fractals

简明释义

英[ˈfræk.təl]美[ˈfræk.təl]

n. 碎形；分形学（fractal 的复数）

英英释义

单词用法

同义词

反义词

例句

1.In particular we point out it is difficult to obtain real fractal dimensions for natural fractals with unknown dynamic system.

特别指出对于未知动力学系统的自然界中的分形，很难获得真正的分形维数。

2.In the fractals pictured above, points that are very close together can be different colors.

在以上不规则描绘里，必须接近的点可以是不同颜色。

3.Several deformation and stress states of offshore structures are described by using variable dimension fractals.

应用变维分形的方法描述了海工结构的几种变形和应力状态。

4.The work in this thesis can explain qualitatively the fractals of DNA sequences.

本论文的研究工作可以定性地解释DNA序列的分形现象。

5.The growth of RF aerogel fractals was simulated by computer.

采用分形概念对RF气凝胶的生长过程进行了计算机模拟。

6.The results show that the crevices in grasslands are the fractals and their spatial structure possesses the self-similarity.

结果得出草原地裂缝是一种分形体，它的分布结构具有自相似性。

7.There are many applications of fractals in logging interpretation.

单一分形在测井解释方面已有许多应用。

8.The fractal characteristics of forest landscape on Mosaic structure model at Baiyun region in Guangzhou was analyzed using fractals.

利用分形理论建立了广州白云区森林景观镶嵌结构的回归模型。

9.The artist used fractals to create stunning visual patterns in her paintings.

这位艺术家使用分形在她的画作中创造了惊艳的视觉图案。

10.In mathematics, fractals are often studied for their complex structures and self-similarity.

在数学中，分形常因其复杂的结构和自相似性而被研究。

11.Computer simulations can generate fractals that mimic natural phenomena like coastlines.

计算机模拟可以生成模拟自然现象（如海岸线）的分形。

12.The concept of fractals can be applied in computer graphics to create realistic landscapes.

在计算机图形学中，可以应用分形的概念来创建逼真的风景。

13.Biologists have found that certain patterns in nature can be described using fractals.

生物学家发现，自然界中的某些模式可以用分形来描述。

作文

In the realm of mathematics and art, fractals are fascinating structures that exhibit self-similarity across different scales. The concept of fractals can be traced back to the work of mathematicians such as Benoit Mandelbrot, who introduced the term in the late 20th century. A fractals is a complex geometric shape that can be split into parts, each of which is a reduced-scale copy of the whole. This property is known as self-similarity, and it is a defining characteristic of fractals. One of the most famous examples of fractals is the Mandelbrot set, which is defined by a simple mathematical equation but produces an infinitely intricate boundary when plotted on a graph. As one zooms in on the boundary of the Mandelbrot set, new patterns emerge, displaying the beauty and complexity inherent in fractals. This infinite detail is what makes fractals not only a subject of mathematical study but also a source of inspiration for artists and designers. The applications of fractals extend beyond pure mathematics and art. In nature, fractals can be observed in various phenomena, such as the branching of trees, the formation of snowflakes, and the structure of coastlines. These natural fractals demonstrate how complex patterns can arise from simple rules, a concept that resonates with both scientists and philosophers alike. In computer graphics, fractals are used to create realistic landscapes and textures. By employing algorithms that mimic the self-similar properties of fractals, artists can generate stunning visual effects that would be difficult to achieve through traditional methods. This intersection of mathematics and art has led to a growing interest in fractals within the digital realm, where they serve as a bridge between creativity and computation. Furthermore, fractals have practical applications in fields such as medicine and telecommunications. For instance, researchers have discovered that certain biological structures, like blood vessels and lungs, exhibit fractals patterns, which can help in understanding their functions and improving medical treatments. In telecommunications, fractals are used in antenna design, allowing for more efficient transmission of signals. In conclusion, fractals represent a captivating intersection of mathematics, art, and nature. Their unique properties and applications make them a rich subject for exploration and discovery. Whether one is drawn to the aesthetic beauty of fractals in art or the profound implications they hold in science, there is no denying the impact of these remarkable structures on our understanding of the world. As we continue to study and appreciate fractals, we gain insight not only into the complexities of mathematics but also into the very fabric of reality itself. The journey through the world of fractals is one that invites curiosity, creativity, and a deeper appreciation for the patterns that surround us.

在数学和艺术的领域中，分形是迷人的结构，展现了不同尺度上的自相似性。分形的概念可以追溯到20世纪末数学家本诺特·曼德博特的工作，他首次提出了这个术语。分形是一种复杂的几何形状，可以被分割成部分，每个部分都是整体的缩小版。这种属性被称为自相似性，是分形的一个定义特征。 最著名的分形例子之一是曼德博特集合，它由一个简单的数学方程定义，但在绘制图形时会产生无穷复杂的边界。当人们放大曼德博特集合的边界时，会出现新的图案，展示出分形固有的美丽和复杂性。这种无限细节使得分形不仅成为数学研究的主题，也是艺术家和设计师的灵感来源。 分形的应用超越了纯数学和艺术。在自然界中，分形可以在各种现象中观察到，例如树木的分枝、雪花的形成和海岸线的结构。这些自然分形展示了如何从简单的规则中产生复杂的图案，这一概念在科学家和哲学家之间引起了共鸣。 在计算机图形学中，分形用于创建逼真的风景和纹理。通过使用模拟分形自相似属性的算法，艺术家可以生成惊人的视觉效果，这些效果通过传统方法难以实现。这种数学与艺术的交汇导致了对数字领域中分形日益增长的兴趣，在这里它们作为创造力与计算之间的桥梁。 此外，分形在医学和电信等领域也有实际应用。例如，研究人员发现某些生物结构，如血管和肺部，表现出分形模式，这有助于理解其功能并改善医疗治疗。在电信中，分形用于天线设计，使信号传输更加高效。 总之，分形代表了数学、艺术和自然的迷人交汇点。它们独特的属性和应用使其成为探索和发现的丰富主题。无论一个人是被艺术中分形的美学吸引，还是被它们在科学中所蕴含的深刻意义所吸引，都无法否认这些非凡结构对我们理解世界的影响。随着我们继续研究和欣赏分形，我们不仅深入了解数学的复杂性，也更深刻地理解现实本身的构造。探索分形的旅程邀请我们保持好奇心、创造力，并对我们周围的图案有更深的欣赏。