n.分形

原形：fractal复数：fractals

The Mandelbrot set is a famous fractal, displaying intricate patterns of self-similarity.
曼德勃罗集是一个著名的分形，展现出自我相似的复杂图案。
Fractals can be found in nature, such as the branching patterns of trees and the shapes of clouds.
分形在自然界中很常见，比如树木的分枝模式和云朵的形状。
The Koch snowflake is an example of a simple fractal, created by repeatedly adding smaller triangles to a shape.
科赫雪花是简单分形的一个例子，通过不断添加小三角形来构建形状。
Fractal geometry helps mathematicians understand the scaling properties of complex systems, like coastlines and mountains.
分形几何帮助数学家理解复杂系统如海岸线和山脉的缩放特性。
Fractal art often involves zooming in on a digital image to reveal more detailed patterns at increasingly smaller scales.
分形艺术常常涉及放大数字图像，以显示越来越小尺度上的更多细节。
Fractal algorithms are used in computer graphics for generating realistic images of natural phenomena, like clouds or fire.
分形算法被用于计算机图形学，以生成自然现象如云朵或火焰的真实图像。
The Hausdorff dimension is a mathematical concept used to describe the complexity of fractals, which can have dimensions between integers.
海德堡维度是描述分形复杂性的数学概念，其维度可以介于整数之间。
Fractals are used in finance to model stock market fluctuations, demonstrating the idea that small changes can lead to significant outcomes.
分形被用于金融领域，模拟股票市场的波动，体现小变化可能导致大影响的概念。
A fractal river network, like the one found in real-world river systems, exhibits a branching pattern that follows a self-similar structure.
分形河流网络，就像现实中河流系统那样，具有分支模式，遵循自我相似的结构。
Fractal analysis has applications in geology, where it helps researchers study rock formations and patterns of erosion over long periods.
分形分析在地质学中有应用，帮助研究人员研究岩石构造和长时间尺度下的侵蚀模式。