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: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=547024
• 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.

大多数人在某一时刻遇到了对分形的美丽绘画描述。 但是，对于许多人来说，分形在数据压缩，分析流网络和对其他物理现象进行建模的科学领域中起着有用的作用，这可能使人感到惊讶。 分形的定义特征是它的自相似性。 也就是说，一小块分形带与整个分形非常相似。 许多自然现象具有相同类型的缩放行为，但通常仅作为近似值。 但是，这通常是一个足够好的近似值，可以在描述上或预测上有用，因此分形已经进入了大多数科学领域。