Geometry of fractals and vector calculus on fractals

分形几何和分形矢量微积分

• 批准号: 238549-2012
• 负责人: Mendivil, Franklin
• 金额: $ 0.87万
• 依托单位: Acadia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=524370
• 关键词: Geometry; fractals; vector; calculus

Most people have encountered beautiful pictorial depictions of fractals at one point or another. However, it may come as a surprise to many that fractals play a useful role in scientific areas such as data compression, analyzing stream networks and modelling other physical phenomena. The defining characteristic of a fractal is its self-similarity. That is, small bits of a fractal bear a striking resemblance to the entire fractal. Many natural phenomena have this same type of scaling behaviour, but usually only as an approximation. However, it is often a good enough approximation to be descriptively or predictively useful and so fractals have found their way into most areas of science.

大多数人都曾在某个时刻看到过分形的美丽图像。 然而，许多人可能会感到惊讶的是，分形在数据压缩，分析流网络和建模其他物理现象等科学领域中发挥着有用的作用。 分形的定义特征是它的自相似性。 也就是说，分形的一小部分与整个分形有着惊人的相似之处。 许多自然现象都有这种类似的标度行为，但通常只是近似值。 然而，它通常是一个足够好的近似值，可以预测或预测有用，因此分形已经进入了大多数科学领域。