许许多多尺度（或者叫标度），这叫做“无标度性”的问题。
如物理学中的湍流，湍流是自然界中普遍现象，小至静室中缭绕的轻烟，巨至木星大气中的涡流，都是十分紊乱的流体运动。流体宏观运动的能量，经过大、中、小、微等许许多度尺度上的漩涡，最后转化成分子尺度上的热运动，同时涉及大量不同尺度上的运动状态，就要借助“无标度性”解决问题，湍流中高漩涡区域，就需要用分形几何学。
数学家柯赫(Koch)从一个正方形的“岛”出发，始终保持面积不变，把它的“海岸线”变成无限曲线，其长度也不断增加，并趋向于无穷大。以后可以看到，分维才是“Koch岛”海岸线的确切特征量，即海岸线的分维均介于1到2之间。
这些自然现象，特别是物理现象和分形有着密切的关系，银河系中的若断若续的星体分布，就具有分维的吸引子。多孔介质中的流体运动和它产生的渗流模型，都是分形的研究对象。这些促使数学家进一步的研究，从而产生了分形几何学。
电子计算机图形显示协助了人们推开分形几何的大门。这座具有无穷层次结构的宏伟建筑，每一个角落里都存在无限嵌套的迷宫和回廊，促使数学家和科学家深入研究。
分形几何的内容
分形几何学的基本思想是：客观事物具有自相似的层次结构，局部与整体在形态、功能、信息、时间、空间等方面具有统计意义上的相似性，成为自相似性。例如，一块磁铁中的每一部分都像整体一样具有南北两极，不断分割下去，每一部分都具有和整体磁铁相同的磁场。这种自相似的层次结构，适当的放大或缩小几何尺寸，整个结构不变。
分形几何学的应用
分形几何学已在自然界与物理学中得到了应用。如在显微镜下观察落入溶液中的一粒花粉，会看见它不间断地作无规则运动(布朗运动)，这是花粉在大量液体分子的无规则碰撞(每秒钟多达十亿亿次)下表现的平均行为。布朗粒子的轨迹，由各种尺寸的折线连成。只要有足够的分辨率，就可以发现原以为是直线段的部分，其实由大量更小尺度的折线连成。这是一种处处连续，但又处处无导数的曲线。这种布朗粒子轨迹的分维是 2，大大高于它的拓扑维数 1。
在某些电化学反应中，电极附近成绩的固态物质，以不规则的树枝形状向外增长。受到污染的一些流水中，粘在藻类植物上的颗粒和胶状物，不断因新的沉积而生长，成为带有许多须须毛毛的枝条状，就可以用分维。
自然界中更大的尺度上也存在分形对象。一枝粗干可以分出不规则的枝杈，每个枝杈继续分为细杈……，至少有十几次分支的层次，可以用分形几何学去测量。
近几年在流体力学不稳定性、光学双稳定器件、化学震荡反映等试验中，都实际测得了混沌吸引子，并从实验数据中计算出它们的分维。学会从实验数据测算分维是最近的一大进展。分形几何学在物理学、生物学上的应用也正在成为有充实内容的研究领域。

Answer 1

Fractal geometry general geometry and the auditorium was generally have integral dimension. For example, the zero-dimensional, one-dimensional line, the two-dimensional surface, the three-dimensional to three-dimensional, as well as four-dimensional space-time. Recently more than 10 years, a new fractal geometry, the space is not necessarily integral dimension, and the existence of a fractal dimension, which is a breakthrough in geometry, a mathematician and natural sciences were aroused great concern. The objective of fractal geometry have many things in nature, is self-similar "level" structure, in ideal circumstances, even with infinite levels. Appropriate enlarged or reduced geometry, the entire structure will not change. Many complex physical phenomena behind this is reflected in the hierarchical structure of fractal geometry. Objective things has its own characteristic length, with appropriate scale of measurement. With a yardstick to measure the Great Wall, too short; E. coli measured with a yardstick, too long. Resulting in the characteristic length. Some things do not feature length, it is necessary to consider many small to large scale (or called scaling). This is called a "scale" problem. If physics of turbulence, turbulence is a common phenomenon in nature, which wind around the small Quiet Room Light Smoke. Jupiter's atmosphere to a huge vortex, are very disordered fluid. Macroscopic fluid movement of energy through large, small and micro scale so many, many degrees in the whirlpool. Finally into molecular-scale movement of hot, a lot of movement on different scales. we must rely on a "scale" to solve the problem, regional turbulence high whirlpool, it is necessary to use fractal geometry. Mathematicians comment (Koch) from a square in the "islands", and always maintain the same area. it is the "coast" into infinite curve, the length has been increased, and tends to infinity. Then you can see that the fractal dimension is the "Koch island," the exact features coastline. that the fractal dimension of the coastline between ranged from one to two. These natural phenomena, particularly physical phenomena are closely related and fractal, if the Galaxy continue if the stars continued distribution It is in the attractor dimension. It fluids in porous media campaigns and the flow model is fractal research. Mathematicians prompted further studies, thus creating a fractal geometry. Computer graphics help people once the door to fractal geometry. The hierarchical structure of this magnificent building with infinite, unlimited nested there every corner of the maze and corridors. Mathematicians and scientists urge depth study. Fractal geometry as fractal geometry : the basic objective is the level of self-similar structure of things. In partial and overall morphology, function, information, time, space and other aspects of the statistical significance of similarity, become self-similarity. For example, a piece of the magnet is the same each and every part of the North and South Poles as a whole, divided indefinitely. and each and every part of the overall magnet with the same magnetic field. Such self-similar structure, and appropriate geometric size enlarged or reduced, the whole structure unchanged. Fractal geometry of the fractal geometry of nature and physics has been applied. If the solution under the microscope into one piece of pollen, it will be seen as an uninterrupted rule Movement (Brownian motion). This is a lot of pollen in the liquid without rules collisions (up Shiyiyi times per second) the average performance of acts. Brown, particle trajectory, from the size of the broken link. Provided there is adequate resolution, we can find that line of thought is, in fact, a lot more small-scale linked to the dogleg. This is a continuous everywhere, but making a derivative of the curve. This is the fractal dimension of particle trajectories Brown 2, which was much higher than the number of one-dimensional topology. In some electrochemical reaction, the solid results near the electrode material to the irregular shape of branches growing outward. Some water pollution, algae in the sticky particles and jelly, constantly grow new deposition. Many have become with the need for everyone shoots like, we can use fractal dimension. There are also greater scale natural fractal object. Crude stem irregular Harbin branch can be set aside each forking…… Harbin continue to be divided into small, at least more than 10 times the level of branches. Fractal geometry can be measured. Hydrodynamic instability in recent years, the two stable optical devices, chemical and other tests to reflect fluctuations, chaotic attractor are actually measured and calculated from the experimental data dimension. Experimental data from the Institute of fractal dimension calculations is a great progress recently. Fractal geometry and physics, biology is becoming a solid content of the research field.